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Can anybody tell me how to quantify the skew in equity options? I would like to analyse the skew and compare it with other equities and through time ... Or can you recommand me any literature about the subject ?

Either look at the Risk Reversals or back out an implied distribution (a la Rubinstein or Maximum Entropy method, for example) and examine it's parameters.Hope this helps.

QuoteOriginally posted by: 9827579Can anybody tell me how to quantify the skew in equity options? I would like to analyse the skew and compare it with other equities and through time ... Or can you recommand me any literature about the subject ?just in case you are asking the obvious.... let me state it.define, as a function of time, your "AMTF (atm forward) skew per 10%" as the difference in implied vol between the put struck at 95%*forward(T) and the call struck at 105% * forward(T).getting those implied numbers will expose you to all kind of issues already discussed in other topics. you can then compare the skew(T) of different underlying. typically you will expect a decreasing function of time.

Thanks for the reply, but actually is was looking for a model which uses a parameter to price the skew through time. In other words: everything unchanged except the time to expiration, the parameter remains unaffected... BTW: great minds discuss ideas, normal minds discuss events, small minds discuss people ...

QuoteOriginally posted by: 9827579Thanks for the reply, but actually is was looking for a model which uses a parameter to price the skew through time. In other words: everything unchanged except the time to expiration, the parameter remains unaffected... a model for time dependance of the skew is easier said than done...you could assume that your skew plotted vs delta remains constant, that will give you an implicit rule for time decay.or you can use stochastic vol, or SVJJ, etc etc.if you need something really simple, I suggest sqrt(T) (for atmf skew)hope it helps

"Thanks for the reply, but actually is was looking for a model which uses a parameter to price the skew through time. In other words: everything unchanged except the time to expiration, the parameter remains unaffected..."To make sure I understand the question, you want a model in which skew is captured by some parameter set where (1) the skew is a function of time and therefore the parameter set must vary with time and (b) the parameter set consists of only one parameter. If I've understood the question properly, you could assume a CEV type process like this:dS = mu.S dt + sigma.(S^n(t)) dWwhere n=1 is the special case of GBM and t is time to expiry if you're fitting to option prices. As you'd expect CEV models don't give particularly brilliant fits (what do you expect with only one parameter?) but you should expect to find values of n between 0 and 1, usually somewhere around 0.6 or so.

Sorry, didn't explain the idea correct! The model can have more than one parameter to fit the skew. I want to use one of these parameters to analyse the skew... How can I expand this one parameter CEV model?

You could use a two parameter model ... any process of the form:dS = mu.S dt + sigma(S,t) dW ... where sigma(S,t) is a function of S and t with two parameters. You can play around with various functions, but maybe the best place to start is to look at some skew slopes and see what shapes you think they are and therefore what functional forms would be appropriate.Eventually you will end up doing what FDAXHunter suggested some time ago:"... back out an implied distribution (a la Rubinstein or Maximum Entropy method, for example) and examine it's parameters."

Thanks, that could help me a bit further...

To be honest, I'm still not sure that I really understand your question. Am I on the right track?

I think that we are on the right track here... Construct a (simple) CEV model to price equity options. Then fit this model with market prices and then examine the parameters...