Turbo-Charged Local Stochastic Volatility Models

12 Pages Posted: 20 Jan 2013 Last revised: 11 Mar 2013

See all articles by Ghislain Vong

Ghislain Vong

Deutsche Bank AG - Global Equity Derivatives

Date Written: February 4, 2010


This article presents an alternative formulation of the standard Local Stochastic Volatility model (LSV) widely used for the pricing and risk-management of FX derivatives and to a lesser extent of equity derivatives. In the standard model, calibration is achieved by solving a non-linear two-factor Kolmogorov forward PDE, where a minimum number of vol points is required to achieve convergence of a finite difference implementation. In contrast, we propose to model the volatility process by a Markov chain defined over an arbitrary small number of states, so that calibration and pricing are achieved by solving a coupled system of one-factor PDEs. The practical benefits are twofolds: existing one-factor PDE solvers can be recycled to model stochastic volatility, while the reduction in number of discretisation points implies a speedup in execution time that enables real-time risk-management of large derivatives position.

Keywords: derivatives, LSV models, stochastic volatility, local volatility, calibration, pricing, PDE, Markov chain

JEL Classification: G13

Suggested Citation

Vong, Ghislain, Turbo-Charged Local Stochastic Volatility Models (February 4, 2010). Available at SSRN: https://ssrn.com/abstract=2203155 or http://dx.doi.org/10.2139/ssrn.2203155

Ghislain Vong (Contact Author)

Deutsche Bank AG - Global Equity Derivatives ( email )

United Kingdom

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