Unbiased Sensitivity Estimation of One-Dimensional Diffusion Processes

Abstract

In this paper, we propose unbiased sensitivity estimators of the expected functionals of one-dimensional diffusion processes. Under general diffusion models, it is common to rely on discretization methods such as the Euler scheme for the generation of sample paths because of the lack of knowledge in the probability distributions associated with the diffusions. The Euler discretization method is easy to apply, but it is difficult to avoid discretization biases. As an alternative approach, we propose unbiased Monte Carlo estimators of sensitivities by taking advantage of the Beskos-Roberts method, which is an exact simulation algorithm for one-dimensional stochastic differential equations (SDEs), and applying the Poisson kernel method. The proposed estimators can be computed by discretely observed Brownian paths, and thus it is simple to implement our algorithms. We illustrate the ideas and algorithms with examples.