Pricing via Quantization in Stochastic Volatility Models

27 Pages Posted: 7 Oct 2015

See all articles by Giorgia Callegaro

Giorgia Callegaro

University of Padua

Lucio Fiorin

University of Padua

Martino Grasselli

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

Date Written: September 29, 2015

Abstract

In this paper we apply a new methodology based on quantization to price options in stochastic volatility models. This method can be applied to any model for which an Euler scheme is available for the underlying process and it allows for pricing vanillas, as well as exotics, thanks to the knowledge of the transition probabilities for the discretized stock process. We apply the methodology to some celebrated stochastic volatility models, including the Stein and Stein (1991) model and the SABR model introduced in Hagan and Woodward (2002). A numerical exercise shows that the pricing of vanillas turns out to be accurate; in addition, when applied to some exotics like equity-volatility options, the quantization-based method overperforms by far the Monte Carlo simulation.

Suggested Citation

Callegaro, Giorgia and Fiorin, Lucio and Grasselli, Martino, Pricing via Quantization in Stochastic Volatility Models (September 29, 2015). Available at SSRN: https://ssrn.com/abstract=2669734 or http://dx.doi.org/10.2139/ssrn.2669734

Giorgia Callegaro

University of Padua ( email )

Via 8 Febbraio, 2
Padova, Vicenza 35122
Italy

Lucio Fiorin

University of Padua ( email )

Martino Grasselli (Contact Author)

University of Padova - Department of Mathematics ( email )

Via Trieste 63
Padova, Padova
Italy

Léonard de Vinci Pôle Universitaire, Research Center, Finance Group ( email )

Paris La Défense
France

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