A new stochastic gradient estimator for American option pricing

In this paper, a new stochastic gradient estimator based on the likelihood ratio (LR) method and infinitesimal perturbation analysis (IPA) will be given, which can be used for sensitivity estimation for a special case of discontinuous performance functions. The estimator is applied to an American call option pricing problem, which can greatly reduce the computational burden compared with other estimators in the literature. By using stochastic approximation and the gradient estimator, the optimal threshold policy for American option pricing can be computed. Numerical examples demonstrate the effectiveness of the proposed method.