Riding on the Smiles

Abstract

Using a data set of vanilla options on the major indexes we investigate the calibration properties of several multifactor 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 attention to the single asset Wishart Multidimensional Stochastic Volatility model introduced in Da Fonseca et al. (2008b) and the Wishart Affine Stochastic Correlation model proposed by Da Fonseca et al. (2007b), 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 to speed up the pricing process. What is more, these approximations allow us to compare different models by aggregating conveniently the parameters and they highlight the ability of the Wishart-based models in controlling separately the smile and the skew effects. This is extremely important in a risk management perspective of a book of derivatives that includes exotic as well as basket options.

Keywords: calibration, implied volatility, Wishart stochasic volatility, FFT, stochastic skew

JEL Classification: G12, G13, C52