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

Result code in 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>

Alternative codes found

RIV/46747885:24510/24:00011880

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

<a href="/en/project/GA22-17028S" target="_blank" >GA22-17028S: Flexible tools for strategic investments and decision-making: analysis, valuation and implementation</a><br>

Continuities

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

Publication year

2024

Confidentiality

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

Name of the periodical

Mathematics and Computers in Simulation

ISSN

0378-4754

e-ISSN

—

Volume of the periodical

220

Issue of the periodical within the volume

JUN

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

32

Pages from-to

309-340

UT code for WoS article

001173946200001

EID of the result in the Scopus database

2-s2.0-85184055278