# Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing

Milev, Mariyan; Tagliani, Aldo

Serdica Mathematical Journal (2010)

- Volume: 35, Issue: 1, page 75-88
- ISSN: 1310-6600

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topMilev, Mariyan, and Tagliani, Aldo. "Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing." Serdica Mathematical Journal 35.1 (2010): 75-88. <http://eudml.org/doc/281413>.

@article{Milev2010,

abstract = {2000 Mathematics Subject Classification: 65M06, 65M12.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.},

author = {Milev, Mariyan, Tagliani, Aldo},

journal = {Serdica Mathematical Journal},

keywords = {Black-Scholes Equation; Finite Difference Schemes; Jacobi Matrix; M-Matrix; Nonsmooth Initial Conditions; Positivity-Preserving; Black-Scholes equation; finite difference schemes; Jacobi matrix; M-matrix; nonsmooth initial conditions; positivity-preserving; option pricing; Crank-Nicolson scheme},

language = {eng},

number = {1},

pages = {75-88},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing},

url = {http://eudml.org/doc/281413},

volume = {35},

year = {2010},

}

TY - JOUR

AU - Milev, Mariyan

AU - Tagliani, Aldo

TI - Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing

JO - Serdica Mathematical Journal

PY - 2010

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 35

IS - 1

SP - 75

EP - 88

AB - 2000 Mathematics Subject Classification: 65M06, 65M12.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.

LA - eng

KW - Black-Scholes Equation; Finite Difference Schemes; Jacobi Matrix; M-Matrix; Nonsmooth Initial Conditions; Positivity-Preserving; Black-Scholes equation; finite difference schemes; Jacobi matrix; M-matrix; nonsmooth initial conditions; positivity-preserving; option pricing; Crank-Nicolson scheme

UR - http://eudml.org/doc/281413

ER -

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