DG method for the numerical pricing of two-asset European-style Asian options with fixed strike
Result description
The evaluation of option premium is a very delicate issue arising from the assumptions made under a financial market model, and pricing of a wide range of options is generally feasible only when numerical methods are involved. This paper is based on our recent research on numerical pricing of path-dependent multi-asset options and ex- tends these results also to the case of Asian options with fixed strike. First, we recall the three-dimensional backward parabolic PDE describing the evolution of European-style Asian option contracts on two assets, whose payoff depends on the difference of the strike price and the average value of the basket of two underlying assets during the life of the option. Further, a suitable transformation of variables respecting this complex form of a payoff function reduces the problem to a two-dimensional equation belonging to the class of convection-diffusion problems and the discontinuous Galerkin (DG) method is applied to it in order to utilize its solving potentials. The whole procedure is accompanied with theoretical results and differences to the floating strike case are discussed. Finally, reference numerical experiments on real market data illustrate comprehensive empirical findings on Asian options.
Keywords
option pricingdiscontinuous Galerkin methodAsian optionbasket optionfixed strike
The result's identifiers
Result code in IS VaVaI
Result on the web
http://articles.math.cas.cz/10.21136/AM.2017.0176-17/?type=F
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
DG method for the numerical pricing of two-asset European-style Asian options with fixed strike
Original language description
The evaluation of option premium is a very delicate issue arising from the assumptions made under a financial market model, and pricing of a wide range of options is generally feasible only when numerical methods are involved. This paper is based on our recent research on numerical pricing of path-dependent multi-asset options and ex- tends these results also to the case of Asian options with fixed strike. First, we recall the three-dimensional backward parabolic PDE describing the evolution of European-style Asian option contracts on two assets, whose payoff depends on the difference of the strike price and the average value of the basket of two underlying assets during the life of the option. Further, a suitable transformation of variables respecting this complex form of a payoff function reduces the problem to a two-dimensional equation belonging to the class of convection-diffusion problems and the discontinuous Galerkin (DG) method is applied to it in order to utilize its solving potentials. The whole procedure is accompanied with theoretical results and differences to the floating strike case are discussed. Finally, reference numerical experiments on real market data illustrate comprehensive empirical findings on Asian options.
Czech name
—
Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
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
—
Volume of the periodical
62
Issue of the periodical within the volume
6
Country of publishing house
CZ - CZECH REPUBLIC
Number of pages
26
Pages from-to
607-632
UT code for WoS article
000419946700005
EID of the result in the Scopus database
2-s2.0-85039867836
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Applied mathematics
Year of implementation
2017