Consider the discrete-time interest rate model, Model I, introduced in our lecture note. The model description is provided below. Description of Model I: Given expected future rates (E[r(+1]) and interest rate volatility (o). Assume the length of one period is A. Rates are continuously compounding. Define the expected change in interest rate in the future as mi = E[ril - ri]/A To construct the interest rate tree, we use the following notation Ti+1,j an "up" movement in interest rates (1+1,/+1 a "down" movement in interest rates and define ri+1, j = nij + mi X A + o (4) 1/2 (71+1,1+1 = nj + mix A - o(4) 1/2 Now suppose 6 months is one period and we have the following information: The current 6-month rate is ro = To,0 = 1.5%. o = 1.3%. The expected 6-month rates six months later and one year later are 1.85% and 2.03%, respectively. The current prices of 1-year zero and 1.5-year zero bonds are 98.1053 and 96.6928, respectively. Use the information to construct the three-period risk-neutral binomial tree for the six- month rate. Use the resulted tree to value a fixed income security that pays $10,000 one and half years later if and only if the 6-month rate goes up twice