# Question: Consider two zero coupon bonds with 2 years and 10 years

Consider two zero-coupon bonds with 2 years and 10 years to maturity. Let a = 0.2, b = 0.1, r = 0.05, σVasicek = 10%, and σCIR = 44.721%. The interest rate risk premium is zero in each case. We will consider a position consisting of one $100 par value 2-year bond, which we will hedge with a position in the 10-year bond.

a. Compute the prices, deltas, and gammas of the bonds using the CIR and Vasicek models. How do delta and gamma compare to duration and convexity?

b. Suppose the Vasicek model is true. You wish to hedge the 2-year bond using the 10-year bond. Consider a 1-day holding period and suppose the interest rate moves one standard deviation up or down. What is the return on the duration-hedged position? What is the return on the Vasicek delta-hedged position?

c. Repeat the previous part, only use the CIR model in place of the Vasicek model.

a. Compute the prices, deltas, and gammas of the bonds using the CIR and Vasicek models. How do delta and gamma compare to duration and convexity?

b. Suppose the Vasicek model is true. You wish to hedge the 2-year bond using the 10-year bond. Consider a 1-day holding period and suppose the interest rate moves one standard deviation up or down. What is the return on the duration-hedged position? What is the return on the Vasicek delta-hedged position?

c. Repeat the previous part, only use the CIR model in place of the Vasicek model.

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