Lie symmetry methods for local volatility models
In: Stochastic Processes and their Applications; Stochastic Processes and their Applications, 2020, 130, (6), 2021, S. 3802-3841
Online
academicJournal
© 2019 Elsevier B.V. We investigate PDEs of the form ut= [Formula presented] σ2(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.
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Lie symmetry methods for local volatility models
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| Autor/in / Beteiligte Person: | Craddock, M ; Grasselli, M |
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| Zeitschrift: | Stochastic Processes and their Applications; Stochastic Processes and their Applications, 2020, 130, (6), 2021, S. 3802-3841 |
| Veröffentlichung: | Elsevier BV, 2021 |
| Medientyp: | academicJournal |
| ISSN: | 0304-4149 (print) |
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