DG Method for Pricing European Options under Merton Jump-Diffusion Model

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dc.contributor.authorHozman, Jiří
dc.contributor.authorTichý, Tomáš
dc.contributor.authorVlasák, Miloslav
dc.date.accessioned2019-10-29T09:01:02Z
dc.date.available2019-10-29T09:01:02Z
dc.date.issued2019
dc.description.abstractUnder real market conditions, there exist many cases when it is inevitable to adopt numerical approximations of option prices due to non-existence of analytical formulae. Obviously, any numerical technique should be tested for the cases when the analytical solution is well known. The paper is devoted to the discontinuous Galerkin method applied to European option pricing under the Merton jump-diffusion model, when the evolution of the asset prices is driven by a Lévy process with finite activity. The valuation of options under such a model with lognormally distributed jumps requires solving a parabolic partial integro-differential equation which involves both the integrals and the derivatives of the unknown pricing function. The integral term related to jumps leads to new theoretical and numerical issues regarding the solving of the pricing equation in comparison with the standard approach for the Black-Scholes equation. Here we adopt the idea of the relatively modern technique that the integral terms in Merton-type models can be viewed as solutions of proper differential equations, which can be accurately solved in a simple way. For practical purposes of numerical pricing of options in such models we propose a two-stage implicit-explicit scheme arising from the discontinuous piecewise polynomial approximation, i.e., the discontinuous Galerkin method. This solution procedure is accompanied with theoretical results and discussed within the numerical results on reference benchmarks.cs
dc.format.extent30 strancs
dc.identifier.doi10.21136/AM.2019.0305-18
dc.identifier.orcid0000-0003-3871-5610 Hozman, Jiří
dc.identifier.urihttps://dspace.tul.cz/handle/15240/154068
dc.identifier.urihttps://link.springer.com/content/pdf/10.21136%2FAM.2019.0305-18.pdf
dc.language.isocscs
dc.publisherSpringer Heidelberg
dc.relation.ispartofApplications of Mathematics
dc.subject35Q91cs
dc.subject65M15cs
dc.subject65M60cs
dc.subject91G60cs
dc.subject91G80cs
dc.subjecta priori error estimatescs
dc.subjectdiscontinuous Galerkin methodcs
dc.subjectintegro-differential equationcs
dc.subjectMerton jump-diffusion modelcs
dc.subjectoption pricingcs
dc.subjectsemi-implicit discretizationcs
dc.titleDG Method for Pricing European Options under Merton Jump-Diffusion Modelcs
local.citation.epage530
local.citation.spage501
local.identifier.publikace290e9ac5-5d8e-4636-ba14-12bbffcf1a0c
local.relation.issue5
local.relation.volume64
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