Adaptive algorithm for solution of early exercise boundary problem of American put option implemented in Mathematica

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23510%2F17%3A43932836" target="_blank" >RIV/49777513:23510/17:43932836 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1051/matecconf/2017/12504028" target="_blank" >http://dx.doi.org/10.1051/matecconf/2017/12504028</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1051/matecconf/2017/12504028" target="_blank" >10.1051/matecconf/2017/12504028</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Adaptive algorithm for solution of early exercise boundary problem of American put option implemented in Mathematica

Popis výsledku v původním jazyce

The paper is focused on American option pricing problem. Assuming non-dividend paying American put option leads to two disjunctive regions, a continuation one and a stopping one, which are separated by an early exercise boundary. We present variational formulation of American option problem with special attention to early exercise action effect. Next, we discuss financially motivated additive decomposition of American option price into a European option price and another part due to the extra premium required by early exercising the option contract. As the optimal exercise boundary is a free boundary, its determination is coupled with the determination of the option price. Therefore, a closed-form expression of the free boundary is not attainable in general. We discuss in detail a derivation of an asymptotic expression of the early exercise boundary. Finally, we present some numerical results of determination of free boundary based upon this approach. All computations are performed by sw Mathematica, and suitable numerical procedure is discussed in detail, as well.

Název v anglickém jazyce

Adaptive algorithm for solution of early exercise boundary problem of American put option implemented in Mathematica

Popis výsledku anglicky

The paper is focused on American option pricing problem. Assuming non-dividend paying American put option leads to two disjunctive regions, a continuation one and a stopping one, which are separated by an early exercise boundary. We present variational formulation of American option problem with special attention to early exercise action effect. Next, we discuss financially motivated additive decomposition of American option price into a European option price and another part due to the extra premium required by early exercising the option contract. As the optimal exercise boundary is a free boundary, its determination is coupled with the determination of the option price. Therefore, a closed-form expression of the free boundary is not attainable in general. We discuss in detail a derivation of an asymptotic expression of the early exercise boundary. Finally, we present some numerical results of determination of free boundary based upon this approach. All computations are performed by sw Mathematica, and suitable numerical procedure is discussed in detail, as well.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

50206 - Finance

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název statě ve sborníku

MATEC Web of Conferences

ISBN

—

ISSN

2261-236X

e-ISSN

neuvedeno

Počet stran výsledku

6

Strana od-do

1-6

Název nakladatele

EDP Sciences

Místo vydání

London

Místo konání akce

Agia Pelagia Beach Heraklion, Greece

Datum konání akce

14. 7. 2017

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—