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Efficient Computation of Hedging Parameters for Discretely Exercisable Options

Fuqua School of Business, Duke University, Durham, North Carolina 27708
McCombs School of Business, University of Texas at Austin, Austin, Texas 78712
Lehman Brothers, New York, New York 10019
ron.kaniel{at}duke.edu
stathis.tompaidis{at}mccombs.utexas.edu
alex.zemlianov{at}lehman.com

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.

Subject classifications: finance; derivative hedging.
History: Received December 2003; revision received May 2007; accepted May 2007.