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A martingale control variate method for option pricing with stochastic volatility

Published online by Cambridge University Press:  01 March 2007

Jean-Pierre Fouque  and
Chuan-Hsiang Han
Jean-Pierre Fouque
Affiliation:
Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA; fouque@pstat.ucsb.edu
Chuan-Hsiang Han
Affiliation:
Department of Quantitative Finance, National Tsing Hua University, Hsinchu, 30013, ROC, Taiwan; chhan@mx.nthu.edu.tw
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Abstract

A generic control variate method is proposed to price options under stochastic volatility models by Monte Carlo simulations. This method provides a constructive way to select control variates which are martingales in order to reduce the variance of unbiased option price estimators. We apply a singular and regular perturbation analysis to characterize the variance reduced by martingale control variates. This variance analysis is done in the regime where time scales of associated driving volatility processes are well separated. Numerical results for European, Barrier, and American options are presented to illustrate the effectiveness and robustness of this martingale control variate method in regimes where these time scales are not so well separated.

Keywords

Option pricingMonte Carlocontrol variatesstochastic volatilitymultiscale asymptotics.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 11: Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthdaySpecial Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday , June 2007 , pp. 40 - 54
Copyright
© EDP Sciences, SMAI, 2007

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References

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