Control variates for sensitivity estimation

Abstract

We adapt a newly proposed generic approach to control variate selection to the problem of efficient estimation of sensitivity of financial security prices to model parameters, the so-called Greeks. We show that estimators based on pathwise and likelihood ratio methods can be cast in a general setting where generic control variates can be systematically defined for their estimation. In general, the means of such controls cannot be exactly calculated. One can use the Biased or Estimated Control Variates approach and estimate the means via simulation, or use the approach of DataBase Monte Carlo (DBMC) which also requires estimation of control means via simulation. We consider a parametric setting where price sensitivities need to be estimated repeatedly at multiple parameters. The fact that the same controls can be used for multiple estimation problems can justify the setup cost. The approach is illustrated via simple examples and preliminary computational results are provided.

Importance sampling for parametric estimation

“…We have considered this approach when using variance reduction techniques of stratification and control variates. (See, e.g., (Zhao and Vakili 2008), (Borogovac and Vakili 2008), and (Borogovac and Vakili 2009). ) In this paper we present some preliminary results for the case where DBMC is used in conjunction with importance sampling.…”