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

markuzick

markuzick

or is it the result of the under/overpricing of otm options by market forces?...logic would seem to dictate that it must be one or the other;(I suppose there could also be some of both things at play, but that it would probably be one or the other hypothesized cause that predominates.) after all, the iv is - or it should be - the result of the factors affecting the future movement of the underlying - not the particular strike or expiration of its options.

If the market is efficient and buying/selling random ATM options was a breakeven strategy before expenses, and if Black-Scholes is correct, then otm calls are really under-priced and otm puts are really over-priced and it would seem to be an easy thing to exploit.

If anyone knows the answer, then I thank you in advance.
 
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There is the model, and then there is the market.

The two should not be confused. Doing so can be extremely costly, as the the namesakes of that model found out all too well...

If I came to you and said I'll take everything you're willing to sell me on XYZ July puts @ 20 strike, will you simply sell me as much as I want at the Black-Scholes model price? If not why not? If your model is right then you should be willing to sell me as much as I want with some % margin baked in above the model price, no?
 
My 2 cents: Short answer: No (IMHO)!
As TD80 well stated, there is the market and then there is the model (I took the liberty of reversing the terms).
Coming from an engineering background, I use the option pricing model as a way to try to understand the option pricing. With the B&S model, all inputs are known but one. That one "unknown" input is the "volatility". So, the correct Implied Volatility for the particular strike/expiration/type option is the value you must plug into the model to get the correct answer. For some products, such as SPX and RUT this skew is fairly well behaved and predictable. I'm pasting a graph of IV for SPY SEP 2015 contracts for reference.
First graph is for OTM options, then for Calls, then for PUTs.
upload_2015-8-13_16-27-36.png

upload_2015-8-13_16-28-9.png


These were taken from TOS. From my perspective the IV skew is merely the market influence and has nothing to do with the model.
 
markuzick said:
or is it the result of the under/overpricing of otm options by market forces?...logic would seem to dictate that it must be one or the other;(I suppose there could also be some of both things at play, but that it would probably be one or the other hypothesized cause that predominates.) after all, the iv is - or it should be - the result of the factors affecting the future movement of the underlying - not the particular strike or expiration of its options.

If the market is efficient and buying/selling random ATM options was a breakeven strategy before expenses, and if Black-Scholes is correct, then otm calls are really under-priced and otm puts are really over-priced and it would seem to be an easy thing to exploit.

If anyone knows the answer, then I thank you in advance.
More...


In my experience, there are a few factors that tend to create the typical equity skew where OTM puts are higher than OTM calls.

-stocks tend to go down faster than they go up.
-when stocks go down, since most investors are long, there is increased fear/uncertainly-Ivol will tend to increase
-when stocks go up, there is reduced fear/uncertainly, Ivol will tend to decrease
-since most investors are long, a typical hedge would be to buy puts and/or sell calls so supply/demand is also a cause

This is not to say that this skew is correct, but don't expect it to invert under normal trading conditions. Many years ago, some of the large tech companies did buy backs using options. They would sell a large block of just OTM puts and buy a large block of just OTM calls. They would also buy stock in the open market. This worked well for them becasue if the stock dropped, they got their buy back at a great price. If the stock ran, they knew they could exercise that call to compete their buy back. The large brokers loved it because they could price it outside the current market price and hedge it over time with other options, because these transactions were OTC, market makers could not play.The companies took advantage of the skew.
 
TD80 said:
There is the model, and then there is the market.

The two should not be confused. Doing so can be extremely costly, as the the namesakes of that model found out all too well...

If I came to you and said I'll take everything you're willing to sell me on XYZ July puts @ 20 strike, will you simply sell me as much as I want at the Black-Scholes model price? If not why not? If your model is right then you should be willing to sell me as much as I want with some % margin baked in above the model price, no?
More...

Assuming Black-Scholes is correct, then there is only one reason one wouldn't be wise to sell as much as someone wanted of overpriced puts: money management; you can be right about value and still go broke.
 
rmorse said:
In my experience, there are a few factors that tend to create the typical equity skew where OTM puts are higher than OTM calls.

-stocks tend to go down faster than they go up.
-when stocks go down, since most investors are long, there is increased fear/uncertainly-Ivol will tend to increase
-when stocks go up, there is reduced fear/uncertainly, Ivol will tend to decrease
-since most investors are long, a typical hedge would be to buy puts and/or sell calls so supply/demand is also a cause

This is not to say that this skew is correct, but don't expect it to invert under normal trading conditions. Many years ago, some of the large tech companies did buy backs using options. They would sell a large block of just OTM puts and buy a large block of just OTM calls. They would also buy stock in the open market. This worked well for them becasue if the stock dropped, they got their buy back at a great price. If the stock ran, they knew they could exercise that call to compete their buy back. The large brokers loved it because they could price it outside the current market price and hedge it over time with other options, because these transactions were OTC, market makers could not play.The companies took advantage of the skew.
More...
I'm familiar with the explanations as to why the iv skew exists, but I'm also skeptical that they're true, though hopeful that they are. I've heard that the otm options are correctly priced and that it's the Black-Scholes model that's defective; it makes sense: it's hard for me to accept that a situation where options remained permanently over/under-valued - it can't be that easy to make money.
 
The Skew comes from assumptions, not the model. For a short period of time after I left the Amex floor, I was going to trade options on sugar. I noticed that the skew was the reverse of equity options. Why, because the fear was from a shortage. The OTM calls were much higher than the OTM puts. On the Amex, I also made markets in GLD options. That had a skew toward calls being higher. I felt it was incorrect becasue there are no shortages of gold and traded call ratio spreads, and bought OTM puts, sold OTM calls and hedged with GLD. My assumptions were different from the market. I did well on those, but the skew never changed in a material way. I had to wait until near expiration to unwind.
 
markuzick said:
or is it the result of the under/overpricing of otm options by market forces?...logic would seem to dictate that it must be one or the other;(I suppose there could also be some of both things at play, but that it would probably be one or the other hypothesized cause that predominates.) after all, the iv is - or it should be - the result of the factors affecting the future movement of the underlying - not the particular strike or expiration of its options.

If the market is efficient and buying/selling random ATM options was a breakeven strategy before expenses, and if Black-Scholes is correct, then otm calls are really under-priced and otm puts are really over-priced and it would seem to be an easy thing to exploit.

If anyone knows the answer, then I thank you in advance.
More...

so your saying because atm options are priced at a lower vol number then otm's it should be easy to to make money off that differential.. ?? It's really really really not that simple.. The otm options are more expensive for good reason, the risk with them is higher.. My next question is find a strategy that effectively isolates skew and then figure out the costs of exploiting it..
 
rmorse said:
The Skew comes from assumptions, not the model. For a short period of time after I left the Amex floor, I was going to trade options on sugar. I noticed that the skew was the reverse of equity options. Why, because the fear was from a shortage. The OTM calls were much higher than the OTM puts. On the Amex, I also made markets in GLD options. That had a skew toward calls being higher. I felt it was incorrect becasue there are no shortages of gold and traded call ratio spreads, and bought OTM puts, sold OTM calls and hedged with GLD. My assumptions were different from the market. I did well on those, but the skew never changed in a material way. I had to wait until near expiration to unwind.
More...
I believe that GLD; TLT; and VXX are examples of fear driven securities; they tend to crash upwards, so naturally, if the skew is an emotion based market idiosyncrasy, it will be the reverse of common stocks: the calls will be used as a portfolio hedge.

You're telling me what I want to hear and it implies that it's easy to make money by simply buying/selling otm options that have iv that's lower/higher than atm iv. I've also heard that weeklies are under-priced compared to monthlies, as the monthly atr of securities is far less than 4.3 times the weekly atr and that this is not fully reflected in the price of weeklies. With this in mind, it would pay to sell otm monthly puts and to buy otm weekly calls.

Is there anyone with a different point of view? I still feel that it's too good to be true.
 
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