1. You are going to borrow $250m at a floating rate for 5 years. You wish to protect yourself against borrowing rates greater than 10.5%. Using each tree, what is the price of a 5-year interest rate cap? (Assume that the cap settles each year at the time you repay the borrowing.)
2. 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?