Lie Symmetry Methods for Local Volatility Models

Mark Craddock and Martino Grasselli
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Mark Craddock: School of Mathematical and Physical Sciences, University of Technology Sydney
Martino Grasselli: Department of Mathematics, University of Padova

No 377, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: We investigate PDEs of the form ut = 1/2 s^2 (t, x)u_xx - 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 standard integral transforms of fundamental solutions of the PDE. We detail explicit computations in the separable volatility case when s(t, x) = h(t)(a + ßx + ?x^2), g = 0, corresponding to the so called Quadratic Normal Volatility Model. We also consider choices of g for which we can obtain exact fundamental solutions that are also positive and continuous probability densities.

Keywords: Lie symmetries; fundamental Solution; PDEs; Local Volatility Models; Normal Quadratic Volatility Model (search for similar items in EconPapers)
Pages: 34 pages
Date: 2016-09-01
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Citations: View citations in EconPapers (3)

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