Efficient control variate methods with applications to exotic options pricing under subordinated Brownian motion models

Abstract In this paper we apply both biased and multivariate control variate methods to some exotic option pricing problems with exponential subordinated Brownian motion models for the underlying asset prices. For both arithmetic Asian and basket options, control variates conditional on geometric means of asset prices are constructed. To reduce biases, we derive expressions of expectations in terms of expectations of subordinators for relevant random variables. Numerical results show that the constructed control variates are more efficient than the classical control variates in reducing variances when pricing Asian and basket options under the normal inverse Gaussian and variance gamma models. We believe that the great variance reduction gains are due to the high correlations between the option playoffs and the constructed control variates. The efficiencies realized by the control variates are even much more significant when they are combined with quasi-Monte Carlo methods. Details are given in Section 6 .

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