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Lie symmetry methods for local volatility models

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  • Craddock, Mark
  • Grasselli, Martino

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.

Suggested Citation

  • Craddock, Mark & Grasselli, Martino, 2020. "Lie symmetry methods for local volatility models," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3802-3841.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:6:p:3802-3841
    DOI: 10.1016/j.spa.2019.10.009
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    References listed on IDEAS

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    Cited by:

    1. Mark Craddock & Martino Grasselli & Andrea Mazzoran, 2023. "Novel exact solutions for PDEs with mixed boundary conditions," Papers 2311.12177, arXiv.org.

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