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

[markuzick]

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..

Is the risk really higher?...there are two kinds of risk in selling an option: 1 - frequency of it going into the money and 2 - the extent it goes into the money. Overpriced options are at less risk of going into the money, but tend to make larger moves when they do. Underpriced options are at greater risk of going into the money, but tend to make smaller moves when they do. On average, in a trendless market, these risks would balance out; and in a bull market, it should be the calls that have higher iv to reflect a volatility bias to the upside. I don't think that Black-Scholes take market trends into consideration, so this would be the only rational reason to accept a skew as fairly priced, but the skew is actually going against the trend.

Iv should have nothing to do with the strike of an option; it's the same security reguardless of the strike. If there are two different iv's for one security, then at least one of them must be wrong.

 

[sonoma]

...Overpriced options are at less risk of going into the money, but tend to make larger moves when they do. Underpriced options are at greater risk of going into the money, but tend to make smaller moves when they do....

You've got a couple of concepts conflated here, but here's something for your question about relative pricing on puts/bullish risk-reversals.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=375784

 

[markuzick]

Look at the work of Neil Chriss relative to the skew or "volatility smile"

http://www.amazon.com/Black-Scholes-Beyond-Option-Pricing-Models/dp/0786310251

http://bfi.cl/papers/Derman Kani Chriss 1996 - Implied trinomial trees of the volatility smile.pdf

https://books.google.com/books?id=ZTkFszCxwdAC&pg=PA613&lpg=PA613&dq=neil+chriss+volatility+smile&source=bl&ots=MK_qncfsAW&sig=GfNXBFfPzJCt2sKIxSw4vDliCvY&hl=en&sa=X&ved=0CCYQ6AEwAjgKahUKEwiFq8Dlv6fHAhWMbD4KHY91Bcw#v=onepage&q=neil chriss volatility smile&f=false

I wouldn't be able to judge the analysis in these books; are they saying that the model is correct?... and, if so, are they explaining the skew as an aberration of the market, where some options are permanently over/under-priced? I see mention of the skew changing after the '87 crash; in that case, the skew either didn't reflect reality before '87; it doesn't now; or as I'm inclined to believe, it never has as long as there's any skew other than making otm calls more expensive in an uptrend and otm puts more expensive in a down trend.

 

[markuzick]

You've got a couple of concepts conflated here, but here's something for your question about relative pricing on puts/bullish risk-reversals.

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=375784

So, essentially then, the models are right and the market is persistently wrong; amazing - I never thought it could be that easy to profit with options. The book mentions that even atm puts have a negative return; to my thinking, this makes sense, because in an uptrending market atm calls should be priced higher than atm puts, but put-call parity prevents this, creating a distortion that can be exploited. The opposite distortion should also happen in a long term downtrend. I also noticed that the book mentioned that buying otm calls wasn't as consistently as profitable as selling the otm puts: what could be the reason for that?...is it possible that both the models and the market pricing have built in flaws?

BTW, I appreciate constructive criticism - I'm here because most here know much more about options than I do: what concepts am I conflating?

 

[trilogic]

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.

Hi What is your opinion on trading fly's or calendar spreads on individual equities right now, ?

 

[cdcaveman]

The map is not the territory... Sorry I have not had enough time to post my thoughts..... Derman has a model called localized vol that accounts for skew... Because of the lower nominal amount of options otm it is cheap leverage and represents potiential rarer events in the distro of stock prices... Before 87 people didn't price otm higher.. After the crash prices went up... There is a convexity your paying for that you don't get with itm or ATM.... Meaning a rate of change of a higher order .... Anyone who has sold otm puts on leverage will tell you... The London whale was one.... These aren't my opinions I'm just telling you what's known and I don't think anyone would disagree... Although in my opinion it's better to sell the meat and buy the wings... A naked straddle I'd like better then a naked put...... Either way no strategy is better then the other it all depends on the market and your desired expression on it

 

[minmike]

So, essentially then, the models are right and the market is persistently wrong; amazing - I never thought it could be that easy to profit with options. The book mentions that even atm puts have a negative return; to my thinking, this makes sense, because in an uptrending market atm calls should be priced higher than atm puts, but put-call parity prevents this, creating a distortion that can be exploited. The opposite distortion should also happen in a long term downtrend. I also noticed that the book mentioned that buying otm calls wasn't as consistently as profitable as selling the otm puts: what could be the reason for that?...is it possible that both the models and the market pricing have built in flaws?

BTW, I appreciate constructive criticism - I'm here because most here know much more about options than I do: what concepts am I conflating?

There are a couple mistakes. Trending has almost nothing to to do with option prices.

As you mentioned put call parity, there is really no practical difference between a put and a call. One can be converted to the other with ease. You are either long or short and above or below the market.

As for the options model. Based on its assumptions it prices options correctly. One of the models assumptions is Geometric Brownian Motion. We have seen that over sized moves to the downside are more frequent and extreme than GBM predicts. Ergo those options are under priced by the model.

 

[minmike]

The map is not the territory... Sorry I have not had enough time to post my thoughts..... Derman has a model called localized vol that accounts for skew... Because of the lower nominal amount of options otm it is cheap leverage and represents potiential rarer events in the distro of stock prices... Before 87 people didn't price otm higher.. After the crash prices went up... There is a convexity your paying for that you don't get with itm or ATM.... Meaning a rate of change of a higher order .... Anyone who has sold otm puts on leverage will tell you... The London whale was one.... These aren't my opinions I'm just telling you what's known and I don't think anyone would disagree... Although in my opinion it's better to sell the meat and buy the wings... A naked straddle I'd like better then a naked put...... Either way no strategy is better then the other it all depends on the market and your desired expression on it

As do most market makers. Hence the volatility smile! Depressed in the center higher on the wings.

 

[cdcaveman]

Trending is a good way to make money off options... Options typically never have long term trends priced in.... Hence the valve of buying leaps...

 

[rmorse]

Hence the valve of buying leaps...

I'd be interested to know, on average, if most leaps are initiated from a buy or sell order. I never activity traded options going out longer than 6 months.