Wishart Stochastic Volatility: Asymptotic Smile and Numerical Framework
In this paper, a study of a stochastic volatility model for asset pricing is described. Originally presented by J. Da Fonseca, M. Grasselli and C. Tebaldi, the Wishart volatility model identifies the volatility of the asset as the trace of a Wishart process. Contrary to a classic multifactor Heston model, this model allows to add degrees of freedom with regard to the stochastic correlation. Thanks to its flexibility, this model enables a better fit of market data than the Heston model. Besides, the Wishart volatility model keeps a clear interpretation of its parameters and conserves an efficient tractability. Firstly, we recall the Wishart volatility model and we present a Monte Carlo simulation method in sight of the evaluation of complex options. Regarding stochastic volatility models, implied volatility surfaces of vanilla options have to be obtained for a short time. The aim of this article is to provide an accurate approximation method to deal with asymptotic smiles and to apply this procedure to the Wishart volatility model in order to well understand it and to make its calibration easier. Inspired by the singular perturbations method introduced by J.P Fouque, G. Papanicolaou, R. Sircar and K. Solna, we suggest an efficient procedure of perturbation for affine models that provides an approximation of the asymptotic smile (for short maturities and for a two-scale volatility). Thanks to the affine properties of the Wishart volatility model, the perturbation of the Riccati equations furnishes the expected approximations. The convergence and the robustness of the procedure are analyzed in practice but not in theory. The resulting approximations allow a study of the parameters influence and can also be used as a calibration tool for a range of parameters.
|Date of creation:||Jun 2008|
|Date of revision:|
|Note:||View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00458014v2|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-00458014. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.