nonparametric approach for implied probabilities from option prices

Caesaria · February 7th, 2011, 4:28 pm

Does anyone know of a clean, slick way of finding implied probabilities from option prices without using Levy distributions/FFT approaches?

frenchX · February 7th, 2011, 4:48 pm

I have heard about a method using cubic spline. Is it closer to what you are searching ? Quite hard to implement it seems.A very easy way could be to have a smoothed volatility smile (with the SVI method of Gatheral for example), to interpolate the volatity smile with the fitted formula for a high resolution curve . Then using BS formula, you transform your vol smile into a price curve and then you numerically twice differentiate that to obtain the implied PDF. Sounds naive but in high resolution it works not so bad it seems.

fab10ab · February 7th, 2011, 5:53 pm

There are two approaches I know of (1) the method of Jackwerth and Rubinstein (2) the method of Breeden and Litzenberger that FrenchX is referring to.

Caesaria · February 7th, 2011, 9:14 pm

QuoteOriginally posted by: fab10abThere are two approaches I know of (1) the method of Jackwerth and Rubinstein (2) the method of Breeden and Litzenberger that FrenchX is referring to.Great, (1) looks neat, going to work it out.