Riding on the Smiles

52 Pages Posted: 24 Aug 2010 Last revised: 9 Feb 2011

See all articles by José Da Fonseca

José Da Fonseca

Auckland University of Technology - Faculty of Business & Law

Martino Grasselli

University of Padova - Department of Mathematics; Léonard de Vinci Pôle Universitaire, Research Center

Date Written: August 23, 2010

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

Suggested Citation

Da Fonseca, José and Grasselli, Martino, Riding on the Smiles (August 23, 2010). Available at SSRN: https://ssrn.com/abstract=1663448 or http://dx.doi.org/10.2139/ssrn.1663448

José Da Fonseca (Contact Author)

Auckland University of Technology - Faculty of Business & Law ( email )

3 Wakefield Street
Private Bag 92006
Auckland Central 1020
New Zealand
64 9 921 9999 5063 (Phone)

Martino Grasselli

University of Padova - Department of Mathematics ( email )

Via Trieste 63
Padova, Padova
Italy

Léonard de Vinci Pôle Universitaire, Research Center ( email )

Paris La Défense
France

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