A Priori Selected Spline-Wavelet Basis for Option Pricing under Black-Scholes and Merton Model

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F22%3A00010398" target="_blank" >RIV/46747885:24510/22:00010398 - isvavai.cz</a>
Result on the web
<a href="https://aip.scitation.org/doi/abs/10.1063/5.0100641" target="_blank" >https://aip.scitation.org/doi/abs/10.1063/5.0100641</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/5.0100641" target="_blank" >10.1063/5.0100641</a>

Result language
angličtina
Original language name
A Priori Selected Spline-Wavelet Basis for Option Pricing under Black-Scholes and Merton Model
Original language description
The paper deals with option pricing under the classical Black-Scholes model and a more sophisticated Merton jump-diffusion model, which allows jumps in the underlying asset price. The Merton model is represented by non-stationary integro-differential equations. Due to the integral term, standard methods are not very efficient because they lead to full discretization matrices. The Black-Scholes model can be considered a particular case of the Merton model, which does not contain the integral term. In the paper, a method is proposed, which is a combination of the Crank-Nicolson scheme and the wavelet-Galerkin method using adaptive quadratic spline wavelet basis selected a priori. This enables to significantly decrease the number of basis functions and size of matrices and vectors involved in computation compared to standard non-adaptive wavelet-Galerkin meth¬ods. Furthermore, the proposed wavelet-based method leads to sparse discretization matrices with uniformly bounded condition numbers.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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