Stochastic local volatility models and the Wei-Norman factorization method

Abstract

<p style='text-indent:20px;'>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 shorter time in numerical computations.</p>

A generalized derivation of the Black-Scholes implied volatility through hyperbolic tangents

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