Properties of Wavelet Discretization of Black-Scholes Equation

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F17%3A00005130" target="_blank" >RIV/46747885:24510/17:00005130 - isvavai.cz</a>
Result on the web
<a href="http://aip.scitation.org/doi/pdf/10.1063/1.4992340" target="_blank" >http://aip.scitation.org/doi/pdf/10.1063/1.4992340</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.4992340" target="_blank" >10.1063/1.4992340</a>

Result language
angličtina
Original language name
Properties of Wavelet Discretization of Black-Scholes Equation
Original language description
Using wavelet methods, the continuous problem is transformed into a well-conditioned discrete problem. And once a non-symmetric problem is given, squaring yields a symmetric positive definite formulation. However squaring usually makes the condition number of discrete problems substantially worse. This note is concerned with a wavelet based numerical solution of the Black-Scholes equation for pricing European options. We show here that in wavelet coordinates a symmetric part of the discretized equation dominates over an unsymmetric part in the standard economic environment with low interest rates. It provides some justification for using a fractional step method with implicit treatment of the symmetric part of the weak form of the Black-Scholes operator and with explicit treatment of its unsymmetric part. Then a well-conditioned discrete problem is obtained.
Czech name
—
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
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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