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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název statě ve sborníku

AIP Conference Proceedings

ISBN

978-073544396-9

ISSN

0094243X

e-ISSN

—

Počet stran výsledku

8

Strana od-do

—

Název nakladatele

American Institute of Physics Inc.

Místo vydání

New York

Místo konání akce

Sozopol

Datum konání akce

1. 1. 2021

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

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