The discontinuous Galerkin method for discretely observed Asian options
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F20%3A10245352" target="_blank" >RIV/61989100:27510/20:10245352 - isvavai.cz</a>
Alternative codes found
RIV/46747885:24510/20:00008636
Result on the web
<a href="https://www.scopus.com/record/display.uri?eid=2-s2.0-85077910683&origin=resultslist&sort=plf-f&src=s&st1=tichy%2c+t&st2=&sid=ae28ceb80f2fa196dac98015bd0ae64a&sot=b&sdt=b&sl=21&s=AUTHOR-NAME%28tichy%2c+t%29&relpos=1&citeCnt=0&searchTerm=" target="_blank" >https://www.scopus.com/record/display.uri?eid=2-s2.0-85077910683&origin=resultslist&sort=plf-f&src=s&st1=tichy%2c+t&st2=&sid=ae28ceb80f2fa196dac98015bd0ae64a&sot=b&sdt=b&sl=21&s=AUTHOR-NAME%28tichy%2c+t%29&relpos=1&citeCnt=0&searchTerm=</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mma.6160" target="_blank" >10.1002/mma.6160</a>
Alternative languages
Result language
angličtina
Original language name
The discontinuous Galerkin method for discretely observed Asian options
Original language description
Asian options represent an important subclass of the path-dependent contracts that are identified by payoff depending on the average of the underlying asset prices over the prespecified period of option lifetime. Commonly, this average is observed at discrete dates, and also, early exercise features can be admitted. As a result, analytical pricing formulae are not always available. Therefore, some form of a numerical approximation is essential for efficient option valuation. In this paper, we study a PDE model for pricing discretely observed arithmetic Asian options with fixed as well as floating strike for both European and American exercise features. The pricing equation for such options is similar to the Black-Scholes equation with 1 underlying asset, and the corresponding average appears only in the jump conditions across the sampling dates. The objective of the paper is to present the comprehensive methodological concept that forms and improves the valuation process. We employ a robust numerical procedure based on the discontinuous Galerkin approach arising from the piecewise polynomial generally discontinuous approximations. This technique enables a simple treatment of discrete sampling by incorporation of jump conditions at each monitoring date. Moreover, an American early exercise constraint is directly handled as an additional nonlinear source term in the pricing equation. The proposed solving procedure is accompanied by an empirical study with practical results compared to reference values.
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
50200 - Economics and Business
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Methods in the Applied Sciences
ISSN
0170-4214
e-ISSN
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Volume of the periodical
43
Issue of the periodical within the volume
13
Country of publishing house
US - UNITED STATES
Number of pages
21
Pages from-to
7726-7746
UT code for WoS article
000549958400018
EID of the result in the Scopus database
2-s2.0-85077910683