Matrix-based numerical modelling of financial differential equations
by Robert Piche, Juho Kanniainen
International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO), Vol. 1, No. 1/2, 2009

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), American option pricing problem (linear complementarity problem), and an optimal maintenance and shutdown model (non-linear 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.

Online publication date: Wed, 09-Dec-2009

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