Consider the binomial tree and the mortgage backed securities obtained in that exercise.
(a) On the tree, obtain the trigger rates ri such that prepayment occurs when ri < ri-
(b) Use Monte Carlo simulations and compute the value of the mortgage. Do you obtain the same value as from the tree?
(c) Use Monte Carlo simulations to obtain the price of the 3.5% pass-through security.
(d) Add some prepayment probability to the model, such as:
i. A PSA related probability of prepayment even when r, > r,. How is the price of the pass through affected by this additional probability? Discuss.
ii. A probability of no prepayment even if r, < r,. How is the price of the pass through affected by this additional probability? Discuss.
(e) Suppose that the price of the mortgage is given by the optimal prepayment policy (i.e., only from the tree), but that homeowners act non-optimally with respect to interest rates, and therefore prepay when they shouldn't and vice versa, as discussed above. Is this good news or bad news for the bank issuing the mortgage?
(f) What is the price of interest only (10) and principal only (PO) strips? Compute their spot rate duration and compare them with the spot rate duration of the pass-through security.