Unbiased Simulation Estimators for Multivariate Jump-Diffusions

TL;DR

This paper introduces a new class of unbiased Monte Carlo estimators tailored for multivariate jump-diffusion processes with state-dependent features, enhancing simulation accuracy and efficiency.

Contribution

The authors extend existing unbiased estimators to include state-dependent jumps using a change of measure approach, providing theoretical guarantees and practical validation.

Findings

Estimators are unbiased and have finite variance.

Numerical experiments demonstrate estimator efficiency.

Method effectively handles state-dependent jump features.

Abstract

We develop and analyze a class of unbiased Monte Carlo estimators for multivariate jump-diffusion processes with state-dependent drift, volatility, jump intensity and jump size. A change of measure argument is used to extend existing unbiased estimators for the inter-arrival diffusion to include state-dependent jumps. Under standard regularity conditions on the coefficient and target functions, we prove the unbiasedness and finite variance properties of the resulting jump-diffusion estimators. Numerical experiments illustrate the efficiency of our estimators.