1. Throughout this question, you should assume that the Vasicek model of the term structure is appropriate. When using this model, set=.10, =.05, =.30, V=.40,T=.5 years, and h=.25. Also assume 0rh=.15.

Part a. Determine the 3 month annualized interest rate (using continuous com-pounding) for all nodes of the Vasicek tree.

Part b. Determine the annualized interest rate (using continuous compounding)for 6 month and 9 month zero coupon bonds with face value of $1.00. These rates should be specified for time period 0. Also determine the potential 6 month rates for the period occurring 3 months after time period 0. In all cases, also specify the prices as well as the interest rates.

Part c. Demonstrate whether or not the above formulation of the term structure generates uniform shifts in the term structure.

Part d. In time period 0, an investor has $1,000.00. He places 40% of this money in 9 month bonds, 35% in 6 month bonds, and 25% in 3 month bonds. Over the next three months, what is the expected return and the standard deviation of the return from this investment?

Part e. As of period 0, what do you forecast the 6 month interest rate to be in three months? Compare this forecast with the forward rate,0 r.25,.75.

Part f. Consider a 6 month bond which pays $25 in 3 months and $125 in 6 months. What is the market value of this bond in period 0? What is the dollar duration ofthis bond in period 0? What is the Vasicek delta of this bond in period 0? What is the Vasicek delta of this bond in 3 months from period 0?