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devito
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Posts: 22
Joined: November 1st, 2007, 11:26 am

How would I make volatility smile numbers more meaningful across maturities in a simple local volatility model?

September 20th, 2011, 4:42 am

I use slope of moneyness and curvature of moneyness to construct the smile. I use simple moneyness as in log (K/F) for all maturities, and use moneyness slope and moneyness square (curvature) to fit the vol smile.When I price in my risk reversal across maturities, it gives me different slope numbers, How would I make these slope numbers more meaningful with respect to each other or relative to each other across maturities.For instance a 25 delta risk reversal in month 1 (with 30 trading days for instance) gives me a slope of -.35; and the same 25 delta risk reversal in month 2 (with 60 trading days) gives me a slope of -.3 (Theoretically should these numbers be higher or I mean trending more towards negative side as one goes further out in time). How would I model vol slope such that, that slope number would be interpreted what risk reversal is cheap or expensive with respect to each other across maturities. Accordingly one can at least take a theoretical bet or be on the right side of the trade.Thanks in advance
 
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Gmike2000
Posts: 801
Joined: September 25th, 2003, 9:49 pm

How would I make volatility smile numbers more meaningful across maturities in a simple local volatility model?

September 20th, 2011, 9:40 pm

This is a very good question. What you want to do is investigate how these simplistic parametrizations of the vol smile (the ones you mention above) affect the underlying risk neutral distribution. Does a constant 'slope' over different maturities lead to the same implied distribution? Do this as an exercise. It is fun, instructive, and won't take more than a full day to figure out. You can IM me if you run into trouble or want to compare results. I may not be online very often though.
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