Options, Futures, and Other Derivatives 9th Edition solutions

Options, Futures, and Other Derivatives 9
Explain the difference between a Markov and a non-Markov model of the short rate.

Options, Futures, and Other Derivatives 9
Prove the relationship between the drift and volatility of the forward rate for the multifactor version of HJM in equation (32.6).

Options, Futures, and Other Derivatives 9
When the forward rate volatility st; T in HJM is constant, the HoLee model results. Verify that this is true by showing that HJM gives a process for bond prices that is consistent with the HoLee model in Chapter 31.

Options, Futures, and Other Derivatives 9
When the forward rate volatility, st; T, in HJM is eaTt , the HullWhite model results. Verify that this is true by showing that HJM gives a process for bond prices that is consistent with the HullWhite model in Chapter 31.

Options, Futures, and Other Derivatives 9
What is the advantage of LMM over HJM?

Options, Futures, and Other Derivatives 9
Provide an intuitive explanation of why a ratchet cap increases in value as the number of factors increase.

Options, Futures, and Other Derivatives 9
Show that equation (32.10) reduces to (32.4) as the i tend to zero.

Options, Futures, and Other Derivatives 9
Explain why a sticky cap is more expensive than a similar ratchet cap.

Options, Futures, and Other Derivatives 9
Explain why IOs and POs have opposite sensitivities to the rate of prepayments.

Options, Futures, and Other Derivatives 9
An option adjusted spread is analogous to the yield on a bond. Explain this statement.

Options, Futures, and Other Derivatives 9
Prove equation (32.15).

Options, Futures, and Other Derivatives 9
Prove the formula for the variance VT of the swap rate in equation (32.17).

Options, Futures, and Other Derivatives 9
Prove equation (32.19).

Options, Futures, and Other Derivatives 9
In an annual-pay cap, the Black volatilities for at-the-money caplets which start in 1, 2, 3, and 5 years and end 1 year later are 18%, 20%, 22%, and 20%, respectively. Estimate the volatility of a 1-year forward rate in the LIBOR Market Model when the time to maturity is (a) 0 to 1 year, (b) 1 to 2

Options, Futures, and Other Derivatives 9
In the flexi cap considered in Section 32.2 the holder is obligated to exercise the first N in-the-money caplets. After that no further caplets can be exercised. (In the example, N 5.) Two other ways that flexi caps are sometimes defined are: (a) The holder can choose whether any caplet is exercised