Lie symmetry methods for local volatility models

Craddock, M; Grasselli, M

Lie symmetry methods for local volatility models

Craddock, M Grasselli, M

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Publisher:: Elsevier BV
Publication Type:: Journal Article
Citation:: Stochastic Processes and their Applications, 2020, 130, (6), pp. 3802-3841
Issue Date:: 2020

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Field	Value	Language
dc.contributor.author	Craddock, M
dc.contributor.author	Grasselli, M
dc.date.accessioned	2021-02-08T03:33:14Z
dc.date.available	2021-02-08T03:33:14Z
dc.date.issued	2020
dc.identifier.citation	Stochastic Processes and their Applications, 2020, 130, (6), pp. 3802-3841
dc.identifier.issn	0304-4149
dc.identifier.uri	http://hdl.handle.net/10453/145933
dc.description.abstract	© 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.
dc.language	en
dc.publisher	Elsevier BV
dc.relation.ispartof	Stochastic Processes and their Applications
dc.relation.isbasedon	10.1016/j.spa.2019.10.009
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	0102 Applied Mathematics, 0104 Statistics, 1502 Banking, Finance and Investment
dc.subject.classification	Statistics & Probability
dc.title	Lie symmetry methods for local volatility models
dc.type	Journal Article
utslib.citation.volume	130
utslib.for	0102 Applied Mathematics
utslib.for	0104 Statistics
utslib.for	1502 Banking, Finance and Investment
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
pubs.organisational-group	/University of Technology Sydney
utslib.copyright.status	closed_access	*
pubs.consider-herdc	true
dc.date.updated	2021-02-08T03:32:46Z
pubs.issue	6
pubs.publication-status	Published
pubs.volume	130
utslib.citation.issue	6

Abstract:

© 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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http://hdl.handle.net/10453/145933