Two factor option pricing with uncertain volatility

Abstract

The practical difficulty of estimating volatility values for underlying assets has lead to the uncertain volatility model for option pricing in finance. The pricing equations in this model are often cast in the form of nonlinear partial differential equations. It is well known that for one factor problems, these equations can be numerically solved by selecting volatility values according to the sign of gamma. However, with two (or more) factors, a small, constrained optimization problem must be solved for each node at every timestep. In this paper, we discuss some technical details of solving these optimization problems in the context of the overall numerical solution process. Examples are provided for max of two asset problems, as well as two asset butterfly options. © Springer-Verlag 2003.