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Section: New Results

A multifractional Hull and White model

Participants : Joachim Lebovits, Jacques Lévy Véhel.

In collaboration with Sylvain Corlay (Paris 6 University).

We have considered the following model, which is an extension of the fractional Hull and White model proposed in [55] : under the risk-neutral measure, the forward price of a risky asset is the solution of the S.D.E.

dFt=FtσtdWt,dln(σt)=θμ-ln(σt)dt+γhdBth+γσdWtσ,σ0>0,θ>0,

where Bth is a multifractional Brownian motion with regularity function h, and Wt,Wtσ are standard Brownian motions. This SDE is interpgreted in the Wick-Itô sense.

Using functional quantization techniques, it is possible to compute numerically implied forward start volatilities for this model. Using an adequate h function estimated from SP500 data, we have shown that this model is able to reproduce to some extent the volatility surface observed on the market [34] .