Is iv skew the result of an error in the Black-Scholes model...

[markuzick]

Sometimes they are priced higher, if market participants bid them so. But put-call parity has nothing to do with the explanation. And in a liquid offering, there's nothing to be exploited.

I've noticed that put-call parity can be violated, but only on a fleeting basis during a sudden move - the parity always comes back. During an established long term uptrend volatility is biased to the upside, so calls have greater value than puts, as selling them represents a greater average risk than selling puts; when the market settles back to parity, there would have to be an exploitable edge - the only unknown is whether it's the atm puts that are overpriced or it's the atm calls that are underpriced; according the book, it's the atm puts that have an expected return of -.26, so it must be the puts that tend to be overpriced. The otm puts are said to have a far greater negative return, so the model, even if it is imperfect, seems, empirically, to be far closer to reality than the way the market prices otm puts - why this mis-pricing by the market doesn't apply as strongly to the skew on otm calls, I'm not certain - possibly, it's the overpricing of atm puts during uptrends - and uptrends last longer than downtrends, as markets climb slow and fall fast - that distorts the otm put option chain to make otm puts even more overpriced than hedging activities alone would make them.
The -.26 expected return on atm puts was, I believe, over a span that included downtrends, so I would assume that during uptrending markets this negative expected return is far worse.

 

[cdcaveman]

Some common sense there in any trend the any options strategies that benefit from Delta in the same direction will benefit...

 

[Mike Okistini]

Thanks for giving us such powerful, new information. Yes, Black-Scholes is a MODEL (who knew?). Yes, empirical evidence shows it's assumptions are violated.

But if it's such a piece of junk, why has it stood the test of time? Why is it still being used today by plenty of very smart people around the world?

Simple, it is best researched and used model out there but many others are used and nobody uses it to price traded options because the price is already dictated by the market just as the IV skews are dictated by the market, NOT the model. B-S is more useful for OTC or unique priced options but other than that it just serves as a means for displaying IV. No smart people are using it for daily trading and market makers are using it more for greek calculations and portfolio hedging. Why do you need to a model to price an option that is showing a heavily traded b/a in the market. If you want to put your own vol assumption then you are just creating error possibility. I find more academics writing papers using it than actual traders (outside of greek portfolio).

Truly there can never be an accurate pricing model because prices are determined by the market or market makers based on human assumptions that a model can never capture. Even the Greeks are theoretical but the best form of risk parameters we have and the true worth if B-S. Skews are created 100% by the trading behaviors which cannot be modeled. That is why it is used by many smart academics who write papers from ivory towers without a penny in the market outside of the IRA.

Just my opinion by B-S is not used to price options, it is used to back into IV calculations to track. And for the more advanced to measure portfolio greeks.

 

[longthewings]

Simple, it is best researched and used model out there but many others are used and nobody uses it to price traded options because the price is already dictated by the market just as the IV skews are dictated by the market, NOT the model. B-S is more useful for OTC or unique priced options but other than that it just serves as a means for displaying IV. No smart people are using it for daily trading and market makers are using it more for greek calculations and portfolio hedging. Why do you need to a model to price an option that is showing a heavily traded b/a in the market. If you want to put your own vol assumption then you are just creating error possibility. I find more academics writing papers using it than actual traders (outside of greek portfolio).

Truly there can never be an accurate pricing model because prices are determined by the market or market makers based on human assumptions that a model can never capture. Even the Greeks are theoretical but the best form of risk parameters we have and the true worth if B-S. Skews are created 100% by the trading behaviors which cannot be modeled. That is why it is used by many smart academics who write papers from ivory towers without a penny in the market outside of the IRA.

Just my opinion by B-S is not used to price options, it is used to back into IV calculations to track. And for the more advanced to measure portfolio greeks.

Ok you do realize though that if someone is delta hedging a position, and they are calculating that delta with Black-Scholes, they are implicitly pricing with Black-Scholes....

Hedging and pricing are essentially the same thing in vol trading. The entire continuous time Black-Scholes model is based on a no-arbitrage hedging argument to arrive at the option price. The greeks are just derivatives that use this pricing result.

So if you just buy/sell an option, plug the market IV into Black-Scholes and delta hedge away, think about what you're doing. You're basically saying, ok, I bought this option at 12% IV and now I'm going to hedge at 12% IV. If the market is efficient and correct in the IV call, you break even. You bought the option at 12 and replicated an offsetting short at 12. You break even. If the market is wrong, you hedged wrong. So it's not like just plugging in the market IV is less prone to error. By hedging with IV, you either break even or you hedged wrong. You might get lucky on the P&L variance and earn, but you still hedged wrong. Whereas if I price and hedge with a different vol, at least if I'm right I expect to make money and not just break even.

 

[markuzick]

Simple, it is best researched and used model out there but many others are used and nobody uses it to price traded options because the price is already dictated by the market just as the IV skews are dictated by the market, NOT the model. B-S is more useful for OTC or unique priced options but other than that it just serves as a means for displaying IV. No smart people are using it for daily trading and market makers are using it more for greek calculations and portfolio hedging. Why do you need to a model to price an option that is showing a heavily traded b/a in the market. If you want to put your own vol assumption then you are just creating error possibility. I find more academics writing papers using it than actual traders (outside of greek portfolio).

Truly there can never be an accurate pricing model because prices are determined by the market or market makers based on human assumptions that a model can never capture. Even the Greeks are theoretical but the best form of risk parameters we have and the true worth if B-S. Skews are created 100% by the trading behaviors which cannot be modeled. That is why it is used by many smart academics who write papers from ivory towers without a penny in the market outside of the IRA.

Just my opinion by B-S is not used to price options, it is used to back into IV calculations to track. And for the more advanced to measure portfolio greeks.

Yes, it's the market that determines iv; but which iv is it that turns out to be the better prediction: the otm iv's, or the atm iv's?... there is only one underlying, and the predicted iv is of that underlying - not the option - so there is only one iv that comes closest to being the statistically best prediction; and I'm guessing that it's the atm call that has the least edge - that, over time, regular purchase/sale of atm calls are a breakeven proposition before transaction costs. If so, then the less accurate iv's are either under/over-priced in comparison to the atm call's iv, which gives an exploitable edge, assuming that the model for translating an option's price into an iv number isn't too seriously flawed for otm options. That the model is better than the market at determining the true value of an otm option relative to the atm call seems to be supported by empirical observations that otm puts have an extreme negative return over time.

 

[cdcaveman]

They only have a negative return because of the tendency for the market today grind up for long periods of time... That implies calls being mispriced.... I just don't agree with they way some of you guys are looking at this... You use a model to reverse out implieds from price as has been stated.. This enables the speculation of other influences on options price ie gamma Delta Vega.. It's a kind of map to influences... One used so much alot of the flaws are known.. Everyone would rather use a simpler model with know flaws then a more complex one period.. Otm options are priced differently because they have more risk then ATM options.. Its the value of the leverage the market puts on them... Higher convexity comes at a cost... Higher hedging costs and explosive gamma

 

[longthewings]

This has basically come down to a debate of whether or not to calibrate to market prices.

 

[cdcaveman]

Or more importantly a way to calculate relative prices!!!

 

[markuzick]

They only have a negative return because of the tendency for the market today grind up for long periods of time... That implies calls being mispriced.... I just don't agree with they way some of you guys are looking at this... You use a model to reverse out implieds from price as has been stated.. This enables the speculation of other influences on options price ie gamma Delta Vega.. It's a kind of map to influences... One used so much alot of the flaws are known.. Everyone would rather use a simpler model with know flaws then a more complex one period.. Otm options are priced differently because they have more risk then ATM options.. Its the value of the leverage the market puts on them... Higher convexity comes at a cost... Higher hedging costs and explosive gamma

Are you saying that the price of otm options is implying more than just the underlying security's expected volatility, but the B-S model is based on the assumption that the only factor behind an option's expected value is the volatility of the underlying? These other factors: aren't they just the consequences of volatility that give volatility its value/cost.

Do otm options really have a greater risk/price ratio?...there's two kinds of risks here: the risk of the frequency of going into the money and the risk of leverage (risking dollars to make pennies); don't the two risks balance out?

 

[Mike Okistini]

Yes, it's the market that determines iv; but which iv is it that turns out to be the better prediction: the otm iv's, or the atm iv's?... there is only one underlying, and the predicted iv is of that underlying - not the option - so there is only one iv that comes closest to being the statistically best prediction; and I'm guessing that it's the atm call that has the least edge - that, over time, regular purchase/sale of atm calls are a breakeven proposition before transaction costs. If so, then the less accurate iv's are either under/over-priced in comparison to the atm call's iv, which gives an exploitable edge, assuming that the model for translating an option's price into an iv number isn't too seriously flawed for otm options. That the model is better than the market at determining the true value of an otm option relative to the atm call seems to be supported by empirical observations that otm puts have an extreme negative return over time.

You ask a great question, which IV is the better predictor. But I have to think that over time the market's estimation of future IV is constantly changing so the snapshot you see becomes no longer relevant pretty fast. Many studies have shown that VIX spikes far great than actual volatility occurs over the projected time period. I would believe the VIX is spiking due to increased put buying during heavy market sell offs which pushes all options higher (calls and puts due to PC Parity). Therefore the demand in puts is to hedge portfolios and this demand is not done to predict specific IV value but results in a specific IV value which spikes the VIX.

You asking which IV out of the whole skew is the accurate IV predictor is like saying, which person can accurately predict future IV. Every option is over or under priced relatively depending on YOUR estimation of IV and prediction of where the underlying market is heading. If OTM puts have an IV of 20% with VIX at 15% but I expect a market sell off to occur over the next few weeks then those puts are not too expensive based on my expectation while a credit spread seller might be all over them as overpriced. To this end, over priced or underpriced or accurate IV is in the eye of the beholder, not a model.

You and I expect a market sell off and you buy OTM puts and I buy OTM FLYS. Both of us make money on a market sell off but our profit will be different depending on what happens to vols once market sells off

I would say OTM options which remain OTM have negative returns over time, except in strong market sell offs or strong market rallies. But how far OTM? and predicting that market move ahead of time? Un-model-able which is why we have a market to begin with:

Constant contradicting predictions of market direction and market volatility.

This is why the original question is too difficult to answer and not answered with B-S. Irrational market behavior will drive prices/vols more randomly than a model can predict. The reason we have skews is due to the errors in B-S predicting future pricing/vols and our differing opinions means we will not be able to exploit the skews as an arbitrage.

Complicated and fascinating discussion in all seriousness and I thank you.