Model Risk of two Assets Derivatives

Abstract

This paper studies a derivative on two assets when there is a model risk. We consider a two-dimensional Black Scholes model whose parameter processes are two drift processes, two volatility processes and one correlation process. It is assumed that true models of all parameter processes are unknown. Usually it is impossible to find a unique price of the derivative in this framework. Our problem is to find the price bounds of the derivative. We show a partial differential equation which the maximum price or the minimum price satisfies. To calculate the price bounds numerically, we propose a two-dimensional trinomial model and we study the model risk of options and their portfolio by a numerical analysis.