Approximating payoffs and pricing formulas

We use the ideas developed by Madan and Milne (1994. Mathematical Finance 3 , 223-745), Lacoste (1996. Mathematical Finance 6, 197-213) to explore the optimality of polynomial approximations in pricing securities. In particula r, we look at the approximations for security payoffs as well as the associ ated pricing formula in a L-2 framework. We apply these ideas to two exampl es, one where the state variable follows an Ornstein-Uhlenbeck process and one based on Brownian motion with reflecting barriers, to illustrate the st rengths and weaknesses of the approach. (C) 2000 Elsevier Science B.V. All rights reserved. JEL classification: C10; C63; G12.