Following is the description of a discrete-time interest rate model. Given expected future rates (Eri+1]) and interest rate volatility (6). Assume the length of one period is A. Rates are continuously compounding. Define the expected change in interest rate in the future as m = E[1+1 ri]/A * To construct the interest rate tree, we use the following notation an up movement in interest rates Maj {ri+1.jta a down movement in interest rates and define Vi+1] =ri.j + m x 4+(4):/2 l'i+1.j+1 = Rus + mix 4 - 0(4)1/2 Now suppose 6 months is one period and the current 6-month rate is ro = 10,0 = 1.8%. o = 1.75%. The expected 6-month rates six months later and one year later are 2.08% and 2.49%, respectively. The current price of one-year zero and 1.5-year zero are 98.1262 and 96.7462, respectively. Use the information to construct the three-period risk-neutral binomial tree for the six- month rate. For the risk-neutral probabilities, listing out the equations without finding the numbers will be sufficient for full mark. Following is the description of a discrete-time interest rate model. Given expected future rates (Eri+1]) and interest rate volatility (6). Assume the length of one period is A. Rates are continuously compounding. Define the expected change in interest rate in the future as m = E[1+1 ri]/A * To construct the interest rate tree, we use the following notation an up movement in interest rates Maj {ri+1.jta a down movement in interest rates and define Vi+1] =ri.j + m x 4+(4):/2 l'i+1.j+1 = Rus + mix 4 - 0(4)1/2 Now suppose 6 months is one period and the current 6-month rate is ro = 10,0 = 1.8%. o = 1.75%. The expected 6-month rates six months later and one year later are 2.08% and 2.49%, respectively. The current price of one-year zero and 1.5-year zero are 98.1262 and 96.7462, respectively. Use the information to construct the three-period risk-neutral binomial tree for the six- month rate. For the risk-neutral probabilities, listing out the equations without finding the numbers will be sufficient for full mark