Riding on the smiles |
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Authors: | José da Fonseca Martino Grasselli |
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Affiliation: | 1. Department of Finance , Auckland University of Technology , Private Bag 92006, 1142 Auckland , New Zealand jose.dafonseca@aut.ac.nz;3. Dipartimento di Matematica , Università degli Studi di Padova , Via Trieste 63 , Padova , Italy;4. Département Mathématiques et Ingénierie Financière , Ecole Supérieure d'Ingénieurs Léonard de Vinci , 92916 Paris La Défense , France |
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Abstract: | Using a data set of vanilla options on the major indexes we investigate the calibration properties of several multi-factor stochastic volatility models by adopting the fast Fourier transform as the pricing methodology. We study the impact of the penalizing function on the calibration performance and how it affects the calibrated parameters. We consider single-asset as well as multiple-asset models, with particular emphasis on the single-asset Wishart Multidimensional Stochastic Volatility model and the Wishart Affine Stochastic Correlation model, which provides a natural framework for pricing basket options while keeping the stylized smile–skew effects on single-name vanillas. For all models we give some option price approximations that are very useful for speeding up the pricing process. In addition, these approximations allow us to compare different models by conveniently aggregating the parameters, and they highlight the ability of the Wishart-based models to control separately the smile and the skew effects. This is extremely important from a risk-management perspective of a book of derivatives that includes exotic as well as basket options. |
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Keywords: | Calibration Implied volatility Wishart stochastic volatility FFT Stochastic skew |
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