EXERCISE 7.5 (Comparison of prices in the models of Vasicek and CIR) Compare the prices according to Vasicek’s model (7.52) and the CIR-model (7.68) of the following securities:

(a) 1 year and 10 year zero-coupon bonds;

(b) 3 month European call options on a 5 year zero-coupon bond with exercise prices of 0.7, 0.75, and 0.8, respectively;

(c) a 10 year 8% bullet bond with annual payments;

(d) 3 month European call options on a 10 year 8% bullet bond with annual payments for three different exercise prices chosen to represent an in-the-money option, a near-the-money option, and an out-ofthe-

money option.

In the comparisons use  = 0.3,  = 0.05, and  = 0 for both models. The current short rate is r = 0.05, and the current volatility on the short rate is 0.03 so that = 0.03 in Vasicek’s model and p0.05 = 0.03 in the CIR model.