A novel higher-order efficient computational method for pricing European and Asian options

In this article, we present a fourth-order accurate numerical method for solving generalized Black-Scholes PDE describing European and Asian options. Initially, we discretize the time derivative by the Crank-Nicolson scheme, and then the resultant semi-discrete problem by the central difference sche...

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Bibliographic Details
Published in:Numerical algorithms Vol. 99; no. 3; pp. 1127 - 1159
Main Authors: Bansal, Saurabh, Natesan, Srinivasan
Format: Journal Article
Language:English
Published: New York Springer US 01.07.2025
Springer Nature B.V
Subjects:
Accuracy
Algebra
Algorithms
Computer Science
Convergence
Crank-Nicholson method
Error analysis
Numeric Computing
Numerical Analysis
Numerical methods
Partial differential equations
Securities prices
Theory of Computation
65M15
Asian options
Option pricing
65M06
65M012
Richardson extrapolation technique
Generalized Black-Scholes equation
European options
Exotic options
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:In this article, we present a fourth-order accurate numerical method for solving generalized Black-Scholes PDE describing European and Asian options. Initially, we discretize the time derivative by the Crank-Nicolson scheme, and then the resultant semi-discrete problem by the central difference scheme on uniform meshes. In order to enhance the order of convergence of the proposed scheme, we employ the Richardson extrapolation method, by using two different meshes to solve the fully discrete problem. The stability and convergence are studied. To validate the proposed technique, several numerical experiments are carried out.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-024-01909-6