The 4/2 Stochastic Volatility Model

21 Pages Posted: 14 Nov 2014 Last revised: 17 Aug 2016

See all articles by Martino Grasselli

Martino Grasselli

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

Date Written: March 16, 2016

Abstract

We introduce a new stochastic volatility model that includes, as special instances, the Heston (1993) and the 3/2 model of Heston (1997) and Platen (1997). Our model exhibits important features: first, instantaneous volatility can be uniformly bounded away from zero, and second, our model is mathematically and computationally tractable, thereby enabling an efficient pricing procedure. This called for using the Lie symmetries theory for PDEs; doing so allowed us to extend known results on Bessel processes. Finally, we provide an exact simulation scheme for the model; this is useful in view of the numerical applications.

Keywords: Stochastic volatility; Volatility modelling; Lie's symmetries; Laplace Transform; Exact Simulation

JEL Classification: C6, C63, G1, G12, G13

Suggested Citation

Grasselli, Martino, The 4/2 Stochastic Volatility Model (March 16, 2016). Available at SSRN: https://ssrn.com/abstract=2523635 or http://dx.doi.org/10.2139/ssrn.2523635

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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