Find the risk-neutral probability p1 of an increase in rates under which the binomial tree model prices the 1-year zero-coupon bond correctly. Once we know p1, find the risk-neutral probability p2 of an increase in rates such that the risk-neutral binomial tree model prices the 1.5- year zero-coupon bond correctly. Lastly, when we know p1 and p2, find the risk-neutral probability p3 of an increase in rates such that the risk-neutral binomial tree model prices the 2- year zero-coupon bond correctly.

2. Constructing a risk-neutral probability binomial short-term interest rate model 2a. We observe the following spot rate curve. Assume semiannual compounding and $1000 par value. Calculate the prices of 0.5y, ly, 1.5y, and 2y zero-coupon Treasury bonds. Time Period 1 2 3 4 Maturity 6 months 12 months 18 months 24 months Annualized Spot Rates 6.0000% 6.1496% 6.2654% 6.4227% 2b. The binomial tree of the annualized 6-month short-term interest rate is in the table below. Each period represents a six-month time interval. The true probability of up and down rates changes are equal (1/2) 0 1 2 3 6-month rates 7.5% 7.0% 6.5% 6.5% 6.0% 3 6.0% 5.5% 5.5% 5.0% 4.5% Find the risk-neutral probability pl of an increase in rates under which the binomial tree model prices the 1-year zero-coupon bond correctly. Once we know pl, find the risk-neutral 2. Constructing a risk-neutral probability binomial short-term interest rate model 2a. We observe the following spot rate curve. Assume semiannual compounding and $1000 par value. Calculate the prices of 0.5y, ly, 1.5y, and 2y zero-coupon Treasury bonds. Time Period 1 2 3 4 Maturity 6 months 12 months 18 months 24 months Annualized Spot Rates 6.0000% 6.1496% 6.2654% 6.4227% 2b. The binomial tree of the annualized 6-month short-term interest rate is in the table below. Each period represents a six-month time interval. The true probability of up and down rates changes are equal (1/2) 0 1 2 3 6-month rates 7.5% 7.0% 6.5% 6.5% 6.0% 3 6.0% 5.5% 5.5% 5.0% 4.5% Find the risk-neutral probability pl of an increase in rates under which the binomial tree model prices the 1-year zero-coupon bond correctly. Once we know pl, find the risk-neutral