Suppose that the yield curve is given by y(t) = 0.10 − 0.07e −0.12t , and that the short-term interest rate process is dr(t) = (θ(t) − 0.15r(t)) + 0.01dZ. Compute the calibrated Hull-White tree for 5 years, with time steps of h = 1.
a. What is the probability transition matrix Q?
b. What is the price of a 5-year 7.5% interest rate cap on a $1 million notional amount?