In earlier chapters, we discussed the basic structures of ABS derivatives such as ABS CDS and the ABX. In this chapter we describe our approach to valuing the subindices of the ABX. Since there are four ABX series, each with five subindices (AAA, AA, A, BBB, and BBB–) and each subindex references 20 subprime MBS securities, this task involves estimating the expected write-downs on 400 securities. In this chapter, we have taken two fundamentally different approaches, one based on a full-blown econometric model and another based on the current delinquency pipeline (our simple model). The two approaches reflect the need for a model that incorporates historical data but one that is also robust and intuitive.
We also illustrate both of these approaches. Both have much to commend them. For our ongoing analysis of the ABX, we use most the simple approach as explained in the previous chapter. We also use the econometric approach for calibrating the simple model and for exploring other implications of changes in speed and default rates.
Before we review the two approaches, it seems useful to briefly review the basic valuation equation for the ABX indices we are attempting to price. The price of an ABX CDS can be represented by the following equation:
Price = 100 + (Expected present value of coupon cash flow – Expected present value of write-downs)
This equation says that if the expected present value of the coupons received ...