Valuation Surface

We start by computing the values of the instruments using a crOAS of 0.  This approach can’t lead us to the actual prices because we miss the liquidity spread¹, but it lets us construct a surface of values in the space of 2 tuning factors in our HPA model − the long-term level and the initial level.  Generally, for the same values, the long-term HPA tuning factor should be stronger than the short-term HPA because the diffusion term transitions rather quickly in our model.  At the same time, the short-term HPA rate is often more uncertain; for example, “balloon-bursting” assumptions made by different analysts and firms varied widely in the fall of 2007.

Exhibit 1 depicts zero-crOAS prices of the instruments in the space of two HPA tuning factors; to save space, we depict and compare only the collateral and the M8 tranche.  As shown, the collateral value changes smoothly and exhibits some negative convexity with respect to each of the HPA factors.  This observation agrees with the fact that the borrower’s default is an option (a positive convexity might have pointed to a flaw in our model).  It also means that, had we resorted to the static valuation method (commonly employed for credit analysis), we would have understated collateral losses.  As for the tranche, its value resembles a short position in digital options: negatively convex when the HPA is high (option is out of the money) and positively convex when it is low (option is in the money).  This is the direct consequence of a typical credit enhancement within the ABS capital structure.  If ABS investors liked to hedge this exposure, they might want to see the CME and ICAP to incept digital home price options.

Page 3 of 6 >