A New Stochastic Derivative Estimator for Discontinuous Payoff Functions with Application to Financial Derivatives

Motivated by infinitesimal perturbation analysis (IPA) and the likelihood ratio (LR) method, we derive a new unbiased stochastic derivative estimator for a class of discontinuous payoff functions that arise in many options pricing settings from finance. Our method includes IPA and the LR method as special cases and can be applied to functions of more general forms containing indicator functions. This new estimator can be computed from a single sample path or simulation, whereas existing estimators generally require additional simulations for the class of discontinuous payoff functions considered here. We apply this method to sensitivity analysis for European call options and American-style call options, and numerical experiments indicate that the estimator is computationally more efficient than other estimators.