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2019•Communication in Statistics- Theory and MethodsRequires access

Efficient multiple control variate method with applications to exotic option pricing

Suhua Zhang, A Chunxiang, Yongzeng Lai

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Abstract

The Monte Carlo simulation method is still the only feasible approach to handle high dimensional problems encountered in many areas so far. The main drawback of this method is its slow convergence. A variance reduction technique is one of the main methods to speed up Monte Carlo simulations. In this paper, we reconsider the multiple control variate method and provide sufficient conditions to ensure that the variance of an m-variate control variate estimator is smaller than that of a k-variate control variate estimator for any k where 1≤k

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What this paper is about

The Monte Carlo simulation method is still the only feasible approach to handle high dimensional problems encountered in many areas so far. The main drawback of this method is its slow convergence. A variance reduction technique is one of the main methods to speed up Monte Carlo simulations. In this paper, we reconsider the multiple control variate method and provide sufficient conditions to ensure that the variance of an m-variate control variate estimator is smaller than that of a k-variate control variate estimator for any k where 1≤k

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Available abstract

The Monte Carlo simulation method is still the only feasible approach to handle high dimensional problems encountered in many areas so far. The main drawback of this method is its slow convergence. A variance reduction technique is one of the main methods to speed up Monte Carlo simulations. In this paper, we reconsider the multiple control variate method and provide sufficient conditions to ensure that the variance of an m-variate control variate estimator is smaller than that of a k-variate control variate estimator for any k where 1≤k

Key concepts: Control variates, Random variate, Estimator, Variance reduction, Monte Carlo method, Convergence (economics), Variance (accounting), Monte Carlo methods for option pricing

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