Option pricing under multifactor Black–Scholes model using orthogonal spline wavelets

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24220%2F24%3A00011880" target="_blank" >RIV/46747885:24220/24:00011880 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/46747885:24510/24:00011880

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0378475424000338" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0378475424000338</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.matcom.2024.01.020" target="_blank" >10.1016/j.matcom.2024.01.020</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Option pricing under multifactor Black–Scholes model using orthogonal spline wavelets

Popis výsledku v původním jazyce

The paper focuses on pricing European-style options on multiple underlying assets under the Black–Scholes model represented by a nonstationary partial differential equation. The numerical solution of such equations is challenging in dimensions exceeding three, primarily due to the so-called curse of dimensionality. The main contribution of the paper is the design and analysis of the method based on combining the sparse wavelet-Galerkin method and the Crank–Nicolson scheme with Rannacher time-stepping enhanced by Richardson extrapolation, which helps overcome the curse of dimensionality. The next contribution is constructing a new orthogonal cubic spline wavelet basis on the interval and a sparse tensor product wavelet basis on the unit cube, which is suitable for the proposed method. The resulting method brings the following important advantages. The method is higher-order convergent with respect to both temporal and spatial variables, and the number of basis functions is significantly reduced compared to a full grid. Furthermore, many matrices involved in the computation are identity matrices, which results in a considerable simplification of the algorithm. Moreover, we prove that the condition numbers of discretization matrices are uniformly bounded and do not depend on the dimension, even without preconditioning, which leads to a small number of iterations when solving the resulting linear system. Numerical experiments are presented for several types of European-style options.

Název v anglickém jazyce

Option pricing under multifactor Black–Scholes model using orthogonal spline wavelets

Popis výsledku anglicky

The paper focuses on pricing European-style options on multiple underlying assets under the Black–Scholes model represented by a nonstationary partial differential equation. The numerical solution of such equations is challenging in dimensions exceeding three, primarily due to the so-called curse of dimensionality. The main contribution of the paper is the design and analysis of the method based on combining the sparse wavelet-Galerkin method and the Crank–Nicolson scheme with Rannacher time-stepping enhanced by Richardson extrapolation, which helps overcome the curse of dimensionality. The next contribution is constructing a new orthogonal cubic spline wavelet basis on the interval and a sparse tensor product wavelet basis on the unit cube, which is suitable for the proposed method. The resulting method brings the following important advantages. The method is higher-order convergent with respect to both temporal and spatial variables, and the number of basis functions is significantly reduced compared to a full grid. Furthermore, many matrices involved in the computation are identity matrices, which results in a considerable simplification of the algorithm. Moreover, we prove that the condition numbers of discretization matrices are uniformly bounded and do not depend on the dimension, even without preconditioning, which leads to a small number of iterations when solving the resulting linear system. Numerical experiments are presented for several types of European-style options.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA22-17028S" target="_blank" >GA22-17028S: Flexibilní nástroje pro strategické investice a rozhodování: analýza, oceňování a implementace</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Mathematics and Computers in Simulation

ISSN

0378-4754

e-ISSN

—

Svazek periodika

220

Číslo periodika v rámci svazku

JUN

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

32

Strana od-do

309-340

Kód UT WoS článku

001173946200001

EID výsledku v databázi Scopus

2-s2.0-85184055278