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A multifactor volatility Heston model

2008; Taylor & Francis; Volume: 8; Issue: 6 Linguagem: Inglês

10.1080/14697680701668418

1469-7696

José Da Fonseca, Martino Grasselli, Claudio Tebaldi,

Insurance, Mortality, Demography, Risk Management

Abstract We model the volatility of a single risky asset using a multifactor (matrix) Wishart affine process, recently introduced in finance by Gourieroux and Sufana. As in standard Duffie and Kan affine models the pricing problem can be solved through the Fast Fourier Transform of Carr and Madan. 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 the stochastic leverage effect, a well-known stylized fact of the FX option markets analysed by Carr and Wu. Keywords: Stochastic volatilityFinancial derivativesVolatility modellingOptions pricingOptions volatility Acknowledgements We thank Fabio Mercurio and the participants at the 2006 Ascona Meeting and the Séminaire Bachelier of Paris for helpful comments. We also thank two anonymous referees for careful reading of the paper. An earlier draft of this paper appeared under the title 'Wishart multi-dimensional stochastic volatility'.