Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2694

 Title: Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing Authors: Milev, MariyanTagliani, Aldo Keywords: Black-Scholes EquationFinite Difference SchemesJacobi MatrixM-MatrixNonsmooth Initial ConditionsPositivity-Preserving 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. URI: http://hdl.handle.net/10525/2694 ISSN: 1310-6600 Appears in Collections: Volume 36, Number 1

Files in This Item:

File Description SizeFormat