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Uncertain Volatility Model: A Monte-Carlo Approach

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

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.

Number of Pages in PDF File: 25

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

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Date posted: January 21, 2010  

Suggested Citation

Guyon, Julien and Henry-Labordere, Pierre, Uncertain Volatility Model: A Monte-Carlo Approach (January 21, 2010). Available at SSRN: https://ssrn.com/abstract=1540043 or http://dx.doi.org/10.2139/ssrn.1540043

Contact Information

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
Feedback to SSRN

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References:  34