Stochastic Local Volatility models and the Wei-Norman factorization method

TL;DR

This paper introduces a novel approach using Wei-Norman factorization and Lie algebra to transform time-dependent local stochastic volatility models into autonomous PDEs, enabling more efficient solutions and comparisons with Monte Carlo simulations.

Contribution

It presents a new method to reduce non-autonomous SLV models to autonomous PDEs using Lie algebraic techniques, improving computational efficiency.

Findings

Explicit solutions match Monte Carlo results

Reduced computational time for solving SLV models

First application of Wei-Norman in this context

Abstract

In this paper, we show that a time-dependent local stochastic volatility (SLV) model can be reduced to a system of autonomous PDEs that can be solved using the Heat kernel, by means of the Wei-Norman factorization method and Lie algebraic techniques. Then, we compare the results of traditional Monte Carlo simulations with the explicit solutions obtained by said techniques. This approach is new in the literature and, in addition to reducing a non-autonomous problem into an autonomous one, allows for reduced time in numerical computations.