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CMO Valuation

Consider an allocation to the investment grade AAA tranche of a CMO. This tranche (call it tranche A) is entitled to 25 percent of the principal and interest on a pool of mortgages consisting of prime and subprime loans that have been structured so as to enhance the credit ratings within the pool, using methods discussed at the beginning of the chapter. To keep things simple, let's refer to tranche A as a single bond and assume that this bond is priced in the market at 103. Is this a fair price?

To price this bond, we first need some facts. First, let's assume that it is August 1, 2008, and that the term structure is a presented in the Ho-Lee and BDT models. Furthermore, assume that 2 percent of the loan pool is prepaid annually except when short rates fall, in which case the prepayment rate rises to 5 percent. The average mortgage rate on the pool is 4 percent. Using the template from Chapter 2, we estimate that the conventional 30-year annual mortgage payment is $5.78 per hundred dollars and that annual interest on this tranche is 25% × 0.04 = $1. Let's assume that tranche B is entitled to 50 percent of the principal and interest in the CMO, and a third tranche C is entitled to 25 percent. Tranche C is subordinated to the first two tranches and receives no payments until tranches A and B are retired. Tranche A received principal and interest first, while tranche B is paid interest only until tranche A is retired. Tranche C accrues interest until the first two tranches ...