Importance sampling for jump processes and applications to finance

TL;DR

This paper extends adaptive importance sampling methods to jump processes by combining jump intensity adjustments with exponential tilting, optimizing parameters via sample average approximation, and demonstrating effectiveness in financial derivative valuation.

Contribution

It introduces a novel importance sampling approach for jump processes that integrates jump intensity change with Brownian tilting, optimized through sample average approximation.

Findings

Efficient valuation of financial derivatives in jump models

Effective variance reduction in importance sampling for jump processes

Demonstrated applicability across multiple jump models

Abstract

Adaptive importance sampling techniques are widely known for the Gaussian setting of Brownian driven diffusions. In this work, we want to extend them to jump processes. Our approach relies on a change of the jump intensity combined with the standard exponential tilting for the Brownian motion. The free parameters of our framework are optimized using sample average approximation techniques. We illustrate the efficiency of our method on the valuation of financial derivatives in several jump models.