The Journal of Futures Markets, Vol. 21, No. 1, 19–42 (2001)  2001 by John Wiley & Sons, Inc. An Application of Finite Elements to Option Pricing MICHAEL J. TOMAS III* KISHORE K. YALAMANCHILI This study applied the finite element method (FEM) to pricing op- tions. The FEM estimates the function that satisfies a governing dif- ferential equation through the assembly of piecewise continuous functions over the domain of the problem. Two common represen- tations, a variational functional representation, and a weighted resid- ual representation are used in the application of the method. The FEM is a versatile alternative to other popular lattice methods used in option pricing. Advantages include the abilities to directly estimate the Greeks of the option and allow nonuniform mesh construction. As an illustration of the advantages that the FEM offers, the method was used to price European put options and discrete barrier knock- out put options.  2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:19– 42, 2001 INTRODUCTION Even though option pricing problems continue to increase in complexity, OTC markets continue to create innovative option structures that pre- clude analytic solutions. In a study of several popular numerical tech- niques, Geske and Shastri (1985) concluded that no one method is best; The authors thank Mark Holder, Hari Krishnan, Robert Webb, and two anonymous referees for their comments. *Correspondence author, Babson College, Finance Division, Babson Park, Massachusetts 02457- 0310; e-mail: mtomas@babson.edu Received March, 1999; Accepted April, 2000 ■ Michael J. Tomas III is an Assistant Professor at Babson College in Babson Park, Massachusetts. ■ Kishore K. Yalamanchili is a Vice President at State Street Research and Management in Boston, Massachusetts.