Lie symmetry methods for local volatility models

Mark Craddock and Martino Grasselli

Stochastic Processes and their Applications, 2020, vol. 130, issue 6, 3802-3841

Abstract: We investigate PDEs of the form ut=12σ2(t,x)uxx−g(x)u which are associated with the calculation of expectations for a large class of local volatility models. We find nontrivial symmetry groups that can be used to obtain Fourier transforms of fundamental solutions of the PDE. We detail explicit computations in the separable volatility case when σ(t,x)=h(t)(α+βx+γx2), g=0, corresponding to the so called Quadratic Normal Volatility Model. We give financial applications and also show how symmetries can be used to compute first hitting distributions.

Keywords: Lie symmetries; Fundamental solution; PDEs; Local volatility models; Normal Quadratic Volatility Model; Hitting times (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:6:p:3802-3841

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DOI: 10.1016/j.spa.2019.10.009

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