Numerical Solution of the Black-Scholes Equation Using Cubic Spline Wavelets

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F16%3A00005100" target="_blank" >RIV/46747885:24510/16:00005100 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1063/1.4968447" target="_blank" >https://doi.org/10.1063/1.4968447</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.4968447" target="_blank" >10.1063/1.4968447</a>

Result language
angličtina
Original language name
Numerical Solution of the Black-Scholes Equation Using Cubic Spline Wavelets
Original language description
The Black-Scholes equation is used in financial mathematics for computation of market values of options at a given time. We use the 0-scheme for time discretization and an adaptive scheme based on wavelets for discretization on the given time level. Advantages of the proposed method are small number of degrees of freedom, high-order accuracy with respect to variables representing prices and relatively small number of iterations needed to resolve the problem with a desired accuracy. We use several cubic spline wavelet and multi-wavelet bases and discuss their advantages and disadvantages. We also compare an isotropic and anisotropic approach. Numerical experiments are presented for the two-dimensional Black-Scholes equation.
Czech name
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Czech description
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Project
<a href="/en/project/GA16-09541S" target="_blank" >GA16-09541S: Robust numerical schemes for pricing of selected options under various market conditions</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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