Control variates for Monte Carlo valuation of American options

Nicki Søndergaard Rasmussen

Abstract

ABSTRACT

This paper considers two applications of control variates to the Monte Carlo valuation of American options. The main contribution of the paper lies in the particular choice of a control variate for American or Bermudan options. It is shown that for any martingale process used as a control variate, it is optimal to sample no later than the time of exercise of the American option, as opposed to the time of expiry. The first application is to the valuation. Numerical examples show that standard errors can be dramatically reduced, allowing for faster valuation using fewer paths. Second, the control variate technique is used for improving the least-squares Monte Carlo (LSM) approach for determining exercise strategies. The suggestions made allow for more efficient estimation of the continuation value, used in determining the strategy. An additional suggestion is made in order to improve the stability of the LSM approach. It is suggested to generate paths for the LSM estimation from an initial distribution rather than the single initial point. Numerical examples show that the two LSMmodifications improve the accuracy and stability of the exercise strategies, which may now be estimated using a lower number of paths.