Stochastic Local Volatility models and the Wei-Norman factorization method

2022/01/27 by Julio Guerrero, Giuseppe Orlando, Guerrero, Julio +1
Economics, Econometrics and Finance · #FOS: Economics and business #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications #q-fin.MF

paper · pdf · doi:10.48550/arxiv.2201.11241

25 latex pages, 16 figures. Accepted in Discrete and Continuous Dynamical Systems Series S

arxiv created 2022/01/27 · openalex publication_date 2022/01/27 · arxiv updated 2022/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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