A Multifactor Volatility Heston Model

Abstract

We consider a model for a single risky asset whose volatility follows a multifactor (matrix)Wishart affine process, recently introduced in finance by Gourieroux and Sufana (2004). As in standard Duffie and Kan (1996) affine models the pricing problem can be solved through the Fast Fourier Transform of Carr and Madan (1999). A numerical illustration shows that this specification provides a separate fit of the long term and short term implied volatility surface and, differently from previous diffusive stochastic volatility models, it is possible to identify a specific factor accounting for a stochastic leverage effect, a well known stylized fact of FX option markets analyzed in Carr and Wu (2004).