Efficient Computation of Hedging Parameters for Discretely Exercisable Options

Abstract

We propose an algorithm to calculate confidence intervals for the values of hedging parameters of discretely exercisable options using Monte-Carlo simulation. The algorithm is based on a combination of the duality formulation of the optimal stopping problem for pricing discretely exercisable options and Monte-Carlo estimation of hedging parameters for European options. We show that the width of the confidence interval for a hedging parameter decreases, with an increase in the computer budget, asymptotically at the same rate as the width of the confidence interval for the price of the option. The method can handle arbitrary payoff functions, general diffusion processes, and a large number of random factors. We also present a fast, heuristic, alternative method and use our method to evaluate its accuracy.