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

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)

ramdabom

great answers, thanks.

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.