A Modified Black-Scholes Methodology for Pricing and Hedging Options with Transaction Costs
by
Tiong Wee LIM
Department of Statistics and Applied Probability, National University of Singapore
Coauthors: Tze Leung LAI

We propose a basis function approach for estimating the pricing formula of an option using regression splines and show how the nonparametric delta can be used to develop a new option hedging strategy in the presence of transaction costs based on minimizing the expected total hedging costs under the constraint that a measure of risk does not exceed a prescribed level. Specifically, we use multivariate adaptive regression splines (MARS) for option pricing while an efficient solution of our optimal hedging strategy makes use of a transformation of the corresponding singular stochastic control problem to an optimal stopping problem associated with Dynkin games. Simulations using a two-year training set of daily option prices show that the nonparametric pricing formula can be used successfully to hedge options out-of-sample. We illustrate the usefulness of our approach with an application on S P 500 futures options from 1987 to 1991.

Date received: April 18, 2007