Adaptive wavelet based scheme for option pricing

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F19%3A00007363" target="_blank" >RIV/46747885:24510/19:00007363 - isvavai.cz</a>

Výsledek na webu

<a href="https://ieeexplore.ieee.org/abstract/document/8769814" target="_blank" >https://ieeexplore.ieee.org/abstract/document/8769814</a>

DOI - Digital Object Identifier

—

Jazyk výsledku

angličtina

Název v původním jazyce

Adaptive wavelet based scheme for option pricing

Popis výsledku v původním jazyce

This contribution deals with the numerical solution of the Black-Scholes equation. The Crank-Nicolson scheme is applied for time discretization and wavelets are applied for space discretization. Hermite cubic spline wavelets with four vanishing moments are adaptively used because they enable higher order approximations, are well-conditioned, have short supports, have a high potential in adaptive methods due to the four vanishing wavelet moments and mainly because arising stiffness matrices are sparse in wavelet coordinates. Due to irregularities of the initial data in the Black-Scholes model, the use of the second-order Crank-Nicolson scheme usually requires a certain amount of damping to compensate for the known weak stability of this scheme. We numerically show here that optimal convergence rate for a proposed adaptive wavelet discretization in space can be obtained without any damping and without any restriction on the time step. A numerical example is given for the Black-Scholes equation with real data from the Frankfurt Stock Exchange. We also compare numerical results for adaptive and non-adaptive wavelet discretization in space.

Název v anglickém jazyce

Adaptive wavelet based scheme for option pricing

Popis výsledku anglicky

This contribution deals with the numerical solution of the Black-Scholes equation. The Crank-Nicolson scheme is applied for time discretization and wavelets are applied for space discretization. Hermite cubic spline wavelets with four vanishing moments are adaptively used because they enable higher order approximations, are well-conditioned, have short supports, have a high potential in adaptive methods due to the four vanishing wavelet moments and mainly because arising stiffness matrices are sparse in wavelet coordinates. Due to irregularities of the initial data in the Black-Scholes model, the use of the second-order Crank-Nicolson scheme usually requires a certain amount of damping to compensate for the known weak stability of this scheme. We numerically show here that optimal convergence rate for a proposed adaptive wavelet discretization in space can be obtained without any damping and without any restriction on the time step. A numerical example is given for the Black-Scholes equation with real data from the Frankfurt Stock Exchange. We also compare numerical results for adaptive and non-adaptive wavelet discretization in space.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA16-09541S" target="_blank" >GA16-09541S: Robustní numerická schémata pro oceňování vybraných opcí za různých tržních podmínek</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název statě ve sborníku

2018 5TH INTERNATIONAL CONFERENCE ON MATHEMATICS AND COMPUTERS IN SCIENCES AND INDUSTRY (MCSI 2018)

ISBN

978-1-5386-7500-7

ISSN

—

e-ISSN

—

Počet stran výsledku

4

Strana od-do

—

Název nakladatele

—

Místo vydání

—

Místo konání akce

Corfu, GREECE

Datum konání akce

1. 1. 2018

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000493389900022