Pricing of interest rate derivatives / Khor Chia Ying - Khor, Chia Ying (2013)
A numerical method is proposed to find the time-t bond price of a zero-coupon bond with maturity time T under the Cox, Ingersoll and Ross (CIR) model described by a Lévy process. When the underlying distribution in the Lévy process is normal, the numerical results thus found for the bond prices are fairly close to the corresponding theoretical values. The similar numerical method is next applied to evaluate the bond price of a zero-coupon bond with maturity time T under the Chan, Karolyi, Longstaff and Sanders (CKLS) model described by a Lévy process. The numerical results obtained show that bond price decreases slightly when the parameter g in the CKLS model increases, and the variation of the bond price is slight as the non-normality of the underlying distribution in the Lévy process varies. A method is also proposed for pricing the European call option with maturity T and strike price K written on a zero-coupon bond with maturity S > T. The numerical results thus found show that option price decreases as the parameter g in the CKLS model increases, and the variation of the option price is slight when the non-normality of underlying distribution in the Lévy process becomes more severe. So far, the parameters in the interest rate models are assumed to be constants. The restriction on constant parameters is lifted by describing the parameters as ones which follow a multivariate non-normal distribution. Compared to the CKLS model with fixed parameters, the CKLS model with stochastic parameters is found to yield more reasonable prediction interval for the future interest rate.