why not discount the lower bound to get the present value?

Thanks

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?

V_{1,U}: upper rate value V_{1,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: V_{1,L} = 100. The value for the upper rate will be determined by the lower rate and the standard deviation: i_{1,U} = i_{1,L} × (e^{2 × s}) = 0.12 × (e^{0.20}) = 0.14657. Thus, V_{1,U} = (112 / 1.14657) = 97.683.