SIAM Journal on Scientific Computing
Numerical methods and software for the pricing of american financial derivatives
Numerical methods and software for the pricing of american financial derivatives
Journal of Computational Physics
Scattered node compact finite difference-type formulas generated from radial basis functions
Journal of Computational Physics
High-order compact finite-difference methods on general overset grids
Journal of Computational Physics
Compact finite difference method for integro-differential equations
Applied Mathematics and Computation
On the numerical solution of nonlinear Black-Scholes equations
Computers & Mathematics with Applications
WSEAS Transactions on Mathematics
An algorithm for multi-resolution grid creation applied to explicit finite difference scheme
ICCOMP'08 Proceedings of the 12th WSEAS international conference on Computers
On modified Mellin transforms, Gauss-Laguerre quadrature, and the valuation of American call options
Journal of Computational and Applied Mathematics
Polynomial algebra for Birkhoff interpolants
Numerical Algorithms
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A compact finite difference method is designed to obtain quick and accurate solutions to partial differential equation problems. The problem of pricing an American option can be cast as a partial differential equation. Using the compact finite difference method this problem can be recast as an ordinary differential equation initial value problem. The complicating factor for American options is the existence of an optimal exercise boundary which is jointly determined with the value of the option. In this article we develop three ways of combining compact finite difference methods for American option price on a single asset with methods for dealing with this optimal exercise boundary. Compact finite difference method one uses the implicit condition that solutions of the transformed partial differential equation be nonnegative to detect the optimal exercise value. This method is very fast and accurate even when the spatial step size h is large (h=0.1). Compact difference method two must solve an algebraic nonlinear equation obtained by Pantazopoulos (1998) at every time step. This method can obtain second order accuracy for space x and requires a moderate amount of time comparable with that required by the Crank Nicolson projected successive over relaxation method. Compact finite difference method three refines the free boundary value by a method developed by Barone-Adesi and Lugano [The saga of the American put, 2003], and this method can obtain high accuracy for space x. The last two of these three methods are convergent, moreover all the three methods work for both short term and long term options. Through comparison with existing popular methods by numerical experiments, our work shows that compact finite difference methods provide an exciting new tool for American option pricing.