# A martingale control variate method for option pricing with stochastic volatility

Jean-Pierre Fouque; Chuan-Hsiang Han

ESAIM: Probability and Statistics (2007)

- Volume: 11, page 40-54
- ISSN: 1292-8100

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topFouque, Jean-Pierre, and Han, Chuan-Hsiang. "A martingale control variate method for option pricing with stochastic volatility." ESAIM: Probability and Statistics 11 (2007): 40-54. <http://eudml.org/doc/250129>.

@article{Fouque2007,

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.
},

author = {Fouque, Jean-Pierre, Han, Chuan-Hsiang},

journal = {ESAIM: Probability and Statistics},

keywords = {Option pricing; Monte Carlo; control variates; stochastic volatility; multiscale asymptotics.; option pricing; multiscale asymptotics},

language = {eng},

month = {3},

pages = {40-54},

publisher = {EDP Sciences},

title = {A martingale control variate method for option pricing with stochastic volatility},

url = {http://eudml.org/doc/250129},

volume = {11},

year = {2007},

}

TY - JOUR

AU - Fouque, Jean-Pierre

AU - Han, Chuan-Hsiang

TI - A martingale control variate method for option pricing with stochastic volatility

JO - ESAIM: Probability and Statistics

DA - 2007/3//

PB - EDP Sciences

VL - 11

SP - 40

EP - 54

AB -
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.

LA - eng

KW - Option pricing; Monte Carlo; control variates; stochastic volatility; multiscale asymptotics.; option pricing; multiscale asymptotics

UR - http://eudml.org/doc/250129

ER -

## References

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