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Uncertain Volatility Model: A Monte-Carlo Approach

25 Pages Posted: 21 Jan 2010  

Julien Guyon

Bloomberg L.P.; Columbia University - Department of Mathematics; New York University - Courant Institute of Mathematical Sciences

Pierre Henry-Labordere

Société Générale - Paris, France

Date Written: January 21, 2010


The uncertain volatility model has long ago attracted the attention of practitioners as it provides worst-case pricing scenario for the sell-side. The valuation of a financial derivative based on this model requires solving a fully non-linear PDE. One can rely on finite difference schemes only when the number of variables (that is, underlyings and path-dependent variables) is small - in practice no more than three. In all other cases, numerical valuation seems out of reach. In this paper, we outline two accurate, easy-to-implement Monte-Carlo-like methods which hardly depend on dimensionality. The first method requires a parameterization of the optimal covariance matrix and consists in a series of backward low-dimensional optimizations. The second method relies heavily on a recently established connection between second-order backward stochastic differential equations and non-linear second-order parabolic PDEs. Both methods are illustrated by numerical experiments.

Keywords: Uncertain volatility model, optimization of non-smooth function, backward stochastic differential equation, Monte-Carlo simulation, regression, Malliavin

Suggested Citation

Guyon, Julien and Henry-Labordere, Pierre, Uncertain Volatility Model: A Monte-Carlo Approach (January 21, 2010). Available at SSRN: or

Julien Guyon

Bloomberg L.P. ( email )

731 Lexington Avenue
New York, NY 10022
United States

Columbia University - Department of Mathematics ( email )

3022 Broadway
New York, NY 10027
United States

New York University - Courant Institute of Mathematical Sciences ( email )

New York University
New York, NY 10012
United States

Pierre Henry-Labordere (Contact Author)

Société Générale - Paris, France ( email )

Paris-La Défense, Paris 92987

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