Expectancy of selling options

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Thesaints
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Re: Expectancy of selling options

Post by Thesaints »

My question is why invest in an individual stock at all, if you can't gain 10x ?
If you want 10%/yr. you invest in the S&P, if you want 5% you can invest in bonds.
Investment in individual stocks should be made for the chance of a much higher return. If you write covered calls that chance is gone and all you have left is cashing in some premium while running the risk of that company going belly up.
Topic Author
y1980
Posts: 18
Joined: Sun Apr 30, 2023 11:26 am

Re: Expectancy of selling options

Post by y1980 »

comeinvest wrote: Sun Jun 09, 2024 4:54 pm
y1980 wrote: Sun Jun 09, 2024 7:04 am
comeinvest wrote: Sat Jun 08, 2024 11:32 pm
Kbg wrote: Wed Jun 05, 2024 1:44 pm You are quite good at challenging other's thoughts and I value the great insights you have provided in some of your posts which have caused me to rethink. However, I felt I needed to challenge your writing off of the basic purpose and only real reason why someone would purchase a put. This then extends to why someone would sell a put and gets directly at whether or not a profit is likely to continue from selling puts into the future.
I don't write off someone wanting to use options for some idiosyncratic portfolio constraint. However I think there is no simplistic explanation for the empirical historical excess returns from options writing.
I think the original question was (re-phrasing it a bit) whether positive returns can be systematically generated with options writing strategies, that are uncorrelated to market returns. The OP doesn't mention explicitly why he is asking; but natural follow-up questions are if and how such strategies might be part of an asset allocation to benefit risk-adjusted expected portfolio returns. I think those interesting questions have not been answered or even seriously examined in this forum. If you say next that it's not boglehead-like, I beg to disagree; and also terminology really doesn't matter. Asset allocation is systematic exposure to systematic risk factors related to assets in financial markets, and how to efficiently implement that exposure, for purpose of maximizing expected risk-adjusted portfolio returns.
Thanks for all the arguments you make here.
However, you have to face the question why would people agree to give insurance to another person if they might lose from it?
Are you claiming that the whole reason for this is because of the expected volatility? I allow myself to doubt this because there are too many people who buy options to insure themselves regardless of an accurate assessment of expected volatility.
Option pricing formulas like Black-Scholes relate volatility to options prices, and are derived by constructing a risk-neutral, hedged portfolio. There is no subjectivity in stochastic calculus; it's pure mathematics. Option writers can hedge their exposure dynamically with the underlying. That means option writers deserve exactly the premium derived from the mathematics, not more and not less. Any perceived profits must come from bets on volatilities as this is the only input variable, e.g. underestimating rare catastrophic events; or from limits to arbitrage. There is no other input that might be subjective. It's hard to argue about mathematics.
The math is wonderful, the problem is the variables.
In the end you have to enter in the formula what the implied standard deviation is, (if I understand correctly, correct me if not), and if the standard deviation you enter is consistently higher than what actually happens, You got the place where the option selling expectation turns positive (emphasis on Put ).

I hope my words are understandable, as I used translation software to write this message.
Topic Author
y1980
Posts: 18
Joined: Sun Apr 30, 2023 11:26 am

Re: Expectancy of selling options

Post by y1980 »

bd7 wrote: Sun Jun 09, 2024 5:14 pm
Thesaints wrote: Sun Jun 09, 2024 1:04 am Writing options is similar to writing insurance. On average one makes money.
That's assuming that some magical force causes everything to priced "correctly". That doesn't happen on its own even for insurance--it's entirely possible for an insurance company to go bankrupt, right? So writing options is only profitable if you have some way of determining the right price to sell them at. A lot of people look at covered call writing as free money and it is the lowest tier (least risky, they'll let anyone do it) of options trading. So I'm thinking that perhaps this artificially lowers the market price of calls.
Right, that's a problem.
But because the market is efficient and has so many traders and so much liquidity, it can be trusted to embody the historical fluctuations and add the right premium to them.
Let's look at it as fire insurance for a specific house, and this insurance is traded on the stock market. Would you expect it to be regularly priced incorrectly?
comeinvest
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Re: Expectancy of selling options

Post by comeinvest »

y1980 wrote: Mon Jun 10, 2024 2:38 am
comeinvest wrote: Sun Jun 09, 2024 4:54 pm
y1980 wrote: Sun Jun 09, 2024 7:04 am
comeinvest wrote: Sat Jun 08, 2024 11:32 pm
Kbg wrote: Wed Jun 05, 2024 1:44 pm You are quite good at challenging other's thoughts and I value the great insights you have provided in some of your posts which have caused me to rethink. However, I felt I needed to challenge your writing off of the basic purpose and only real reason why someone would purchase a put. This then extends to why someone would sell a put and gets directly at whether or not a profit is likely to continue from selling puts into the future.
I don't write off someone wanting to use options for some idiosyncratic portfolio constraint. However I think there is no simplistic explanation for the empirical historical excess returns from options writing.
I think the original question was (re-phrasing it a bit) whether positive returns can be systematically generated with options writing strategies, that are uncorrelated to market returns. The OP doesn't mention explicitly why he is asking; but natural follow-up questions are if and how such strategies might be part of an asset allocation to benefit risk-adjusted expected portfolio returns. I think those interesting questions have not been answered or even seriously examined in this forum. If you say next that it's not boglehead-like, I beg to disagree; and also terminology really doesn't matter. Asset allocation is systematic exposure to systematic risk factors related to assets in financial markets, and how to efficiently implement that exposure, for purpose of maximizing expected risk-adjusted portfolio returns.
Thanks for all the arguments you make here.
However, you have to face the question why would people agree to give insurance to another person if they might lose from it?
Are you claiming that the whole reason for this is because of the expected volatility? I allow myself to doubt this because there are too many people who buy options to insure themselves regardless of an accurate assessment of expected volatility.
Option pricing formulas like Black-Scholes relate volatility to options prices, and are derived by constructing a risk-neutral, hedged portfolio. There is no subjectivity in stochastic calculus; it's pure mathematics. Option writers can hedge their exposure dynamically with the underlying. That means option writers deserve exactly the premium derived from the mathematics, not more and not less. Any perceived profits must come from bets on volatilities as this is the only input variable, e.g. underestimating rare catastrophic events; or from limits to arbitrage. There is no other input that might be subjective. It's hard to argue about mathematics.
The math is wonderful, the problem is the variables.
In the end you have to enter in the formula what the implied standard deviation is, (if I understand correctly, correct me if not), and if the standard deviation you enter is consistently higher than what actually happens, You got the place where the option selling expectation turns positive (emphasis on Put ).

I hope my words are understandable, as I used translation software to write this message.
I think the problem is not the language or the translation, but we are really going in circles here. You are just re-phrasing what I said in my previous comment, if you were to read it again.
In your second-last comment, you posed 2 questions. I answered them crisp and clear, almost literally word for word.
The second sentence of your last comment is a tautology. (Yes, if you found an arbitrage opportunity, then you will profit.) The point of this thread is whether it is actually an arbitrage opportunity, or not. We reduced the problem mathematically to the input assumption of volatility. If your volatility model is better than that of the rest of the market, then your will profit. The big question is if your model and that of other unsophisticated (no offense) options writers is indeed better, or if there is a catch that "others" know that we don't know. Like I said: "Any perceived profits must come from bets on volatilities as this is the only input variable, e.g. underestimating rare catastrophic events; or from limits to arbitrage."
comeinvest
Posts: 2861
Joined: Mon Mar 12, 2012 6:57 pm

Re: Expectancy of selling options

Post by comeinvest »

y1980 wrote: Mon Jun 10, 2024 2:49 am
bd7 wrote: Sun Jun 09, 2024 5:14 pm
Thesaints wrote: Sun Jun 09, 2024 1:04 am Writing options is similar to writing insurance. On average one makes money.
That's assuming that some magical force causes everything to priced "correctly". That doesn't happen on its own even for insurance--it's entirely possible for an insurance company to go bankrupt, right? So writing options is only profitable if you have some way of determining the right price to sell them at. A lot of people look at covered call writing as free money and it is the lowest tier (least risky, they'll let anyone do it) of options trading. So I'm thinking that perhaps this artificially lowers the market price of calls.
Right, that's a problem.
But because the market is efficient and has so many traders and so much liquidity, it can be trusted to embody the historical fluctuations and add the right premium to them.
Let's look at it as fire insurance for a specific house, and this insurance is traded on the stock market. Would you expect it to be regularly priced incorrectly?
The analogy of fire insurance is invalid on many fronts. 1. Your home fire insurance company cannot hedge the risk of your house catching fire by shorting the underlying (your house), which is clearly a limit to arbitrage; 2. doing a financial arbitrage trade requires no capital investment. You are not a business. The options pricing models are derived using pure mathematics, with volatility as input variable. The problem is therefore mathematically reduced to bets on volatility. Financial markets can be readily arbitraged, except relatively small limits to arbitrage. If you bet against the market, you have to question if your model is right or if the rest of the market is right.
seajay
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Re: Expectancy of selling options

Post by seajay »

alex_686 wrote: Fri May 31, 2024 11:00 am Options are zero sum game. Sort of - the reason why it isn’t are usually covered in graduate level courses.

This is my day job. This is a deep nuanced subject. Feel free to ask me anything.

The standard in options pricing is the Black-Scholes Model followed by the put-call parity formula.

Options, Futures, and Other Derivatives by John Hull is a good place to start.
If you use a investment method that defines at what price a certain amount of holdings should be added/sold then writing/selling Options can yield additional benefits/rewards. Robert Lichello's AIM for instance supports calculating the next trade price/amount that you would add/reduce at. Match that (at least in part) with selling Options and ... you were going to buy (sell) that amount at that price anyway and you captured a bit more 'interest' along the way. But when you factor in the time/costs etc. the benefit for most is inclined to be relatively little - but in some cases can be more reasonable.
Topic Author
y1980
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Re: Expectancy of selling options

Post by y1980 »

comeinvest wrote: Mon Jun 10, 2024 2:55 am
y1980 wrote: Mon Jun 10, 2024 2:38 am The math is wonderful, the problem is the variables.
In the end you have to enter in the formula what the implied standard deviation is, (if I understand correctly, correct me if not), and if the standard deviation you enter is consistently higher than what actually happens, You got the place where the option selling expectation turns positive (emphasis on Put ).

I hope my words are understandable, as I used translation software to write this message.
I think the problem is not the language or the translation, but we are really going in circles here. You are just re-phrasing what I said in my previous comment, if you were to read it again.
In your second-last comment, you posed 2 questions. I answered them crisp and clear, almost literally word for word.
The second sentence of your last comment is a tautology. (Yes, if you found an arbitrage opportunity, then you will profit.) The point of this thread is whether it is actually an arbitrage opportunity, or not. We reduced the problem mathematically to the input assumption of volatility. If your volatility model is better than that of the rest of the market, then your will profit. The big question is if your model and that of other unsophisticated (no offense) options writers is indeed better, or if there is a catch that "others" know that we don't know. Like I said: "Any perceived profits must come from bets on volatilities as this is the only input variable, e.g. underestimating rare catastrophic events; or from limits to arbitrage."
I am not claiming that my model is more sophisticated or that there is arbitrage on the market here. I argue that the model of the entire market calculates a higher volatility than it was in the past, because without this assumption there is no point in risking selling a put.
I argue that it is precisely the efficiency of the market that should direct it to such an equilibrium that selling a put will be profitable. It's not a bug, it's a feature.
And don't worry, I'm not offended at all. I spent my school years in other fields and I don't regret it at all. On the contrary, the clearer and sharper you are, the more useful it will be to me, so just thanks.
JackoC
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Joined: Sun Aug 12, 2018 11:14 am

Re: Expectancy of selling options

Post by JackoC »

On 'it's all math', Black-Scholes is (relatively) simple but just a 'lingua franca' of the market, or interpolation device for estimating market prices of options very similar to ones actually quoted. Its limited fundamental validity is obvious from the fact the implied volatility (the volatility input to the equation necessary to replicate the observed market price along with interest rate, div yield and time) varies so widely depending on the maturity and particularly the strike. If it's a 'brownian motion' process there would be *a* vol at least for a particular maturity, not a different one for every strike. There are more complicated models but no neat solution to this. Those models must assume at least some market prices are correct to derive their more complex parameters and therefore identify if *some* prices are not correct, or more likely to be attractive.

Anyway finding arbitrages from the retail investor perch is usually 'don't bother trying' and equity options are not among the few exceptions IMO. As to whether options are priced 'neutrally' that's literally a matter of perspective. Among the oversimplified assumptions of B-S is that you can risklessly hedge. So there's no risk parameter input. But in reality delta hedging short positions in far below money index puts you suffer unpredictable losses to elevated gamma (rate of change in what delta hedge is correct) in the rare cases suddenly big drops in the index/rises in the realized vol bring those options seriously 'into play'. The higher implied vols of low strike index options are reasonably interpreted as partly risk premium. There should be positive expected return selling (and delta hedging, not just 'putting in a drawer') far below money index puts in a risk (ie negative skew) averse market, negative expected return buying them. For other option types/strikes it's not as clear in all cases.

Just sticking with that example though, why buy OTM index puts? Not to make money on the puts. Rather, to allow a higher stock allocation than what you could tolerate with no put protection. If you can tolerate the full downside of 100% stocks and would never consider levering beyond that, moot point, puts won't work. If you're a natural 60/40 person, it's *arguable*, it's *possible*, 80/20 with some OTM put protection might suit you better. But obviously it's book length to deal with every possible use of options. As a rule the retail investor who knows little of options and doesn't get involved will not be making a big mistake. Doing something dumb with a little knowledge could be. Doing something optimal might improve things a bit.
Topic Author
y1980
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Re: Expectancy of selling options

Post by y1980 »

JackoC wrote: Mon Jun 10, 2024 7:11 am On 'it's all math', Black-Scholes is (relatively) simple but just a 'lingua franca' of the market, or interpolation device for estimating market prices of options very similar to ones actually quoted. Its limited fundamental validity is obvious from the fact the implied volatility (the volatility input to the equation necessary to replicate the observed market price along with interest rate, div yield and time) varies so widely depending on the maturity and particularly the strike. If it's a 'brownian motion' process there would be *a* vol at least for a particular maturity, not a different one for every strike. There are more complicated models but no neat solution to this. Those models must assume at least some market prices are correct to derive their more complex parameters and therefore identify if *some* prices are not correct, or more likely to be attractive.

Anyway finding arbitrages from the retail investor perch is usually 'don't bother trying' and equity options are not among the few exceptions IMO. As to whether options are priced 'neutrally' that's literally a matter of perspective. Among the oversimplified assumptions of B-S is that you can risklessly hedge. So there's no risk parameter input. But in reality delta hedging short positions in far below money index puts you suffer unpredictable losses to elevated gamma (rate of change in what delta hedge is correct) in the rare cases suddenly big drops in the index/rises in the realized vol bring those options seriously 'into play'. The higher implied vols of low strike index options are reasonably interpreted as partly risk premium. There should be positive expected return selling (and delta hedging, not just 'putting in a drawer') far below money index puts in a risk (ie negative skew) averse market, negative expected return buying them. For other option types/strikes it's not as clear in all cases.

Just sticking with that example though, why buy OTM index puts? Not to make money on the puts. Rather, to allow a higher stock allocation than what you could tolerate with no put protection. If you can tolerate the full downside of 100% stocks and would never consider levering beyond that, moot point, puts won't work. If you're a natural 60/40 person, it's *arguable*, it's *possible*, 80/20 with some OTM put protection might suit you better. But obviously it's book length to deal with every possible use of options. As a rule the retail investor who knows little of options and doesn't get involved will not be making a big mistake. Doing something dumb with a little knowledge could be. Doing something optimal might improve things a bit.
Could you please explain the marked sentence to me?
By the way, I'm talking about European options, so the volatility throughout the period doesn't bother me.
JackoC
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Re: Expectancy of selling options

Post by JackoC »

y1980 wrote: Mon Jun 10, 2024 8:22 am
JackoC wrote: Mon Jun 10, 2024 7:11 am On 'it's all math', Black-Scholes is (relatively) simple but just a 'lingua franca' of the market, or interpolation device for estimating market prices of options very similar to ones actually quoted. Its limited fundamental validity is obvious from the fact the implied volatility (the volatility input to the equation necessary to replicate the observed market price along with interest rate, div yield and time) varies so widely depending on the maturity and particularly the strike. If it's a 'brownian motion' process there would be *a* vol at least for a particular maturity, not a different one for every strike. There are more complicated models but no neat solution to this. Those models must assume at least some market prices are correct to derive their more complex parameters and therefore identify if *some* prices are not correct, or more likely to be attractive.

Anyway finding arbitrages from the retail investor perch is usually 'don't bother trying' and equity options are not among the few exceptions IMO. As to whether options are priced 'neutrally' that's literally a matter of perspective. Among the oversimplified assumptions of B-S is that you can risklessly hedge. So there's no risk parameter input. But in reality delta hedging short positions in far below money index puts you suffer unpredictable losses to elevated gamma (rate of change in what delta hedge is correct) in the rare cases suddenly big drops in the index/rises in the realized vol bring those options seriously 'into play'. The higher implied vols of low strike index options are reasonably interpreted as partly risk premium. There should be positive expected return selling (and delta hedging, not just 'putting in a drawer') far below money index puts in a risk (ie negative skew) averse market, negative expected return buying them. For other option types/strikes it's not as clear in all cases.

Just sticking with that example though, why buy OTM index puts? Not to make money on the puts. Rather, to allow a higher stock allocation than what you could tolerate with no put protection. If you can tolerate the full downside of 100% stocks and would never consider levering beyond that, moot point, puts won't work. If you're a natural 60/40 person, it's *arguable*, it's *possible*, 80/20 with some OTM put protection might suit you better. But obviously it's book length to deal with every possible use of options. As a rule the retail investor who knows little of options and doesn't get involved will not be making a big mistake. Doing something dumb with a little knowledge could be. Doing something optimal might improve things a bit.
Could you please explain the marked sentence to me?
By the way, I'm talking about European options, so the volatility throughout the period doesn't bother me.
Nothing much to do with European vs other exercise rules. The basic idea from which the formula is derived is that the hedging process involves no risk, just a cost, as the ever changing slight mismatch in the 'delta' hedge (short/long some of the underlying to hedge the option) is adjusted with movement in the underlying price, a cost always against the delta-hedging seller. The formula determines the cumulative hedging cost and therefore option value. Just look at the equation: no risk parameter appears. But in the real world, delta hedging options in some situations is much riskier than other situations. Far below money puts, if they ever get near the money, are likely to do so in an environment of very high (but impossible to predict) realized volatility. It makes sense that people shorting and delta hedging those options* demand a risk premium to expose themselves to that possibility. Given that the equation has no risk input, it shows up in a higher implied volatility for the market option price.

*pure speculators just selling far below money options with no hedges, just hoping they never go in the money, are another possible type of seller but the 'vol skew' itself suggests they aren't that numerous.
bd7
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Re: Expectancy of selling options

Post by bd7 »

y1980 wrote: Mon Jun 10, 2024 2:49 am But because the market is efficient and has so many traders and so much liquidity, it can be trusted to embody the historical fluctuations and add the right premium to them.
So what is the "correct price" for my GOGL $15 call for Jan 2025? $1 or $2? What if the bid is $0.50 and the ask is $2.00--what is the "correct price" then?
Let's look at it as fire insurance for a specific house, and this insurance is traded on the stock market. Would you expect it to be regularly priced incorrectly?
I don't think insurance is a good way to think about an asset class that is mostly used for speculation. Having just purchased insurance for my house, I'd say there's enough variation to make it pretty difficult to say that everyone agrees on a price. So if Insurance companies A, B and C give me quotes of $3000, $1500 and "no quote--go away", which one is correct?

I don't think of prices as being 'correct' or not since that is just based on circular arguments of market efficiency. And if you disgree, please tell me the correct price of GME.
bd7
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Re: Expectancy of selling options

Post by bd7 »

Thesaints wrote: Sun Jun 09, 2024 11:56 pm Investment in individual stocks should be made for the chance of a much higher return. If you write covered calls that chance is gone and all you have left is cashing in some premium while running the risk of that company going belly up.
I've been writing calls on this stock since it was below $5 and it hasn't gotten away from me yet. I haven't made 10X yet and it is a bit of work, but whatver success I've had--probably 5X in 7 years--is due to me not blindly accepting the market valuation of the options. For this option, at $2 I sell and at $0.50 I buy back--that's my assessment of the price.
Thesaints
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Re: Expectancy of selling options

Post by Thesaints »

bd7 wrote: Mon Jun 10, 2024 10:11 am I don't think insurance is a good way to think about an asset class that is mostly used for speculation.
It is not. Options are mostly used for hedging. But there are always those who think “here’s a few easy bucks!”. Truth is they are oblivious of actual risk.
comeinvest
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Re: Expectancy of selling options

Post by comeinvest »

y1980 wrote: Mon Jun 10, 2024 6:22 am
comeinvest wrote: Mon Jun 10, 2024 2:55 am
y1980 wrote: Mon Jun 10, 2024 2:38 am The math is wonderful, the problem is the variables.
In the end you have to enter in the formula what the implied standard deviation is, (if I understand correctly, correct me if not), and if the standard deviation you enter is consistently higher than what actually happens, You got the place where the option selling expectation turns positive (emphasis on Put ).

I hope my words are understandable, as I used translation software to write this message.
I think the problem is not the language or the translation, but we are really going in circles here. You are just re-phrasing what I said in my previous comment, if you were to read it again.
In your second-last comment, you posed 2 questions. I answered them crisp and clear, almost literally word for word.
The second sentence of your last comment is a tautology. (Yes, if you found an arbitrage opportunity, then you will profit.) The point of this thread is whether it is actually an arbitrage opportunity, or not. We reduced the problem mathematically to the input assumption of volatility. If your volatility model is better than that of the rest of the market, then your will profit. The big question is if your model and that of other unsophisticated (no offense) options writers is indeed better, or if there is a catch that "others" know that we don't know. Like I said: "Any perceived profits must come from bets on volatilities as this is the only input variable, e.g. underestimating rare catastrophic events; or from limits to arbitrage."
I am not claiming that my model is more sophisticated or that there is arbitrage on the market here. I argue that the model of the entire market calculates a higher volatility than it was in the past, because without this assumption there is no point in risking selling a put.
I argue that it is precisely the efficiency of the market that should direct it to such an equilibrium that selling a put will be profitable. It's not a bug, it's a feature.
And don't worry, I'm not offended at all. I spent my school years in other fields and I don't regret it at all. On the contrary, the clearer and sharper you are, the more useful it will be to me, so just thanks.
You are acknowledging mathematics, and then you are negating it in the next sentence. That makes no sense. The pricing formula is based on a perfect hedge given a certain volatility assumption. If you say "yes, this is the fair price, but the actual price should be higher than the fair price because I deserve an extra profit", then you are basically negating the definition of "fair price", and your are tossing out pure mathematics. Why do you think you deserve an extra profit form writing options; why should the buyer not deserve an extra profit from buying options? Agnostic of any pricing, both sides of the transaction incur a risk of losing money in comparison to simply holding the underlying either long or short, at a delta neutral ratio to their respective options positions.
To be honest, I think you are not thinking this through; it sounds a bit backwards. I am learning myself though, so I'm happy to stand corrected.
Topic Author
y1980
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Re: Expectancy of selling options

Post by y1980 »

Thesaints wrote: Mon Jun 10, 2024 10:21 am
bd7 wrote: Mon Jun 10, 2024 10:11 am I don't think insurance is a good way to think about an asset class that is mostly used for speculation.
It is not. Options are mostly used for hedging. But there are always those who think “here’s a few easy bucks!”. Truth is they are oblivious of actual risk.
Hedging is also a form of insurance, isn't it?
Topic Author
y1980
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Re: Expectancy of selling options

Post by y1980 »

comeinvest wrote: Mon Jun 10, 2024 12:12 pm
y1980 wrote: Mon Jun 10, 2024 6:22 am
comeinvest wrote: Mon Jun 10, 2024 2:55 am
y1980 wrote: Mon Jun 10, 2024 2:38 am The math is wonderful, the problem is the variables.
In the end you have to enter in the formula what the implied standard deviation is, (if I understand correctly, correct me if not), and if the standard deviation you enter is consistently higher than what actually happens, You got the place where the option selling expectation turns positive (emphasis on Put ).

I hope my words are understandable, as I used translation software to write this message.
I think the problem is not the language or the translation, but we are really going in circles here. You are just re-phrasing what I said in my previous comment, if you were to read it again.
In your second-last comment, you posed 2 questions. I answered them crisp and clear, almost literally word for word.
The second sentence of your last comment is a tautology. (Yes, if you found an arbitrage opportunity, then you will profit.) The point of this thread is whether it is actually an arbitrage opportunity, or not. We reduced the problem mathematically to the input assumption of volatility. If your volatility model is better than that of the rest of the market, then your will profit. The big question is if your model and that of other unsophisticated (no offense) options writers is indeed better, or if there is a catch that "others" know that we don't know. Like I said: "Any perceived profits must come from bets on volatilities as this is the only input variable, e.g. underestimating rare catastrophic events; or from limits to arbitrage."
I am not claiming that my model is more sophisticated or that there is arbitrage on the market here. I argue that the model of the entire market calculates a higher volatility than it was in the past, because without this assumption there is no point in risking selling a put.
I argue that it is precisely the efficiency of the market that should direct it to such an equilibrium that selling a put will be profitable. It's not a bug, it's a feature.
And don't worry, I'm not offended at all. I spent my school years in other fields and I don't regret it at all. On the contrary, the clearer and sharper you are, the more useful it will be to me, so just thanks.
You are acknowledging mathematics, and then you are negating it in the next sentence. That makes no sense. The pricing formula is based on a perfect hedge given a certain volatility assumption. If you say "yes, this is the fair price, but the actual price should be higher than the fair price because I deserve an extra profit", then you are basically negating the definition of "fair price", and your are tossing out pure mathematics. Why do you think you deserve an extra profit form writing options; why should the buyer not deserve an extra profit from buying options? Agnostic of any pricing, both sides of the transaction incur a risk of losing money in comparison to simply holding the underlying either long or short, at a delta neutral ratio to their respective options positions.
To be honest, I think you are not thinking this through; it sounds a bit backwards. I am learning myself though, so I'm happy to stand corrected.
Would you agree to go with me for a moment?
1. The only figure that does not have a source in the Black-Schulz formula is predicted volatility, right?
2. By what is the predicted volatility estimated?
3. If on average the seller of the option receives only his investment, what does he sell the options for?

Maybe I'm just wrong about one of these questions, correct me if I am. Thanks.
Topic Author
y1980
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Re: Expectancy of selling options

Post by y1980 »

bd7 wrote: Mon Jun 10, 2024 10:11 am
y1980 wrote: Mon Jun 10, 2024 2:49 am But because the market is efficient and has so many traders and so much liquidity, it can be trusted to embody the historical fluctuations and add the right premium to them.
So what is the "correct price" for my GOGL $15 call for Jan 2025? $1 or $2? What if the bid is $0.50 and the ask is $2.00--what is the "correct price" then?
No one knows the absolute right price.
What we have is the market pricing, which can be assumed to include all open knowledge.
I guess the average market price is the best approximation of the 'correct' price.
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Re: Expectancy of selling options

Post by comeinvest »

JackoC wrote: Mon Jun 10, 2024 7:11 am On 'it's all math', Black-Scholes is (relatively) simple but just a 'lingua franca' of the market, or interpolation device for estimating market prices of options very similar to ones actually quoted. Its limited fundamental validity is obvious from the fact the implied volatility (the volatility input to the equation necessary to replicate the observed market price along with interest rate, div yield and time) varies so widely depending on the maturity and particularly the strike. If it's a 'brownian motion' process there would be *a* vol at least for a particular maturity, not a different one for every strike. There are more complicated models but no neat solution to this. Those models must assume at least some market prices are correct to derive their more complex parameters and therefore identify if *some* prices are not correct, or more likely to be attractive.

Anyway finding arbitrages from the retail investor perch is usually 'don't bother trying' and equity options are not among the few exceptions IMO. As to whether options are priced 'neutrally' that's literally a matter of perspective. Among the oversimplified assumptions of B-S is that you can risklessly hedge. So there's no risk parameter input. But in reality delta hedging short positions in far below money index puts you suffer unpredictable losses to elevated gamma (rate of change in what delta hedge is correct) in the rare cases suddenly big drops in the index/rises in the realized vol bring those options seriously 'into play'. The higher implied vols of low strike index options are reasonably interpreted as partly risk premium. There should be positive expected return selling (and delta hedging, not just 'putting in a drawer') far below money index puts in a risk (ie negative skew) averse market, negative expected return buying them. For other option types/strikes it's not as clear in all cases.

...
Nothing said so far in this thread was specific to BS or any other model. Everybody knows that BS is an approximation, that's why the models are volatility surfaces.

The question was whether the perceived "premium" has a risk-based explanation, or whether we can assume that for whatever reason the model of the "other side" is wrong, such that we can have positive excess returns writing options in the long run. If there is a risk-based explanation, then the "premium" would not translated to long-term expected excess returns.

"The higher implied vols of low strike index options are reasonably interpreted as partly risk premium. There should be positive expected return selling (and delta hedging, not just 'putting in a drawer') far below money index puts" - These two sentences contradict each other. If the explanation is risk of rare catastrophic drawdowns events that doesn't show up in backtests but is nevertheless nonzero, then the expected returns would need to reflect those rare occasional occurrences - unless, again, your model of rare catastrophic risk (i.e. the volatility surface) is better than that of the rest of the market.

Like I mentioned earlier in the thread, selling vertical credit spreads also has been a winning strategy. Vertical credit spreads incur no risk of large market drawdown events.

So we still have no explanation.
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Re: Expectancy of selling options

Post by comeinvest »

JackoC wrote: Mon Jun 10, 2024 7:11 am ...
Just sticking with that example though, why buy OTM index puts? Not to make money on the puts. Rather, to allow a higher stock allocation than what you could tolerate with no put protection. If you can tolerate the full downside of 100% stocks and would never consider levering beyond that, moot point, puts won't work. If you're a natural 60/40 person, it's *arguable*, it's *possible*, 80/20 with some OTM put protection might suit you better. But obviously it's book length to deal with every possible use of options. As a rule the retail investor who knows little of options and doesn't get involved will not be making a big mistake. Doing something dumb with a little knowledge could be. Doing something optimal might improve things a bit.
Following up on my previous reply, this paragraph of yours also does not make sense in my opinion. If you think that you can leverage 60/40 more if you buy some OTM puts at the same time for overall higher expected risk-adjusted returns in the long run, then you are again basically saying that your modeling of rare, large drawdown events is better than that of the rest of the market. You are basically betting against the market: You are making a bet that rare large drawdowns are more likely to occur than reflected by the price of the options, all the while small to medium drawdown events are less likely to occur or are less detrimental on average than implied by the market. If everybody agreed that large drawdowns are worth "insuring" for the purpose of increased portfolio leverage, and small to medium drawdowns are not worth insuring but in fact are worth leveraging, then the options would be mispriced, and the premium would be higher. The risk of the leveraged 60/40 investor with OTM put options is that the put option premia slowly but surely drag down long-term returns, all the while small and medium drawdowns occur more often than expected, putting the investor at an overall loss or underperformance in comparison to an unleveraged portfolio with no put option "protection".

Long story, but in the end it's a bet on volatilities and nothing else. If you are adverse to market drawdowns, the first, naive action would be to buy less equities. The decision to buy more equities along with put options is a bet on volatilities against the market.

Any and all reasoning in regards to hedging properties of options strategies has to be in the context of the alternative of undoing both the hedge and the underlyings that are to be hedged. You cannot just argue options in isolation, separate from the underlying or without questioning why you own the underlying in the first place. The components, delta and volatility, need to be separated for conclusive reasoning. That is because of Black/Scholes or whatever other model you use, relate volatility surfaces to options prices, i.e. to the theoretical value of a bet on the underlying passing a certain threshold (strike price) or not. The latter is pure mathematics and cannot be argued against. The delta can be perfectly hedged. Higher derivatives basically represent volatility surfaces, and directly result in one specific fair value price for a certain option.
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Re: Expectancy of selling options

Post by comeinvest »

JackoC wrote: Mon Jun 10, 2024 9:19 am
y1980 wrote: Mon Jun 10, 2024 8:22 am
JackoC wrote: Mon Jun 10, 2024 7:11 am On 'it's all math', Black-Scholes is (relatively) simple but just a 'lingua franca' of the market, or interpolation device for estimating market prices of options very similar to ones actually quoted. Its limited fundamental validity is obvious from the fact the implied volatility (the volatility input to the equation necessary to replicate the observed market price along with interest rate, div yield and time) varies so widely depending on the maturity and particularly the strike. If it's a 'brownian motion' process there would be *a* vol at least for a particular maturity, not a different one for every strike. There are more complicated models but no neat solution to this. Those models must assume at least some market prices are correct to derive their more complex parameters and therefore identify if *some* prices are not correct, or more likely to be attractive.

Anyway finding arbitrages from the retail investor perch is usually 'don't bother trying' and equity options are not among the few exceptions IMO. As to whether options are priced 'neutrally' that's literally a matter of perspective. Among the oversimplified assumptions of B-S is that you can risklessly hedge. So there's no risk parameter input. But in reality delta hedging short positions in far below money index puts you suffer unpredictable losses to elevated gamma (rate of change in what delta hedge is correct) in the rare cases suddenly big drops in the index/rises in the realized vol bring those options seriously 'into play'. The higher implied vols of low strike index options are reasonably interpreted as partly risk premium. There should be positive expected return selling (and delta hedging, not just 'putting in a drawer') far below money index puts in a risk (ie negative skew) averse market, negative expected return buying them. For other option types/strikes it's not as clear in all cases.

Just sticking with that example though, why buy OTM index puts? Not to make money on the puts. Rather, to allow a higher stock allocation than what you could tolerate with no put protection. If you can tolerate the full downside of 100% stocks and would never consider levering beyond that, moot point, puts won't work. If you're a natural 60/40 person, it's *arguable*, it's *possible*, 80/20 with some OTM put protection might suit you better. But obviously it's book length to deal with every possible use of options. As a rule the retail investor who knows little of options and doesn't get involved will not be making a big mistake. Doing something dumb with a little knowledge could be. Doing something optimal might improve things a bit.
Could you please explain the marked sentence to me?
By the way, I'm talking about European options, so the volatility throughout the period doesn't bother me.
Nothing much to do with European vs other exercise rules. The basic idea from which the formula is derived is that the hedging process involves no risk, just a cost, as the ever changing slight mismatch in the 'delta' hedge (short/long some of the underlying to hedge the option) is adjusted with movement in the underlying price, a cost always against the delta-hedging seller. The formula determines the cumulative hedging cost and therefore option value. Just look at the equation: no risk parameter appears. But in the real world, delta hedging options in some situations is much riskier than other situations. Far below money puts, if they ever get near the money, are likely to do so in an environment of very high (but impossible to predict) realized volatility. It makes sense that people shorting and delta hedging those options* demand a risk premium to expose themselves to that possibility. Given that the equation has no risk input, it shows up in a higher implied volatility for the market option price.

*pure speculators just selling far below money options with no hedges, just hoping they never go in the money, are another possible type of seller but the 'vol skew' itself suggests they aren't that numerous.
I think that jump risk reasoning comes close to an explanation, although it is not entirely conclusive. The options premia would be fair compensation for risk than can actually occur, but has not materialized in the ca. 40-year history of options markets. In any case, it would not imply that money can be made writing options in the long run. None of that reasoning implies that risk-adjusted returns would be higher writing far OTM options than an outright position in the stock market adjusted to the same risk, whatever risk model you use.
The fact that small delta-hedged options writing credit spreads (sell one put option, buy another put option at a little lower strike price than the first) had consistent positive returns is also not explained, if I'm not mistaken. The latter is not dependent on jump risk models, at least not on rare risk events, if I'm not mistaken.
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Re: Expectancy of selling options

Post by comeinvest »

y1980 wrote: Mon Jun 10, 2024 12:42 pm Would you agree to go with me for a moment?
1. The only figure that does not have a source in the Black-Schulz formula is predicted volatility, right?
2. By what is the predicted volatility estimated?
3. If on average the seller of the option receives only his investment, what does he sell the options for?

Maybe I'm just wrong about one of these questions, correct me if I am. Thanks.
The same question applies to the buyer. Both parties can hedge their options exposure with the underlying. The math reduces the optimization problem to a bet on volatility surfaces for both sides of the trade, including jump risk as JackoC mentioned. I'm not sure how the latter can be mathematically included in the framework of stochastic calculus, but I think that is just a technical detail that is not essential to the question and the reasoning at hand. Let's just say it's a bet on the stochastic process, that results in the volatility surface.
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Re: Expectancy of selling options

Post by bd7 »

y1980 wrote: Mon Jun 10, 2024 12:42 pm 1. The only figure that does not have a source in the Black-Schulz formula is predicted volatility, right?
2. By what is the predicted volatility estimated?
3. If on average the seller of the option receives only his investment, what does he sell the options for?
The information I see in a brokerage option chain listing is "implied volatility". So they take the market-determined price and figure out what volatility number makes their formula come up with the same price. Sort of circular reasoning. If they determined the volatility independently and listed that along with the resultant price that their formula expects, then maybe there would be some useful information in there.

The issue of the sellers motivation is an excellent question and IMO there is not really any sort of parity between buyers and sellers. Selling an option cannot really hedge anything, unless you count the case where you use the premium to buy another option that does serve as a hedge. Buying an option can be hedging or speculative. So based on that, I'd expect there to be a tilt towards option sellers where selling is profitable on the average and buying is not. But there's probably a lot more to the story. And, as I like to harp on, whether your option sale or purchase is profitable depends a lot on what you pay for it or sell it at.
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Re: Expectancy of selling options

Post by JackoC »

comeinvest wrote: Mon Jun 10, 2024 10:16 pm
JackoC wrote: Mon Jun 10, 2024 7:11 am ...
Just sticking with that example though, why buy OTM index puts? Not to make money on the puts. Rather, to allow a higher stock allocation than what you could tolerate with no put protection. If you can tolerate the full downside of 100% stocks and would never consider levering beyond that, moot point, puts won't work. If you're a natural 60/40 person, it's *arguable*, it's *possible*, 80/20 with some OTM put protection might suit you better. But obviously it's book length to deal with every possible use of options. As a rule the retail investor who knows little of options and doesn't get involved will not be making a big mistake. Doing something dumb with a little knowledge could be. Doing something optimal might improve things a bit.
Following up on my previous reply, this paragraph of yours also does not make sense in my opinion. If you think that you can leverage 60/40 more if you buy some OTM puts at the same time for overall higher expected risk-adjusted returns in the long run, then you are again basically saying that your modeling of rare, large drawdown events is better than that of the rest of the market. You are basically betting against the market:
The problem with each of your three responses, IMO, is centered on 'risk adjusted'.

First, sticking with the example of the people with net positions writing far below money index puts. I specifically said a risk premium in one particular direction in BS 'implied vol' was not clear in other cases but let's stick with this one to illustrate. The sell side of those options is predominantly delta hedging dealers, an empirical not theoretical fact. There is no natural end user need for 'anti-insurance' which is what writing those options is. There could as I mentioned be punters writing them naked but the empirical fact is as I said. It wouldn't make sense for those predominant delta hedging dealers to write those options at true 'neutral', zero expected return so, looking through the BS lens, it makes sense to assume the higher implied vol contains a risk premium. I never said anything about their 'risk adjusted' return. That depends on defining 'risk adjusted' which isn't actually any easier than finding the 'true' options model.

But retail investors are really unlikely (and would be ill advised IMO) to write and sit home delta hedging far below money index puts. OTOH buying far below money index puts, despite their likely negative expected return, is *potentially* attractive. Obviously not because the options are a free lunch at negative E[r], that would be contradiction if I'd said it but I didn't. :happy Rather, 80/20 including buying some OTM puts v 60/40 without might be attractive as a matter of *individual* risk tolerance/gain seeking, not, not, not a way to 'beat' or 'outguess' the market', which I tried to be clear I was not saying, but not hard enough apparently.

For example on this forum many people implicitly (even if they reject the terminology) believe the expected return of stock is the historical average realized return 6%+ real pre tax (something like). The market now seems to say more like 3-4% (1/CAPE etc). But the realized return is inherently unknowable, somebody was always right/wrong in hindsight with a more +/- take. Say the typical BH optimist is right, which they could be (I'd go with the market indicator for E[r], but what do I know?). Then there's a lot of juicy upside. But a particular individual might still be limited in enjoying this upside by consideration of the worst case (and their self-perceived ability to 'stay the course' if it materializes), therefore limiting themselves to 60% (full downside) stock. One solution might be to read lots of optimistic talk, reduce their fear of big downside and just 'person up' and raise their allocation, period. But another might be to keep the (plausible) 'max' (in their view) downside to about that of 60% stock, while upping their allocation to 80% stock and buying some (say 25%) OTM index puts. If so they'd be using a different tool to tailor their portfolio more closely to their *own risk preference*, in the details of downside/upside aversion/seeking. It's not about simplistic 'risk adjustment' like Sharpe Ratio, by definition blind to particular aversion to big downside (or intense FOMO on big upside) by defining 'risk' as annualized std dev. And the real and true metric for 'risk adjustment' that applies to everyone is not defined. Saying 'superior risk adjusted return' tends to imply arbitrage, which is why I did *not* use that term. A risk/return profile more suited to that individual in their own view. That is *possible* using OTM puts IMO, depending on the person and the numbers. It's not 'betting against the market'.
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Re: Expectancy of selling options

Post by comeinvest »

JackoC wrote: Tue Jun 11, 2024 10:10 am But retail investors are really unlikely (and would be ill advised IMO) to write and sit home delta hedging far below money index puts. OTOH buying far below money index puts, despite their likely negative expected return, is *potentially* attractive. Obviously not because the options are a free lunch at negative E[r], that would be contradiction if I'd said it but I didn't. :happy Rather, 80/20 including buying some OTM puts v 60/40 without might be attractive as a matter of *individual* risk tolerance/gain seeking, not, not, not a way to 'beat' or 'outguess' the market', which I tried to be clear I was not saying, but not hard enough apparently.

For example on this forum many people implicitly (even if they reject the terminology) believe the expected return of stock is the historical average realized return 6%+ real pre tax (something like). The market now seems to say more like 3-4% (1/CAPE etc). But the realized return is inherently unknowable, somebody was always right/wrong in hindsight with a more +/- take. Say the typical BH optimist is right, which they could be (I'd go with the market indicator for E[r], but what do I know?). Then there's a lot of juicy upside. But a particular individual might still be limited in enjoying this upside by consideration of the worst case (and their self-perceived ability to 'stay the course' if it materializes), therefore limiting themselves to 60% (full downside) stock. One solution might be to read lots of optimistic talk, reduce their fear of big downside and just 'person up' and raise their allocation, period. But another might be to keep the (plausible) 'max' (in their view) downside to about that of 60% stock, while upping their allocation to 80% stock and buying some (say 25%) OTM index puts. If so they'd be using a different tool to tailor their portfolio more closely to their *own risk preference*, in the details of downside/upside aversion/seeking. It's not about simplistic 'risk adjustment' like Sharpe Ratio, by definition blind to particular aversion to big downside (or intense FOMO on big upside) by defining 'risk' as annualized std dev. And the real and true metric for 'risk adjustment' that applies to everyone is not defined. Saying 'superior risk adjusted return' tends to imply arbitrage, which is why I did *not* use that term. A risk/return profile more suited to that individual in their own view. That is *possible* using OTM puts IMO, depending on the person and the numbers. It's not 'betting against the market'.
But the individual investor typically has no statistical data and no specific risk and return model of options on hand. By "blindly" going with a higher allocation to equities and buying put options the investor would assume that his own personal utility profile is different from that of the counterparty to the trade, i.e. he is more risk averse to large drawdowns in relation to medium drawdowns, than the counterparty. How can an investor make that assumption without even knowing the counterparty. It's fair to assume that most investor including dealers are more adverse to large drawdowns, as those typically force margin calls or deleveraging.
I guess it might also well be possible that the 80/20 plus put options results in lower returns than 60/40 for most realized trajectories, defeating the purpose of this portfolio construction in any possible sense i.e. for any possible personal utility function that I can imagine. So in the end the I think investor should and must have his own options risk model, or else would be well advised to do no such complicated thing, i.e. stick with his 60/40.
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Re: Expectancy of selling options

Post by comeinvest »

JackoC wrote: Tue Jun 11, 2024 10:10 am The problem with each of your three responses, IMO, is centered on 'risk adjusted'.

First, sticking with the example of the people with net positions writing far below money index puts. I specifically said a risk premium in one particular direction in BS 'implied vol' was not clear in other cases but let's stick with this one to illustrate. The sell side of those options is predominantly delta hedging dealers, an empirical not theoretical fact. There is no natural end user need for 'anti-insurance' which is what writing those options is. There could as I mentioned be punters writing them naked but the empirical fact is as I said. It wouldn't make sense for those predominant delta hedging dealers to write those options at true 'neutral', zero expected return so, looking through the BS lens, it makes sense to assume the higher implied vol contains a risk premium. I never said anything about their 'risk adjusted' return. That depends on defining 'risk adjusted' which isn't actually any easier than finding the 'true' options model.
Principally no-arbitrage principles in financial markets don't depend on existence of "natural" users or parties. Parties will show up if arbitrage opportunities exist, and they are commonly expected to close. But I accept your explanation as common "limits to arbitrage", similar to for example the index futures basis trade or the swap spread trade which can result in risk-free profits of ca. 0.5% p.a.

But is there a reason why you explicitly say "far" out of the money options?
Also, how can the empirical positive returns from volatility exposure with vertical credit spread be explained, which are well protected on the downside? A vertical credit spread, delta hedged. For example sell 5000 put, buy 4800 put, and also sell ES futures to delta hedge the exposure. Some recently created ETFs do something similar. You have net negative exposure to volatility, at pretty much no significant other risk. If it has consistently positive returns, it seems like an opportunity to make "free" money with little risk in the long run, which should not exist.
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Re: Expectancy of selling options

Post by Kbg »

We're in a semantics dead end here. Let's not confuse cause and effect via Black-Scholes...yep, it is primarily all about volatility but you refuse to address what causes volatility and why someone would hedge it. I assume you are aware of the assumption made about volatility in the theory. Lastly, why an option (selling) premium exists has been studied. It exists empirically and Black-Scholes theory doesn't handle it theoretically due to some not accurate assumptions.

Math is often not a particularly good method for describing human behavior. Kahneman got his Nobel a little later in history on this point than Scholes and Merton got theirs.
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Re: Expectancy of selling options

Post by unemployed_pysicist »

comeinvest wrote: Tue Jun 11, 2024 2:07 pm Also, how can the empirical positive returns from volatility exposure with vertical credit spread be explained, which are well protected on the downside? A vertical credit spread, delta hedged. For example sell 5000 put, buy 4800 put, and also sell ES futures to delta hedge the exposure. Some recently created ETFs do something similar. You have net negative exposure to volatility, at pretty much no significant other risk. If it has consistently positive returns, it seems like an opportunity to make "free" money with little risk in the long run, which should not exist.
Do you have a link for these empirical results? Any idea about the time period where the research was performed? And just to clarify: is this a position where you are selling or buying volatility?

The textbooks always show the volatility smirk, where implied volatility decreases with increasing strike price. Like the cartoon shown in the link below, for example:
https://www.investopedia.com/terms/v/vo ... y-skew.asp

However, this has not quite been what I have observed in SPX options in recent years. Some examples:

SPX-at-time-2021-Jun-07-15-48
Image

SPX-at-time-2022-Jun-28-16-02
Image

SPX-at-time-2023-May-31-07-58:
Image

Some single stock examples, where this... non-smirk behavior is more apparent:

GME-at-time-2021-Jun-10-15-52
Image

NVDA-at-time-2023-May-31-10-36
Image

If the "textbook" picture of an implied volatility smirk were true, it would seem that with vertical credit spreads using puts, you would be buying volatility. Because you sell the option at a higher strike and lower IV, and buy the one with a lower strike and higher IV. But, if implied volatility is more "smile-shaped" as in my examples, then you would be selling volatility, because you sell the option at the higher strike having higher IV and buy the one at the lower strike having lower IV.

Edit: I realize now that I was only thinking about the vertical credit spread for strikes above the forward price. I see from your example of 5000 and 4800 that you are probably only referring to OTM put options, with strikes below the forward price. In both the smirk and non-smirk case for OTM put options, the higher strike put always has a lower IV (for strikes below the forward price).

This suggests to me that the position you described is buying volatility. Is this correct?
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Re: Expectancy of selling options

Post by comeinvest »

unemployed_pysicist wrote: Wed Jun 12, 2024 3:06 am
comeinvest wrote: Tue Jun 11, 2024 2:07 pm Also, how can the empirical positive returns from volatility exposure with vertical credit spread be explained, which are well protected on the downside? A vertical credit spread, delta hedged. For example sell 5000 put, buy 4800 put, and also sell ES futures to delta hedge the exposure. Some recently created ETFs do something similar. You have net negative exposure to volatility, at pretty much no significant other risk. If it has consistently positive returns, it seems like an opportunity to make "free" money with little risk in the long run, which should not exist.
Do you have a link for these empirical results? Any idea about the time period where the research was performed? And just to clarify: is this a position where you are selling or buying volatility?

The textbooks always show the volatility smirk, where implied volatility decreases with increasing strike price. Like the cartoon shown in the link below, for example:
https://www.investopedia.com/terms/v/vo ... y-skew.asp

However, this has not quite been what I have observed in SPX options in recent years. Some examples:

...

If the "textbook" picture of an implied volatility smirk were true, it would seem that with vertical credit spreads using puts, you would be buying volatility. Because you sell the option at a higher strike and lower IV, and buy the one with a lower strike and higher IV. But, if implied volatility is more "smile-shaped" as in my examples, then you would be selling volatility, because you sell the option at the higher strike having higher IV and buy the one at the lower strike having lower IV.

Edit: I realize now that I was only thinking about the vertical credit spread for strikes above the forward price. I see from your example of 5000 and 4800 that you are probably only referring to OTM put options, with strikes below the forward price. In both the smirk and non-smirk case for OTM put options, the higher strike put always has a lower IV (for strikes below the forward price).

This suggests to me that the position you described is buying volatility. Is this correct?
I think your charts show implied volatilities, but not the sensitivity of the option ("vega") to the implied volatility. In other words, the implied volatilities describe the stochastic process of the underlying, independent of a derivatives product. Vega describes the sensitivity of an option to the volatility of the underlying at the strike price of the option.
Refer to: https://quant.stackexchange.com/questio ... en-strikes
https://www.schwab.com/learn/story/gree ... strategies : "Vega is highest ATM but shrinks as price pulls away in either direction."

Example of an actual fund employing a credit spread sell strategy: https://www.simplify.us/etfs/high-simpl ... income-etf
Explanation of the strategy: https://www.simplify.us/etfs-use-case/c ... redit-risk
I can't find a backtest chart at the moment; but I think the idea is to sell volatility with a hedge, with net negative volatility exposure.
My understanding is that it is a defined risk strategy, and as such probably also more margin efficient.
Like I said, it's not immediately clear to me why this should theoretically result in better risk-adjusted returns, or even reasonably be expected to do so, unless you blindly trust the premise that whenever you are net negative volatility you will earn a premium in the long run, which is not clear to my why that should be the case. Perhaps you can shed some theoretical light or rationale on this.

Similar ETFs and strategies:
THTA (SoFi Enhanced Yield ETF) fund page with positions: https://www.sofi.com/invest/etfs/thta currently holds options 7.55% Spxw Us 06/28/24 P4650 / -8.68% Spxw Us 06/28/24 P4700
Zega options strategy: https://halbertwealth.com/assets/strate ... tSheet.pdf https://zegafinancial.com/products/hipos https://static.twentyoverten.com/5b313b ... il2024.pdf
CSHI: https://neosfunds.com/cshi/ https://neosfunds.com/cshi-comparison/ current positions: https://neosfunds.com/wp-content/upload ... -Sheet.pdf
Last edited by comeinvest on Wed Jun 12, 2024 4:30 am, edited 3 times in total.
unemployed_pysicist
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Re: Expectancy of selling options

Post by unemployed_pysicist »

comeinvest wrote: Wed Jun 12, 2024 4:10 am
I think your charts show implied volatilities, but not the sensitivity of the option ("vega") to the implied volatility.
Refer to: https://quant.stackexchange.com/questio ... en-strikes
https://www.schwab.com/learn/story/gree ... strategies : "Vega is highest ATM but shrinks as price pulls away in either direction."
You are correct, my charts only show the implied volatilities and not vega. I will read your links to get a better understanding of how this strategy works, or is supposed to work.
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Re: Expectancy of selling options

Post by JackoC »

comeinvest wrote: Tue Jun 11, 2024 2:07 pm
JackoC wrote: Tue Jun 11, 2024 10:10 am The problem with each of your three responses, IMO, is centered on 'risk adjusted'.
1. Principally no-arbitrage principles in financial markets don't depend on existence of "natural" users or parties. Parties will show up if arbitrage opportunities exist, and they are commonly expected to close. But I accept your explanation as common "limits to arbitrage", similar to for example the index futures basis trade or the swap spread trade which can result in risk-free profits of ca. 0.5% p.a.

2. But is there a reason why you explicitly say "far" out of the money options?

3. But the individual investor typically has no statistical data and no specific risk and return model of options on hand. By "blindly" going with a higher allocation to equities and buying put options the investor would assume that his own personal utility profile is different from that of the counterparty to the trade

4. I guess it might also well be possible that the 80/20 plus put options results in lower returns than 60/40 for most realized trajectories, defeating the purpose of this portfolio
1. Still stuck on a basic point. A risk premium in a price is pretty much by definition *not* an arbitrage, not sure why you keep equating 'risk premium' and 'arbitrage'. Risk premium in a price means you take on the risk, you harvest the premium. Arbitrage means you can hedge out all risk and still collect a premium. But there's no way to fully hedge out the risk of being short far below money index puts as delta hedger w/ exploding gamma near maturity if the market has dropped to near that strike and realized vol spiked. You get burned in that case, maybe badly, on an option for which you got paid relatively few absolute bps to begin with. The long side OTOH are non-delta hedging end users purchasing insurance. Insurance buyers must as a rule justify negative expected return on bought insurance. It makes sense that part of the high BS implied vol on those option is risk premium to sellers, to take unhedgeable residual risk, not free money.

2. To give a simple clear example (lower the strike, more pronounced that relative risk to the short delta hedger v the whole premium) and not go off in a bunch of different directions with basic principles still misunderstood. Crawl, walk, run.

3. When I buy stock, somebody must sell it to me. Do I need to care why they want to sell at this level? Obviously not. This entire line of reasoning is mistaken. And in the specific case in question as we've already covered, the price on a broker screen for far below money SPX put can be assumed a dealer who is going to delta hedge*. Their risk preference, doing something entirely different than I am, has zero to do with whether their price is attractive to me.

4. This is conceding my very simple and limited point :happy . It *may* be that the cases where 80/20 w/ some puts comes out behind 60/40 w/o puts (ie. w/ mediocre to somewhat poor but not terrible index returns) outweighs, in that investor's view, the greater upside that can be captured 80/20 w/ puts if things go well, all while limiting the downside to that of 60/40 unhedged. Which means it also *may* be that the greater upside capture *is* worth it to that investor (I inserted 'may', 'possible', 'arguable' every single time). It depends on visible market pricing, the investor's (detailed, not simplistic) risk preference, and return expectation. Again, many here clearly believe stock expected return is equal to average past realized return. If index E[r] is really still 6.5% real, that's a lot more outcomes where greater upside in the 80/20 hedged case will beat 60/40 unhedged than if index E[r}=4%, generously, as I believe the market would indicate (via div/earnings yield but I won't say 'they're betting against the market' :happy ). Also depends on the riskless return: tail hedging to increase equity alloc was more attractive with TIPS yields -1+% in 2021 than +2+% now (with div/earnings yields having barely moved).

*in some overall position of SPX options of many strikes, but highly likely net short in the portion that's far below money strikes.
comeinvest
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Re: Expectancy of selling options

Post by comeinvest »

JackoC wrote: Wed Jun 12, 2024 10:58 am
comeinvest wrote: Tue Jun 11, 2024 2:07 pm
JackoC wrote: Tue Jun 11, 2024 10:10 am The problem with each of your three responses, IMO, is centered on 'risk adjusted'.
1. Principally no-arbitrage principles in financial markets don't depend on existence of "natural" users or parties. Parties will show up if arbitrage opportunities exist, and they are commonly expected to close. But I accept your explanation as common "limits to arbitrage", similar to for example the index futures basis trade or the swap spread trade which can result in risk-free profits of ca. 0.5% p.a.

2. But is there a reason why you explicitly say "far" out of the money options?

3. But the individual investor typically has no statistical data and no specific risk and return model of options on hand. By "blindly" going with a higher allocation to equities and buying put options the investor would assume that his own personal utility profile is different from that of the counterparty to the trade

4. I guess it might also well be possible that the 80/20 plus put options results in lower returns than 60/40 for most realized trajectories, defeating the purpose of this portfolio
1. Still stuck on a basic point. A risk premium in a price is pretty much by definition *not* an arbitrage, not sure why you keep equating 'risk premium' and 'arbitrage'. Risk premium in a price means you take on the risk, you harvest the premium. Arbitrage means you can hedge out all risk and still collect a premium. But there's no way to fully hedge out the risk of being short far below money index puts as delta hedger w/ exploding gamma near maturity if the market has dropped to near that strike and realized vol spiked. You get burned in that case, maybe badly, on an option for which you got paid relatively few absolute bps to begin with. The long side OTOH are non-delta hedging end users purchasing insurance. Insurance buyers must as a rule justify negative expected return on bought insurance. It makes sense that part of the high BS implied vol on those option is risk premium to sellers, to take unhedgeable residual risk, not free money.
It's probably inaccurate terminology, but I kept on bringing the word "arbitrage" because many, possibly the majority of retail investors who get bombarded with the options writing marketing hype believe that it's "free" additional cash flow, not only compensation for risk. (The favorite buzzword is "income" as in dividends and distributions, even if it's just ROC, that seems to trigger a nearly complete outage of any rational functioning of the brain, if you read the investment forums like Seeking Alpha. But that's a different story, as I hope in this forum we are on the same page that total return matters along with risk incurred, not "income".)
Also because of the fact that neither the implied volatility nor the catastrophic drawdown events that you mentioned have on average sufficiently materialized in the 40 year history of options markets, or else the options writing strategies would not have had superior risk-adjusted returns with the observable historical realized risk and realized returns.
For purpose of asset allocation and whether to not including an options selling strategy makes sense, I think the question is whether the excess returns have a risk based or behavioral based explanation; and if a combination of both, then to what degree. Similar to the explanations of the equity market factor premia.
I think we have not yet conclusively answered that question. I like to bring up the example of a vertical put spread again, that has a very limited risk profile which can also nearly perfectly directionally hedged with the underlying, and the likelihood and magnitude of short-term up and down movements of the market within a given vertical range near the money has many thousands of data points of backtesting data during the 40 years of options market history. I still struggle with the concept that money can be made on average with derivatives that cannot be made with the underlying itself, and I don't immediately see a conclusive risk based explanation.

If the explanation is risk based, another important question is to what extent is the risk correlated with the general market risk, and to what extent is it an independent risk premium to be harvested.
JackoC wrote: Wed Jun 12, 2024 10:58 am ...

3. When I buy stock, somebody must sell it to me. Do I need to care why they want to sell at this level? Obviously not. This entire line of reasoning is mistaken. And in the specific case in question as we've already covered, the price on a broker screen for far below money SPX put can be assumed a dealer who is going to delta hedge*. Their risk preference, doing something entirely different than I am, has zero to do with whether their price is attractive to me.

4. This is conceding my very simple and limited point :happy . It *may* be that the cases where 80/20 w/ some puts comes out behind 60/40 w/o puts (ie. w/ mediocre to somewhat poor but not terrible index returns) outweighs, in that investor's view, the greater upside that can be captured 80/20 w/ puts if things go well, all while limiting the downside to that of 60/40 unhedged. Which means it also *may* be that the greater upside capture *is* worth it to that investor (I inserted 'may', 'possible', 'arguable' every single time). It depends on visible market pricing, the investor's (detailed, not simplistic) risk preference, and return expectation. Again, many here clearly believe stock expected return is equal to average past realized return. If index E[r] is really still 6.5% real, that's a lot more outcomes where greater upside in the 80/20 hedged case will beat 60/40 unhedged than if index E[r}=4%, generously, as I believe the market would indicate (via div/earnings yield but I won't say 'they're betting against the market' :happy ). Also depends on the riskless return: tail hedging to increase equity alloc was more attractive with TIPS yields -1+% in 2021 than +2+% now (with div/earnings yields having barely moved).

*in some overall position of SPX options of many strikes, but highly likely net short in the portion that's far below money strikes.
You are just saying the exact same thing that I am saying just with different words. You keep using the word "may". Basically the same semantics that I was using, when for example I said the investor may have an idiosyncratic preference scenario, constraints, or boundary conditions, that might prompt him to use options one or another way.
But if we just leave it at "may", we would just keep expressing tautologies, but not getting anywhere. Eventually we want to examine the nature of risk and return, especially when using options as part of a systematic strategy. For that purpose, one of the ingredients is commonly to investigate who the counterparties are and their motivation for the trade. The line of reasoning is not mistaken. The counterparties, their motivations, and their risk and returns matter for purpose of evaluating an investment strategy using options and for explaining the historical excess returns, unless you have your own independent volatility surface model which most don't have; certainly not the retail investors.

When the passive retail investor buys a stock, he typically doesn't care about the counterparty to the trade, nor about valuations. He adds a stock to his portfolio because he assumes that in the long run the expected return of a diversified portfolio of stocks will be positive, or simply because he has money left over that he doesn't need now but some time later. I think the ultimate rationale and justification for positive any returns positive or negative is the supply and demand for storing capital on the time axis which determines the risk-free return, along with intermediate and terminal drawdown risks of any asset, which determine the risk premia. If you have capital left over to save for retirement, you have to invest it somehow in the markets, and you are probably going to buy a diversified basket of some parts of some assets in some markets regardless of valuation, or perhaps you do some quantitative valuation (often futile). Absent an individual quantitive asset valuation, you probably generally want to invest in a basket of long-term assets if you have a long time horizon, as you expect somewhat higher returns reflecting the intermediate drawdown risk, that is not a risk for you.
I think this concept and rationale doesn't immediately apply to derivatives like options: Options positions don't arise from the real-life need to store or borrow capital, but they rather express an "active" opinion on the volatility surface model. Without a volatility surface model the individual investor has no way of determining wether a premium received at strike price X is worth the risk, or a premium paid at strike price Y is worth the protection, even if he thinks he knows his individual utility function of his NAV up and down movements. You would not only have to know your exact utility function of x% drawdown vs. y% drawdown or gain, but also have to relate this to the volatility model. I think it is impossible for a retail investor to make a rational decision between (for example) 60/4O and 80/20 plus put options, in any possible way other than gut feeling (a bad idea to go by, in finance). Opening options positions makes only sense if you either believe you have a superior quantitative model to that of your counterparties, or that there is some systematic liquidity based or behavioral bias in the markets, or that the risk premium is uncorrelated to the market risk premium, i.e. not simply directional market risk based. I think the last two are the questions that we want to answer. To be clear, we are talking about volatility risk exposure as part of an asset allocation and a systematic strategy, not a singular special idiosyncratic scenario.
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y1980
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Re: Expectancy of selling options

Post by y1980 »

comeinvest wrote: Mon Jun 10, 2024 11:29 pm
y1980 wrote: Mon Jun 10, 2024 12:42 pm Would you agree to go with me for a moment?
1. The only figure that does not have a source in the Black-Schulz formula is predicted volatility, right?
2. By what is the predicted volatility estimated?
3. If on average the seller of the option receives only his investment, what does he sell the options for?

Maybe I'm just wrong about one of these questions, correct me if I am. Thanks.
The same question applies to the buyer. Both parties can hedge their options exposure with the underlying. The math reduces the optimization problem to a bet on volatility surfaces for both sides of the trade, including jump risk as JackoC mentioned. I'm not sure how the latter can be mathematically included in the framework of stochastic calculus, but I think that is just a technical detail that is not essential to the question and the reasoning at hand. Let's just say it's a bet on the stochastic process, that results in the volatility surface.
Sorry for my delay, I was unable to respond.
This question does not apply to the buyer because it is John Smith who is about to retire in the coming year, and is afraid that his portfolio will fall sharply that he cannot bear. On the other hand, he still wants to get the average return of the market, so he prefers to give up a bite of the unguaranteed return to hedge his risk of a big fall.
comeinvest
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Re: Expectancy of selling options

Post by comeinvest »

y1980 wrote: Thu Jun 13, 2024 6:30 pm
comeinvest wrote: Mon Jun 10, 2024 11:29 pm
y1980 wrote: Mon Jun 10, 2024 12:42 pm Would you agree to go with me for a moment?
1. The only figure that does not have a source in the Black-Schulz formula is predicted volatility, right?
2. By what is the predicted volatility estimated?
3. If on average the seller of the option receives only his investment, what does he sell the options for?

Maybe I'm just wrong about one of these questions, correct me if I am. Thanks.
The same question applies to the buyer. Both parties can hedge their options exposure with the underlying. The math reduces the optimization problem to a bet on volatility surfaces for both sides of the trade, including jump risk as JackoC mentioned. I'm not sure how the latter can be mathematically included in the framework of stochastic calculus, but I think that is just a technical detail that is not essential to the question and the reasoning at hand. Let's just say it's a bet on the stochastic process, that results in the volatility surface.
Sorry for my delay, I was unable to respond.
This question does not apply to the buyer because it is John Smith who is about to retire in the coming year, and is afraid that his portfolio will fall sharply that he cannot bear. On the other hand, he still wants to get the average return of the market, so he prefers to give up a bite of the unguaranteed return to hedge his risk of a big fall.
Special idiosyncratic circumstances of individual market participants (not to mention gut feelings of retail investors) don't make a market. Like JackoC mentioned, there might be more "natural" buyers, which may or may not slightly tilt the equilibrium price; but the existence of "natural" market participants in and by itself does not "justify" a return (earnings) to the counterparty. The word arbitrage or arbitrageur may not be the right one here depending on how you define it; but eventually, a mathematically "fair" price based on risk, return, and correlations, along with capital expense and limits to arbitrage or to efficient markets, determine the equilibrium price. The non-hedgeable jump risk that JackoC mentioned might be an ingredient, together with the degree of its correlation to the overall market. That reasoning however would be totally different from the reasoning that you should be "entitled" to a return because you just entered the "insurance business", which is really too simplistic and inconclusive; I would even say it's outright wrong and misleading, because directional risk per se is really not what is being insured - directional market downside risk (delta) can be hedged; what would be "insured" if anything is volatility beyond delta (e.g. sudden market moves). But like I said, that sort of semantics really does not matter; in the end it's mathematics based on non-hedgeable risk, correlations, etc.

On another one, like I mentioned in previous posts, the decision of John Smith is hard to rationalize. Absent a sophisticated volatility model of John Smith that allows him to evaluate the drawdown risk at various strike prices, and match his model against the actual cost of the options in the market and against his personal utility function surface of terminal outcomes in time and space, the best advise to him would be to simply reduce his basket of equities positions based on his age and investment horizon. There are plenty of possibilities to invest, for example 60/40, 20/80, or only T-bills if you can't afford any drawdowns; and any combination in between. But regardless the decision of John Smith, his gut feeling or even his personal utility function of drawdowns should not affect the pricing of financial products in an efficient market. Options can be mathematically converted to a volatility estimation problem and will be priced on the statistics of the 40 year history of the options market and the about 100 years history of the stock market, or the market makers' estimation of future volatilities and risk; it won't be priced based on the gut feelings of John Smith.
JackoC
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Re: Expectancy of selling options

Post by JackoC »

comeinvest wrote: Wed Jun 12, 2024 11:35 pm

1. It's probably inaccurate terminology, but I kept on bringing the word "arbitrage" because many, possibly the majority of retail investors who get bombarded with the options writing marketing hype believe that it's "free" additional cash flow, not only compensation for risk.

2. Also because of the fact that neither the implied volatility nor the catastrophic drawdown events that you mentioned have on average sufficiently materialized in the 40 year history of options markets, or else the options writing strategies would not have had superior risk-adjusted returns with the observable historical realized risk and realized returns.

3. You are just saying the exact same thing that I am saying just with different words. But if we just leave it at "may", we would just keep expressing tautologies, but not getting anywhere.

4. When the passive retail investor buys a stock, he typically doesn't care about the counterparty to the trade, nor about valuations.
I think this concept and rationale doesn't immediately apply to derivatives like options: Options positions don't arise from the real-life need to store or borrow capital, but they rather express an "active" opinion on the volatility surface model.
1. It is basically inaccurate to mix up 'there's a risk premium' with 'there's an abritrage'. It doesn't seem reasonable to me to ignore the distinction I made between those two repeatedly because 'options investors get bombarded by marketing hype'. :happy

2. Again I did NOT say 'superior risk adjusted returns' YOU keep saying that. And the 40 yr history of OTM index puts is clear: ever since the 1987 crash there's been a distinctly bigger implied vol premium on far below money options. For the obvious reason I've stated several times: the sell side of that part of the market is predominantly delta hedging dealers. They will collect a pretty small premium for some possibility of having to hedge those in a high>very high gamma (not predictable) environment if the market drops near the strike near maturity. It stands to reason they write them at positive expected (delta hedged) return or why would they? Whether that gives them 'superior risk adjusted return' is a question I made a point from the get go of not addressing. It's quite difficult to say in any objective way ('Sharpe Ratio' etc means basically nothing from a professional trading POV) and not very relevant to the retail investor anyway. It's just a simple example of a prevailing risk premium, nothing claimed about 'risked adjusted return', in options prices. Crawl, walk, run.

3. If it's 'the exact same thing' why object in the first place? And 'may' does not make the discussion meaningless. It points to how it's a matter of personal return outlook and risk preference. Again, think about the differences people express here in their return expectation. One concrete implication of an optimistic expected return outlook, for a person who still doubts their ability to withstand the full downside of more than 60% stock would be to increase allocation but hedge some of that downside. It's what options markets actually exist to do.

4. The easiest way to see this is wrong is the simplest derivative, stock index futures. If I buy 500 shares of SPY or go long 1 ES contract and put ~$270 some k in the bank it's basically the same in risk and return (the return is a little higher/lower depending on how the best bank account rate compares to the implied financing rate in the futures price, at times best retail bank account rates have exceeded the impliced financing rate, not lately though). Do I need to know why the ES counterparty wants to go short 'because it's a derivative', but not need to know why the SPX owner wants to sell to me? That wouldn't make sense and should enable you to see it doesn't make sense for options either. If the option at the price offered results in a pay off pattern more suited to my risk preference and return outlook that not buying, it's preferrable for me to buy it. It has nothing to do with why seller wants to sell it other than how that manifests in the price. And 'volatility surface' is a 'running' topic, we're still trying to crawl here.

And as to 'gut feeling' having no place in investing this is also transparently wrong even just sticking to cash investment in stocks. Perhaps some investors would like to *think* the BH method gets them away from their gut but it doesn't. The basic question of how much stock risk one can tolerate is gut. BHism is about disciplining the gut, but investing can't get away from gut feelings altogether. Using tail hedging is just an extension of that.
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