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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Orthogonal spline-wavelet method for two-asset Black-Scholes and Merton model
Original language description
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.
Czech name
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Czech description
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Project
<a href="/en/project/GA22-17028S" target="_blank" >GA22-17028S: Flexible tools for strategic investments and decision-making: analysis, valuation and implementation</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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