DG Method for Pricing European Options under Merton Jump-Diffusion Model
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F19%3A00007427" target="_blank" >RIV/46747885:24510/19:00007427 - isvavai.cz</a>
Alternative codes found
RIV/61989100:27510/19:10242953
Result on the web
<a href="https://articles.math.cas.cz/10.21136/AM.2019.0305-18" target="_blank" >https://articles.math.cas.cz/10.21136/AM.2019.0305-18</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.21136/AM.2019.0305-18" target="_blank" >10.21136/AM.2019.0305-18</a>
Alternative languages
Result language
angličtina
Original language name
DG Method for Pricing European Options under Merton Jump-Diffusion Model
Original language description
Under 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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA16-09541S" target="_blank" >GA16-09541S: Robust numerical schemes for pricing of selected options under various market conditions</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applications of Mathematics
ISSN
0862-7940
e-ISSN
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Volume of the periodical
64
Issue of the periodical within the volume
5
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
30
Pages from-to
501-530
UT code for WoS article
000491496200002
EID of the result in the Scopus database
2-s2.0-85073620538