deterministic vols for equity derivative portfolio

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Optiongeek
Posts: 2
Joined: Thu Jun 21, 2012 2:17 pm

deterministic vols for equity derivative portfolio

Postby Optiongeek » Mon Jul 02, 2012 3:43 pm

I would like to perform a Monte Carlo VaR on a portfolio that contains many equities and options (assume only one underlier sensitivity per option - ie. no cross-gamma). In order to avoid the problems that arise when using stochastic volatilites (i.e. difficult to calculate correlations between multiple volatilities and underlier prices), I'm thinking about an approach that assumes that volatilities are deterministic in the sense that they can be read directly from the skew curve corresponding to each option maturity. For instance, assume that my standard normal draw for underlier A calls for a sample return of -10%. If the t-maturity option on underlier A with strike 10% below ATM is trading on an implied volatility of 50%, then I would use a volatility of 50% for all t-maturity options written on A for this particular sample. The only dificultly is to calculate a skew curve for every distinct option maturity.

I like this approach since it is easy to implement (I can calculate skew curves, and underlier correlations fairly easily) yet incorporates both realistic volatility levels as well as underlier correlation. In fact, in my trading experience, I have found that equity options do tend to follow skew curves fairly closely as the underliers move so this assumption is not terribly unrealistic.

I've looked through Vol 4 fairly carefully but I haven't found any discussion of this technique. I'm wondering if there's something I'm missing in this approach. Feedback, anyone?

Thanks.

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: deterministic vols for equity derivative portfolio

Postby coalexander » Thu Jul 05, 2012 8:12 pm

I think you are correct that this is a good approach, and not one that I have discussed in Vol IV. However, if you have Vol III, I suggest you take a look at Section III.4.4 where I present a case study which incorporates not only the skew, but switching dynamics for the ATM vol, with an application to hedging options.

In a second edition I should definitely extend Vol IV to incorporate your approach, and the more advanced one of Section III.4.4. for VaR (and now, of course, ETL) applications.

Best Wishes, Carol

Optiongeek
Posts: 2
Joined: Thu Jun 21, 2012 2:17 pm

Re: deterministic vols for equity derivative portfolio

Postby Optiongeek » Fri Jul 13, 2012 4:37 am

Appreciate your feedback. In fact I did order the rest of the series and I'll go over the section you recommended,


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