Valuation of derivatives based on single-factor interest rate models

The CKLS [Chan, K.C., Karolyi, G.A., Longstaff, F.A., & Sanders, A.B. (1992). An empirical comparison of the short-term interest rate, Journal of Finance, 1(7), 1209-1227] short-term risk-free interest rate process leads to a valuation model for both default-free bonds and contingent claims that can only be solved numerically for the general case. Valuation equations of this nature in the past have been solved using the Crank Nicolson scheme. In this paper, we introduce a new numerical scheme - the Box method, and compare it with the traditional Crank Nicolson scheme. We find that in specific cases of the CKLS process where analytical prices are available, the new scheme leads to more accurate results than the Crank Nicolson scheme.