1.0 3. The Ho-Lee Model - 40 points Use the following zero coupon bond table to answer this question. Maturity (years) Price Yield 0.5 99.1338 1.74 97.8925 2.13 96.1462 2.62 2.0 94.1011 3.04 2.5 91.7136 3.46 3.0 89.2258 3.80 3.5 86.8142 4.04 4.0 84.5016 4.21 4.5 82.1848 4.36 5.0 79.7718 4.52 1.5 +1j Consider the simple Ho-Lee model. Let's fix the time step such that A = 0.5. Let rj be the continuously compounded interest rate in node ; between steps i and i +1. Then, for every (i, j), the Ho-Lee model postulates that roj +*A +ox V with probability p 14+1+1 Mes +xA-oxV with probability p= where 8, are step-dependent free parameters and o is a constant. Also, let P.;(k) denote the price of a zero coupon bond at time t at node ; with maturity at k. Use the zero table given above to construct the interest rate tree up to 5 years and compute the estimated 0, for each step using the procedure outlined below. (a) Find the root of the tree, 70,0, using the 1-period zero bond. (b) Given r9.0, apply the laws of motion of interest rates stated above to find 11,0 and (c) Assuming a = 0.0173, choose 6, such that the fair value of the 2-period zero bond equals to corresponding price in the data. (d) Compute no and r, using 6, found in Part (C). (e) Repeat the procedure iteratively with different zeros at higher maturities. Discuss the advantages and drawbacks of the Ho-Lee model you have just operational- ized. 1.0 3. The Ho-Lee Model - 40 points Use the following zero coupon bond table to answer this question. Maturity (years) Price Yield 0.5 99.1338 1.74 97.8925 2.13 96.1462 2.62 2.0 94.1011 3.04 2.5 91.7136 3.46 3.0 89.2258 3.80 3.5 86.8142 4.04 4.0 84.5016 4.21 4.5 82.1848 4.36 5.0 79.7718 4.52 1.5 +1j Consider the simple Ho-Lee model. Let's fix the time step such that A = 0.5. Let rj be the continuously compounded interest rate in node ; between steps i and i +1. Then, for every (i, j), the Ho-Lee model postulates that roj +*A +ox V with probability p 14+1+1 Mes +xA-oxV with probability p= where 8, are step-dependent free parameters and o is a constant. Also, let P.;(k) denote the price of a zero coupon bond at time t at node ; with maturity at k. Use the zero table given above to construct the interest rate tree up to 5 years and compute the estimated 0, for each step using the procedure outlined below. (a) Find the root of the tree, 70,0, using the 1-period zero bond. (b) Given r9.0, apply the laws of motion of interest rates stated above to find 11,0 and (c) Assuming a = 0.0173, choose 6, such that the fair value of the 2-period zero bond equals to corresponding price in the data. (d) Compute no and r, using 6, found in Part (C). (e) Repeat the procedure iteratively with different zeros at higher maturities. Discuss the advantages and drawbacks of the Ho-Lee model you have just operational- ized
