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Vanilla options as controls for estimating the conditional expectation of a European derivative payoff

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  • Chiu Eddie W. K.

    (Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong, P. R. China)

Abstract

One way to estimate conditional expectations based on a simulation sample is to fit a parametric model to the data set and compute the conditional expectations based on the fitted model. This method may be enhanced by the control variates method. The choice of controls is critical to the effectiveness of the method. We propose the use of vanilla options as controls for estimating conditional expectations of derivative payoffs, and we provide a theoretical analysis on the uniform approximation property of vanilla options for estimating conditional expectations. Our theory suggests that vanilla options can reduce the variance of a target payoff to an arbitrarily small level subject to some assumptions. We provide examples to illustrate our proposed approach and also discuss several considerations when applying vanilla options as controls for estimating conditional expectations.

Suggested Citation

  • Chiu Eddie W. K., 2025. "Vanilla options as controls for estimating the conditional expectation of a European derivative payoff," Monte Carlo Methods and Applications, De Gruyter, vol. 31(3), pages 225-246.
    • Handle: RePEc:bpj:mcmeap:v:31:y:2025:i:3:p:225-246:n:1004
    DOI: 10.1515/mcma-2025-2013
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