Numerical pricing of financial derivatives using Jain’s high-order compact scheme

Abstract

Purpose: This paper develops new fast and accurate computational schemes for pricing European and American bond options under generalised Chan-Karoyli-Longstaff-Sanders term structure models. Methods: We use high-order compact discretisations of the pricing equations and an operator splitting method for American options. Results: Highly accurate numerical solutions can be computed using relatively coarse grid sizes and numerical solutions exhibiting fourth-order convergence are obtained for bond and bond option prices. The scheme is also stable and efficient for pricing financial problems with time dependent parameters. Conclusions: The new schemes are efficient alternatives to schemes based on the Crank-Nicolson discretisation for the pricing of interest rate derivatives.