00:03
To compute the expected 6 month treasury rate, we can calculate the weighted average of the two possible rates at time t equals to 0 .5.
00:14
So e r1 can be calculated as p multiplied by r1 ,u plus 1 minus p multiplied by r1 ,d.
00:29
So it will be 1 divided by 2 multiplied by 4 percent plus 1 divided by 2 multiplied by 1 percent.
00:42
It will be 2 percent plus 0 .5 percent which will result in 2 .5 percent.
00:51
Therefore, the expected 6 month treasury rate is 2 .5 percent.
00:55
B part, the continuously compounded forward rate for the periods i equals to 1 to i equals to 2 can be calculated using the formula f is equals to ln p02 minus ln p01 whole divided by t2 minus t1 where p01 is the current price of the 6 month treasury bill and p02 is the current price of the 1 year treasury bill.
01:35
So f will be equals to 97 .4845 less 100 whole divided by 0 .5 which will be negative 0 .0504 or we can say negative 5 .04 percent.
02:04
The forward rate calculated in part b is different from the expected rate computed in part a because the forward rate takes into account the market prices of the treasury bill while the expected rate is based on the probabilities of different interest rate movements.
02:20
C part, the market price of risk lambda can be computed using the formula lambda is equals to 1 divided by t multiplied by ln p divided by 1 minus p where p is the risk neutral probability.
02:38
Given p is equals to 1 divided by 2 and t is equals to 0 .5, we can calculate the market price of risk by lambda is equals to 1 whole divided by 0 .5 multiplied by 0 .5 divided by 1 minus 0 .5...