Fixed Income, Options, Binomial Tree..with standard deviatio first, interest, standard, situation

Fdez

qbank #89432
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?
the answer is:
upper rate value = 97.683
lower rate value = 100
this is the explanation
*****How on earth do they come up with (e^.20)?*****
***** also, where is this found in the textbook? ******
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

ba736

yeah… u can find this waht CPK wrote in CFAI textbook.
But it is only in one place. Covered in a few sentences, and they they do not mention it later, even in the EOCQ.

ramdabom

great answers, thanks.

Benjiko

This is mentioned in both the text book and in Schweser somewhere –
if the lower bound is 12% and the volatility = 10% - upper bound = 12 * e ^ (2*0.1)
e^(2*volatility)