Monte Carlo Greeks for financial products via approximative transition densities

TL;DR

This paper presents efficient Monte Carlo methods for valuing high-dimensional financial derivatives and their sensitivities using approximate transition densities derived from the WKB method, demonstrated within a Libor market model.

Contribution

It introduces Monte Carlo estimators based on approximative transition densities, enhancing valuation efficiency for complex derivatives.

Findings

Effective Monte Carlo estimators for high-dimensional derivatives.

Application of WKB-based densities in Libor market models.

Improved sensitivity calculations (Greeks) for financial products.

Abstract

In this paper we introduce efficient Monte Carlo estimators for the valuation of high-dimensional derivatives and their sensitivities (''Greeks''). These estimators are based on an analytical, usually approximative representation of the underlying density. We study approximative densities obtained by the WKB method. The results are applied in the context of a Libor market model.