Finite difference scheme versus piecewise binomial lattice for interest rates under the skew CEV model

Abstract

Interest rates frequently exhibit regulated or controlled characteristics, for example, the prevailing zero interest rate policy, or the leading role of central banks in short rate markets. In order to capture the regulated dynamics of interest rates, we introduce the skew constant-elasticity-of-variance (skew CEV) model. We then propose two numerical approaches: an improved finite difference scheme and a piecewise binomial lattice to evaluate bonds and European/American bond options. Numerical simulations show that both of these two approaches are efficient and satisfactory, with the finite difference scheme being more superior.