why not discount the lower bound to get the present value?
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) 97.683 100.000 B) 97.680 101.125 C) 94.676 97.664
Your answer: C was incorrect. The correct answer was A) 97.683 100.000
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 × (e2 × s) = 0.12 × (e0.20) = 0.14657. Thus, V1,U = (112 / 1.14657) = 97.683.