Bond Option Pricing under the CKLS Model

Consider the European call option written on a zero-coupon bond. Suppose the call option has maturity T and strike price K while the bond has maturity S>T. We propose a numerical method for evaluating the call option price under the Chan, Karolyi, Longstaff and Sanders (CKLS) model in which the increment of the short rate over a time interval of length dt, apart from being independent and stationary, is having the quadratic-normal distribution with mean zero and variance dt. The key steps in the numerical procedure include (i) the discretization of the CKLS model; (ii) the quadratic approximation of the time-T bond price as a function of the short rate r(T) at time T; and (iii) the application of recursive formulas to find the moments of r(t+dt) given the value of r(T). The numerical results thus found show that the option price decreases as the parameter γ in the CKLS model increases and the variation of the option price is slight when the underlying distribution of the increment departs from the normal distribution.