# Question

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?

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?

## Answer to relevant Questions

Using Monte Carlo, simulate the process dr = a(b − r)dt + σdZ, assuming that r = 6%, a = 0.2, b = 0.08, φ = 0, and σ = 0.02. Compute the prices of 1-, 2-, and 3-year zero-coupon bonds, and verify that your answers match ...What is the price of a 3-year interest rate cap with an 11.5% (effective annual) cap rate? Consider the expression in equation (26.6). What is the exact probability that, over a 1-day horizon, stock A will have a loss? Using the same assumptions as in Example 26.3, compute VaR with and without the mean, assuming correlations of −1, −0.5, 0, 0.5, and 1. Is risk eliminated with a correlation of −1? If not, why not? Using Monte Carlo simulation, reproduce Tables 27.10 and 27.11. Produce a similar table assuming a default correlation of 25%.Post your question

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