Option Pricing by the Legendre Wavelets Method

Reza Doostaki () and Mohammad Mehdi Hosseini ()
Additional contact information
Reza Doostaki: Shahid Bahonar University of Kerman
Mohammad Mehdi Hosseini: Shahid Bahonar University of Kerman

Computational Economics, 2022, vol. 59, issue 2, No 12, 749-773

Abstract: Abstract This paper presents the numerical solution of the Black–Scholes partial differential equation (PDE) for the evaluation of European call and put options. The proposed method is based on the finite difference and Legendre wavelets aproximation scheme. We derive a matrix structure for the Legendre wavelets integral operator which has been widely used so far. Moreover, in order to use the payoff function, another operational matrix is derived. By the proposed combined method, the solving Black–Scholes PDE problem reduces to those of solving a Sylvester equation. The proposed algorithms show that in compared to literature methods, the proposed method is easy to be implemented and have high execution speed. Furthermore, we prove that the obtained Sylvester equation has a unique solution. In addition, the effect of the finite difference space step size to the computational accuracy is studied. For having suitable solution, the numerical solutions show that there is no need to select very small step size. Also only a small number of basis functions in the Legendre wavelets series is needed. The numerical results demonstrate efficiency and capability of the proposed method.

Keywords: Black–Scholes PDE; European options; Legendre wavelets polynomials; Integral operator matrix; Sylvester equation (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10614-021-10100-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:kap:compec:v:59:y:2022:i:2:d:10.1007_s10614-021-10100-1

Ordering information: This journal article can be ordered from
http://www.springer. ... ry/journal/10614/PS2

DOI: 10.1007/s10614-021-10100-1

Access Statistics for this article

Computational Economics is currently edited by Hans Amman

More articles in Computational Economics from Springer, Society for Computational Economics Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().