Bond option pricing under the CKLS model

Khor, C. Y. and Pooi, Ah Hin * and Ng, Kok Haur (2012) Bond option pricing under the CKLS model. In: Regional Conference on Applied and Engineering Mathematics (2nd). Proceedings, 30 - 31 May 2012, Penang.

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Abstract

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  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.

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