Extrapolation of difference methods in option valuation

In the present investigation, the fully implicit and Crank–Nicolson difference schemes for solving option prices are analyzed. It is proved that the error expansions for the difference methods have the correct form for applying Richardson extrapolation to increase the order of accuracy of the approximations. The difference methods are applied to European, American, and down-and-out knock-out call options. Computational results indicate that Richardson extrapolation significantly decreases the amount of computational work (by as much as a factor of 16) in estimation of option prices. 2003 Elsevier Inc. All rights reserved.