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AD& Co.’s Credit OAS system has been linked to the HPI stochastic process (see my 2006 and 2007 AD&Co Conferences Presentations for more details). The process can be risk-neutralized by changing two mathematical variables: the long-term equilibrium and the initial diffusion. In practical terms, we can alter the long-term behavior and the short-term behavior rather easily. For example, by using real estate forward contracts we can change the model to best approximate the forward HPI curve.
In addition, we incorporated “HPI Greeks,” i.e. duration and convexity to the change in long-term and short-term HPI rates. These are important measures for hedging the real estate risk embedded in MBS and ABS. For example, when analyzing the CW0708 sub-prime deal, we found that the collateral losses and their Greeks generally agree with the option theory. The HPI convexity of losses is positive (default is an option!), but becomes close to zero for bad loans and bad home price scenarios (i.e. with a deep in the money default option). The duration of losses to the long-term HPI rate is found to be about 5 – 10 years; exposure to the short-term HPI rate is about 2 – 3 times smaller. As usual, a 5 year duration means that “instrument” (the loan’s loss piece in our case) will go up 5% in value when the HPI rate is down 1%. Note that the duration of losses can be expressed relative to the price of the bond (up to 0.75 yr for the same deal) rather than the value of losses.
Static Versus Stochastic
Theoretically, in the presence of any convexity, the stochastic framework cannot be omitted without loss of accuracy. During my talk at the 2007 AD&Co Conference, I illustrated the role of randomness: deterministic HPI forecast may understate a loss estimate by 25% for a cohort of loans. For ABS tranches, which are purposely designed to be nonlinear in the credit structure, the difference between loss estimates obtained via static and random HPI forecast can be substantial. In fact, we expect that senior tranches cannot be fairly valued using the static framework – their prices reflect potential losses that can materialize in adverse HPI cases only.
For any particular credit protection, the HPI volatility effect can be replaced by an artificial loss-equivalent single static scenario. However, such a scenario can’t be selected universally across the capital structure. Suppose we have a AA tranche that is fully protected unless losses reach 25%. The tranche’s market quote carries a credit spread of, say 50 bps, which is equivalent to a 2 point price discount. A single HPI scenario that triggers such losses in the AA tranche is likely to fully demolish junior and mezzanine classes and thereby contradicts their observed market prices. The AD&Co Implied Default Model (IDM) synthesizes a default rate distribution rather than a single default rate in order to explain market quotes across credit protection layers. The default rate distribution, in turn, can be explained by the HPI randomness thereby connecting the IDM and the Credit OAS concepts.
