Journal of Applied Mathematics and Stochastic Analysis 
Volume 2008 (2008), Article ID 275217, 20 pages
doi:10.1155/2008/275217
Research Article

A Time-Series Approach to Non-Self-Financing Hedging in a Discrete-Time Incomplete Market

N. Josephy, L. Kimball, and V. Steblovskaya

Department of Mathematical Sciences, Bentley College, 175 Forest Street, Waltham, MA 02452-4705, USA

Received 16 May 2008; Accepted 30 July 2008

Recommended by Nikolai Leonenko

Abstract

We present an algorithm producing a dynamic non-self-financing hedging strategy in an incomplete market corresponding to investor-relevant risk criterion. The optimization is a two-stage process that first determines market calibrated model parameters that correspond to the market price of the option being hedged. In the second stage, an optimal set of model parameters is chosen from the market calibrated set. This choice is based on stock price simulations using a time-series model for stock price jump evolution. Results are presented for options traded on the New York Stock Exchange.