Path weighting sensitivities

TL;DR

This paper introduces a novel path weighting method with variance reduction and covariance inflation techniques for computing sensitivities of path-dependent financial derivatives across various stock models.

Contribution

It proposes explicit path weighting formulas, variance reduction adjustments, and covariance inflation to improve sensitivity computation accuracy and stability.

Findings

Effective variance reduction in sensitivity estimates.

Robustness in degenerate covariance cases.

Applicability to multiple stock dynamics models.

Abstract

In this paper, we study the computation of sensitivities with respect to spot of path dependent financial derivatives by means of path weighting. We propose explicit path weighting formula and variance reduction adjustment in order to address the large variance happening when the first simulation time step is small. We also propose a covariance inflation technique to addresses the degenerator case when the covariance matrix is singular. The stock dynamics we consider is given in a general functional form, which includes the classical Black-Scholes model, the implied distribution model, and the local volatility model.