Numerical Pricing of American Lookback Options with Continuous Sampling of the Maximum

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F20%3A10247790" target="_blank" >RIV/61989100:27510/20:10247790 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/46747885:24510/20:00009603

Výsledek na webu

<a href="https://www.webofscience.com/wos/woscc/full-record/WOS:000668460800028" target="_blank" >https://www.webofscience.com/wos/woscc/full-record/WOS:000668460800028</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Numerical Pricing of American Lookback Options with Continuous Sampling of the Maximum

Popis výsledku v původním jazyce

Exotic options whose payoff depends on the extrema of the underlying asset over a certain period of time form a class of the lookback options. Moreover, the American constraint admits early exercise and thus these contingent claims have become increasingly popular hedging and speculation instrument over recent years. In this paper we restrict ourselves to the floating and fixed strike contracts with the continuously observed maximum only. Since no analytic formulae exist for this case, we follow a PDE approach. The corresponding American lookback option pricing problem leads to the parabolic partial differential inequality subject to a constraint, which can be handled by penalty techniques. As a result, we obtain an option pricing equation of the Black-Scholes type, where the path-dependent variable appears as a parameter only in the initial and boundary conditions. The numerical approach proposed is based on the modification of the discontinuous Galerkin method incorporating a penalty term that handles the early-exercise constraint. The capabilities of the numerical scheme are demonstrated within a simple empirical study on the reference experiments.

Název v anglickém jazyce

Numerical Pricing of American Lookback Options with Continuous Sampling of the Maximum

Popis výsledku anglicky

Exotic options whose payoff depends on the extrema of the underlying asset over a certain period of time form a class of the lookback options. Moreover, the American constraint admits early exercise and thus these contingent claims have become increasingly popular hedging and speculation instrument over recent years. In this paper we restrict ourselves to the floating and fixed strike contracts with the continuously observed maximum only. Since no analytic formulae exist for this case, we follow a PDE approach. The corresponding American lookback option pricing problem leads to the parabolic partial differential inequality subject to a constraint, which can be handled by penalty techniques. As a result, we obtain an option pricing equation of the Black-Scholes type, where the path-dependent variable appears as a parameter only in the initial and boundary conditions. The numerical approach proposed is based on the modification of the discontinuous Galerkin method incorporating a penalty term that handles the early-exercise constraint. The capabilities of the numerical scheme are demonstrated within a simple empirical study on the reference experiments.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

50200 - Economics and Business

Projekt

<a href="/cs/project/GA18-13951S" target="_blank" >GA18-13951S: Nové přístupy k modelování finančních časových řad pomocí soft-computingu</a><br>

Návaznosti

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

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název statě ve sborníku

38th International Conference on Mathematical Methods in Economics (MME 2020) : conference proceedings : September 9-11, 2020, Mendel University in Brno, Czech Republic

ISBN

978-80-7509-734-7

ISSN

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e-ISSN

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Počet stran výsledku

7

Strana od-do

186-192

Název nakladatele

Mendel University in Brno

Místo vydání

Brno

Místo konání akce

Brno

Datum konání akce

9. 9. 2020

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000668460800028