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Stochastic Local Volatility models and the Wei-Norman factorization method

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  • Julio Guerrero
  • Giuseppe Orlando

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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  • Julio Guerrero & Giuseppe Orlando, 2022. "Stochastic Local Volatility models and the Wei-Norman factorization method," Papers 2201.11241, arXiv.org.
    • Handle: RePEc:arx:papers:2201.11241
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    References listed on IDEAS

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    Cited by:

    1. Francesco Cesarone & Raffaello Cesetti & Giuseppe Orlando & Manuel Luis Martino & Jacopo Maria Ricci, 2022. "Comparing SSD-Efficient Portfolios with a Skewed Reference Distribution," Mathematics, MDPI, vol. 11(1), pages 1-20, December.

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