The discontinuous Galerkin method for discretely observed Asian options

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/46747885:24510/20:00008636

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

The discontinuous Galerkin method for discretely observed Asian options

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

The discontinuous Galerkin method for discretely observed Asian options

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50200 - Economics and Business

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematical Methods in the Applied Sciences

ISSN

0170-4214

e-ISSN

—

Svazek periodika

43

Číslo periodika v rámci svazku

13

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

7726-7746

Kód UT WoS článku

000549958400018

EID výsledku v databázi Scopus

2-s2.0-85077910683