Perpetual American Put Option: an Error Estimator for Non-Standard Finite Difference Scheme

2014/12/04 by Fazio, Riccardo
#34B40 #65L12 #91B #FOS: Mathematics #G.1.7 #J.4 #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1412.1621

Abstract

In this paper we present a MATLAB version of a non-standard finite difference scheme for the numerical solution of the perpetual American put option models of financial markets. These models can be derived from the celebrated Black-Scholes models letting the time goes to infinity. The considered problem is a free boundary problem defined on a semi-infinite interval, so that it is a non-linear problem complicated by a boundary condition at infinity. By using non-uniform maps, we show how it is possible to apply the boundary condition at infinity exactly. Moreover, we define a posteriori error estimator that is based on Richardson's classical extrapolation theory. Our finite difference scheme and error estimator are favourably tested for a simple problem with a known exact analytical solution.

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