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Matrix-based numerical modelling of financial differential equations

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Matrix-based numerical modelling of financial differential equations. / Piche, R.; Kanniainen, J.

In: International Journal of Mathematical Modelling and Numerical Optimization, Vol. 1, No. 1/2, 2009, p. 88-100.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

Piche, R & Kanniainen, J 2009, 'Matrix-based numerical modelling of financial differential equations', International Journal of Mathematical Modelling and Numerical Optimization, vol. 1, no. 1/2, pp. 88-100. https://doi.org/10.1504/IJMMNO.2009.030089

APA

Piche, R., & Kanniainen, J. (2009). Matrix-based numerical modelling of financial differential equations. International Journal of Mathematical Modelling and Numerical Optimization, 1(1/2), 88-100. https://doi.org/10.1504/IJMMNO.2009.030089

Vancouver

Piche R, Kanniainen J. Matrix-based numerical modelling of financial differential equations. International Journal of Mathematical Modelling and Numerical Optimization. 2009;1(1/2):88-100. https://doi.org/10.1504/IJMMNO.2009.030089

Author

Piche, R. ; Kanniainen, J. / Matrix-based numerical modelling of financial differential equations. In: International Journal of Mathematical Modelling and Numerical Optimization. 2009 ; Vol. 1, No. 1/2. pp. 88-100.

Bibtex - Download

@article{5b00d9482fcc4f67a95bb041899c0410,
title = "Matrix-based numerical modelling of financial differential equations",
abstract = "Differentiation matrices provide a compact and unified formulation for a variety of differential equation discretisation and time-stepping algorithms. This paper illustrates their use for solving three differential equations of finance: the classic Black-Scholes equation (linear initial-boundary value problem), an American option pricing problem (linear complementarity problem), and an optimal maintenance and shutdown model (nonlinear boundary value problem with free boundary). We present numerical results that show the advantage of an L-stable time-stepping method over the Crank-Nicolson method, and results that show how spectral collocation methods are superior for boundary value problems with smooth solutions, while finite difference methods are superior for option-pricing problems.",
author = "R. Piche and J. Kanniainen",
note = "Contribution: organisation=mat,FACT1=0.5<br/>Contribution: organisation=tta,FACT2=0.5",
year = "2009",
doi = "10.1504/IJMMNO.2009.030089",
language = "English",
volume = "1",
pages = "88--100",
journal = "International Journal of Mathematical Modelling and Numerical Optimization",
issn = "2040-3607",
publisher = "Inderscience",
number = "1/2",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Matrix-based numerical modelling of financial differential equations

AU - Piche, R.

AU - Kanniainen, J.

N1 - Contribution: organisation=mat,FACT1=0.5<br/>Contribution: organisation=tta,FACT2=0.5

PY - 2009

Y1 - 2009

N2 - Differentiation matrices provide a compact and unified formulation for a variety of differential equation discretisation and time-stepping algorithms. This paper illustrates their use for solving three differential equations of finance: the classic Black-Scholes equation (linear initial-boundary value problem), an American option pricing problem (linear complementarity problem), and an optimal maintenance and shutdown model (nonlinear boundary value problem with free boundary). We present numerical results that show the advantage of an L-stable time-stepping method over the Crank-Nicolson method, and results that show how spectral collocation methods are superior for boundary value problems with smooth solutions, while finite difference methods are superior for option-pricing problems.

AB - Differentiation matrices provide a compact and unified formulation for a variety of differential equation discretisation and time-stepping algorithms. This paper illustrates their use for solving three differential equations of finance: the classic Black-Scholes equation (linear initial-boundary value problem), an American option pricing problem (linear complementarity problem), and an optimal maintenance and shutdown model (nonlinear boundary value problem with free boundary). We present numerical results that show the advantage of an L-stable time-stepping method over the Crank-Nicolson method, and results that show how spectral collocation methods are superior for boundary value problems with smooth solutions, while finite difference methods are superior for option-pricing problems.

U2 - 10.1504/IJMMNO.2009.030089

DO - 10.1504/IJMMNO.2009.030089

M3 - Article

VL - 1

SP - 88

EP - 100

JO - International Journal of Mathematical Modelling and Numerical Optimization

JF - International Journal of Mathematical Modelling and Numerical Optimization

SN - 2040-3607

IS - 1/2

ER -