Orthogonal spline-wavelet method for two-asset Black-Scholes and Merton model

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F23%3A00011879" target="_blank" >RIV/46747885:24510/23:00011879 - isvavai.cz</a>

Výsledek na webu

<a href="https://pubs.aip.org/aip/acp/article-abstract/2939/1/100002/2929112/Orthogonal-spline-wavelet-method-for-two-asset?redirectedFrom=fulltext" target="_blank" >https://pubs.aip.org/aip/acp/article-abstract/2939/1/100002/2929112/Orthogonal-spline-wavelet-method-for-two-asset?redirectedFrom=fulltext</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/5.0178624" target="_blank" >10.1063/5.0178624</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Orthogonal spline-wavelet method for two-asset Black-Scholes and Merton model

Popis výsledku v původním jazyce

The paper deals with the valuation of two-asset options using the classical Black-Scholes model and a more so-phisticated Merton jump-diffusion model, allowing jumps in the underlying asset price. The Merton model is represented by non-stationary integro-differential equations with two state variables, and the Black-Scholes model can be considered its particular case without the integral term. The drawback of most classical methods is that system matrices are full and poorly conditioned due to the integral term. In this paper, we transform the equation into logarithmic prices and localize it. Then, we use a recently constructed cubic orthogonal spline-wavelet basis and anisotropic tensor-product approach to construct a two-dimensional wavelet basis. We show that the Galerkin method with this basis combined with the Crank-Nicholson scheme for temporal discretization leads to sparse matrices, and due to the orthogonality of the basis, the matrices are well-conditioned even without preconditioning the system. Moreover, higher-order spline wavelets result in higher-order convergence of the method. Numerical experiments are presented for European-type put and call options on the maximum of two assets.

Název v anglickém jazyce

Orthogonal spline-wavelet method for two-asset Black-Scholes and Merton model

Popis výsledku anglicky

The paper deals with the valuation of two-asset options using the classical Black-Scholes model and a more so-phisticated Merton jump-diffusion model, allowing jumps in the underlying asset price. The Merton model is represented by non-stationary integro-differential equations with two state variables, and the Black-Scholes model can be considered its particular case without the integral term. The drawback of most classical methods is that system matrices are full and poorly conditioned due to the integral term. In this paper, we transform the equation into logarithmic prices and localize it. Then, we use a recently constructed cubic orthogonal spline-wavelet basis and anisotropic tensor-product approach to construct a two-dimensional wavelet basis. We show that the Galerkin method with this basis combined with the Crank-Nicholson scheme for temporal discretization leads to sparse matrices, and due to the orthogonality of the basis, the matrices are well-conditioned even without preconditioning the system. Moreover, higher-order spline wavelets result in higher-order convergence of the method. Numerical experiments are presented for European-type put and call options on the maximum of two assets.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA22-17028S" target="_blank" >GA22-17028S: Flexibilní nástroje pro strategické investice a rozhodování: analýza, oceňování a implementace</a><br>

Návaznosti

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

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název statě ve sborníku

AIP Conference Proceedings

ISBN

978-073544763-9

ISSN

0094-243X

e-ISSN

—

Počet stran výsledku

7

Strana od-do

—

Název nakladatele

American Institute of Physics

Místo vydání

—

Místo konání akce

Sozopol

Datum konání akce

1. 1. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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