BulDML at Institute of Mathematics and Informatics >
IMI Periodicals >
Serdica Mathematical Journal >
2010 >
Volume 36, Number 1 >

Please use this identifier to cite or link to this item:

Title: Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing
Authors: Milev, Mariyan
Tagliani, Aldo
Keywords: Black-Scholes Equation
Finite Difference Schemes
Jacobi Matrix
Nonsmooth Initial Conditions
Issue Date: 2010
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 35, No 1, (2010), 75p-88p
Abstract: The paper is devoted to pricing options characterized by discontinuities in the initial conditions of the respective Black-Scholes partial differential equation. Finite difference schemes are examined to highlight how discontinuities can generate numerical drawbacks such as spurious oscillations. We analyze the drawbacks of the Crank-Nicolson scheme that is most frequently used numerical method in Finance because of its second order accuracy. We propose an alternative scheme that is free of spurious oscillations and satisfy the positivity requirement, as it is demanded for the financial solution of the Black-Scholes equation.
Description: 2000 Mathematics Subject Classification: 65M06, 65M12.
ISSN: 1310-6600
Appears in Collections:Volume 36, Number 1

Files in This Item:

File Description SizeFormat
2010-075-088.pdf470.53 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.


Valid XHTML 1.0!   Creative Commons License