Variance Reduction for MC/QMC Methods to Evaluate Option Prices

Jean-Pierre Fouque, Chuan-Hsiang Han and Yongzeng Lai
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Jean-Pierre Fouque: Department of Statistics and Applied Probability, University of California, Santa Barbara, USA
Chuan-Hsiang Han: Department of Quantitative Finance, National Tsing Hua University, Taiwan
Yongzeng Lai: Department of Mathematics, Wilfrid Laurier University, Canada

Chapter 2 in Recent Advances in Financial Engineering, 2009, pp 27-48 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractSeveral variance reduction techniques including importance sampling, (martingale) control variate, (randomized) Quasi Monte Carlo method, QMC in short, and some possible combinations are considered to evaluate option prices. By means of perturbation methods to derive some option price approximations, we find from numerical results in Monte Carlo simulations that the control variate method is more efficient than importance sampling to solve European option pricing problems under multifactor stochastic volatility models. As an alternative, QMC method also provides better convergence than basic Monte Carlo method. But we find an example where QMC method may produce erroneous solutions when estimating the low-biased solution of an American option. This drawback can be effectively fixed by adding a martingale control to the estimator adopting Quasi random sequences so that low-biased estimates obtained are more accurate than results from Monte Carlo method. Therefore by taking advantages of martingale control variate and randomized QMC, we find significant improvement on variance reduction for pricing derivatives and their sensitivities. This effect should be understood as that martingale control variate plays the role of a smoother under QMC method to permit better convergence.

Keywords: Financial Engineering; Mathematical Finance; Real Options; Credit Risk; Option Pricing; Transaction Cost; Market Microstructure (search for similar items in EconPapers)
Date: 2009
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