Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
On smoothing of the Crank-Nicolson scheme and higher order schemes for pricing barrier options
Journal of Computational and Applied Mathematics
Numerical pricing of options using high-order compact finite difference schemes
Journal of Computational and Applied Mathematics
A fast high-order finite difference algorithm for pricing American options
Journal of Computational and Applied Mathematics
Pricing Options in Jump-Diffusion Models: An Extrapolation Approach
Operations Research
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Various finite difference methods for option pricing have been proposed. In this paper we demonstrate how a very simple approach, namely the repeated spatial extrapolation, can perform extremely better than the finite difference schemes that have been developed so far. In particular, we consider the problem of pricing vanilla and digital options under the Black-Scholes model, and show that, if the payoff functions are dealt with properly, then errors close to the machine precision are obtained in only some hundredths of a second.