A bond with a 12% annual coupon will mature in two years at par value. The current one-year spot rate is 14%. For the second year, the yield volatility model forecasts a lower bound of 12% for the one-year rate and a standard deviation of 10%. In a binomial interest rate tree describing this situation, what are the forecasted values for the bond in the first nodal period? V1,U: upper rate value V1,L: lower rate value A) 94.676 97.664 B) 97.683 100.000 C) 101.125 100.000 D) 97.680 101.125
B
Don’t know the exact methodology for solving the question. However, the lower coupon after first year is equal to the yield at that node. So the bond is trading at par. Only B has the option with 100 = V1,L. My answer is B. Someone please post the exact solution.
Kindly post the complete solution. Thanks
Your answer: B was correct! The value of the bond for the lower rate is easy; since that forecasted rate is the coupon rate: V1,L = 100. The value for the upper rate will be determined by the lower rate and the standard deviation: i1,U = i1,L × (e^2*SD) = 0.12 × (e^.20) = 0.14657. Thus, V1,U = (112 / 1.14657) = 97.683. I thought the answer was interesting. I just used reasoning to figure it out.