The valuation of discretely sampled European lookback options: a DG approach

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F17%3A00006305" target="_blank" >RIV/46747885:24510/17:00006305 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27510/17:10240853

Výsledek na webu

<a href="http://fim2.uhk.cz/mme/index.php?page=conferenceproceedings" target="_blank" >http://fim2.uhk.cz/mme/index.php?page=conferenceproceedings</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

The valuation of discretely sampled European lookback options: a DG approach

Popis výsledku v původním jazyce

Path-dependent options represent an important part of the derivatives traded in financial markets. One of the commonly used and popular subclasses of path-dependent options is formed by so-called lookback options with payoff depending on the minimum or maximum price of the underlying asset attained during the lifetime of the option and enabling the investors to sell at the highest or buy at the lowest price, i.e., the most favourable one. Commonly, the maximum or minimum are monitored at discrete dates so that there is no analytical pricing formulae and one has to rely on numerical techniques. In this paper we present a PDE approach to European lookback options leading to the usual Black-Scholes equation, where the path-dependent variable appears as a parameter only and discrete sampling is balanced by introducing the jump conditions across the sampling dates. Since the pricing equation is the same as for the plain vanilla option, the discontinuous Galerkin (DG) method is applied to the problem in the same manner, except for the treatment of jump conditions at each monitoring date. Finally, reference numerical experiments illustrate empirical findings.

Název v anglickém jazyce

The valuation of discretely sampled European lookback options: a DG approach

Popis výsledku anglicky

Path-dependent options represent an important part of the derivatives traded in financial markets. One of the commonly used and popular subclasses of path-dependent options is formed by so-called lookback options with payoff depending on the minimum or maximum price of the underlying asset attained during the lifetime of the option and enabling the investors to sell at the highest or buy at the lowest price, i.e., the most favourable one. Commonly, the maximum or minimum are monitored at discrete dates so that there is no analytical pricing formulae and one has to rely on numerical techniques. In this paper we present a PDE approach to European lookback options leading to the usual Black-Scholes equation, where the path-dependent variable appears as a parameter only and discrete sampling is balanced by introducing the jump conditions across the sampling dates. Since the pricing equation is the same as for the plain vanilla option, the discontinuous Galerkin (DG) method is applied to the problem in the same manner, except for the treatment of jump conditions at each monitoring date. Finally, reference numerical experiments illustrate empirical findings.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA16-09541S" target="_blank" >GA16-09541S: Robustní numerická schémata pro oceňování vybraných opcí za různých tržních podmínek</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název statě ve sborníku

35TH INTERNATIONAL CONFERENCE MATHEMATICAL METHODS IN ECONOMICS (MME 2017)

ISBN

978-80-7435-678-0

ISSN

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e-ISSN

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Počet stran výsledku

6

Strana od-do

242-247

Název nakladatele

Univerzita Hradec Králové

Místo vydání

Hradec Králové

Místo konání akce

Hradec Králové

Datum konání akce

1. 1. 2017

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

000427151400042