European Option Pricing Under Jump Diffusion with Proportional Transaction Costs

• Activity Number: 662
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Yang Yu*+ and Haipeng Xing and Tiong Wee Lim
• Companies: SUNY at Stony Brook and SUNY at Stony Brook and National University of Singapore
• Keywords: Jump-diffusion processes ; Transaction costs ; Singular stochastic control

Abstract

This paper considers the problem of European option pricing in the presence of proportional transaction costs when the price of the underlying follows a jump diffusion process. Using an approach that is based on maximization of the expected utility of terminal wealth, we transform the option pricing into stochastic optimal control problems, and argue that the value functions of these problems are the solutions of a free boundary problem, in particular, a partial integro-differential equation, under different boundary conditions. To solve the singular stochastic control problems associated with utility maximization and compute the value function and no-transaction boundaries, we develop a coupled backward induction algorithm that is based on the connection of the free boundary problem to an optimal stopping problem. Numerical examples of option pricing under a double exponential jump diffusion model are also provided.