Footnote:
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments October 19, 2022 erstellt
Description:
When valuing American options with simulations and regressions, Rasmussen (2005) demonstrated that the variance-minimizing control variate is sampled at the recorded exercise time. The present article further discusses the application of optimal control variates in the context of the Least-Squares Monte Carlo (LSM) algorithm of Longstaff and Schwartz (2001). We demonstrate theoretically that, when the exercise strategy and option cashflows are estimated simultaneously, since estimated exercise times are not stopping times, optimally sampled control variates are not martingales. Hence, the optimal sampling design introduces bias. Furthermore, our numerical results show that the bias of control variates is an accurate proxy for the bias of the American option estimate, and optimal control variates may effectively eliminate the foresight bias. Consequently, the sign of the bias of an optimally controlled estimator is ambiguous, and care must be taken when constructing upper and lower bounds