The Mathematical Institute, University of Oxford, Eprints Archive

Convergence analysis of Crank-Nicolson and Rannacher time-marching

Giles, M. B. and Carter, R. (2005) Convergence analysis of Crank-Nicolson and Rannacher time-marching. Technical Report. Unspecified. (Submitted)

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Abstract

This paper presents a convergence analysis of Crank-Nicolson and Rannacher time-marching methods which are often used in finite difference discretisations of the Black-Scholes equations. Particular attention is paid to the important role of Rannacher's startup procedure, in which one or more initial timesteps use Backward Euler timestepping, to achieve second order convergence for approximations of the first and second derivatives. Numerical results confirm the sharpness of the error analysis which is based on asymptotic analysis of the behaviour of the Fourier transform. The relevance to Black-Scholes applications is discussed in detail, with numerical results supporting recommendations on how to maximise the accuracy for a given computational cost.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1137
Deposited By:Lotti Ekert
Deposited On:12 May 2011 08:35
Last Modified:12 May 2011 08:35

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