Hi all,
in quiz 26-1 (page 552) we are told:
the risk neutral process for interest rates is
dr(t)= -.01 dt + .08 dZsquiggle
The sharpe ratio for assets perfectly correlated with the original browniani motion Z(t) is .2. r(0) = .05. Calculate the probability that r(4) > .06.
So here, to find the drift when we sent up the Probability formula, it says we should use:
drift = -.01 - sigma* sharpe ratio = -.01 - .08*.2 = -.026.
I set up the formula this way to get the same answer:
-.01= alpha + sigma*sharperatio = alpha + .08*.2 -----> alpha = -.026
Now in example 26B, it says:
interest rates follow a rendleman-bartter model with a=.001, sigma = .01. Current rates are .04.
Calculate the probability that rates will be higher than .04 three months from now.
To calculate the drift to set into our Probability formula, it says we should use
ln (.04) + .25*(.001-.5(.01)^2)
Why in example 26B, do we subtract .5*sigma squared, where in Quiz 26-1, we didn't do this??
in quiz 26-1 (page 552) we are told:
the risk neutral process for interest rates is
dr(t)= -.01 dt + .08 dZsquiggle
The sharpe ratio for assets perfectly correlated with the original browniani motion Z(t) is .2. r(0) = .05. Calculate the probability that r(4) > .06.
So here, to find the drift when we sent up the Probability formula, it says we should use:
drift = -.01 - sigma* sharpe ratio = -.01 - .08*.2 = -.026.
I set up the formula this way to get the same answer:
-.01= alpha + sigma*sharperatio = alpha + .08*.2 -----> alpha = -.026
Now in example 26B, it says:
interest rates follow a rendleman-bartter model with a=.001, sigma = .01. Current rates are .04.
Calculate the probability that rates will be higher than .04 three months from now.
To calculate the drift to set into our Probability formula, it says we should use
ln (.04) + .25*(.001-.5(.01)^2)
Why in example 26B, do we subtract .5*sigma squared, where in Quiz 26-1, we didn't do this??
Equilibrium Interest Rate Models - ASM Examples