A computational scheme for uncertain volatility model in option pricing

Authors:
Kai Zhang;Song Wang
Affiliations:
Business School, Department of Finance, Shenzhen University, Shenzhen, Guangdong, 518060, China and School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Hwy, Craw ...;School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Hwy, Crawley, WA 6009, Australia
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

In this paper we develop a novel numerical scheme for a nonlinear partial differential equation arising from the uncertain volatility model in option pricing. The fitted finite volume method is developed for the space discretization with implicit scheme in time discretization, which results in a nonlinear discrete system. We prove that this method is consistent, stable and monotone, hence it ensures the convergence to the viscosity solution. We also propose an iteration scheme for the nonlinear discrete scheme and show its convergence property. Numerical experiments are implemented to verify the efficiency and usefulness of this method.