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Risk or bias? One can’t firmly separate the ultimate drift or parameter value found in a risk-neutral model into “bias” and “price of risk”. All empirical models constructed for the real world are somewhat subjective. A steep forward curve can serve an evidence of a high price of risk, or the expectation that the rate will go up, or both.
Risk-Neutral Prepayment Modeling
In analyzing MBS, Levin [2004] and Levin and Davidson [2005] offer a theory attributing the very existence of an OAS to bearing prepay model risk, i.e. the risk of a systematic difference between actual and modeled prepay speeds. In a simplified view, the market fears faster refinancing (loss to the premium sector) and slower turnover (loss to the discount sector).
Refinancing and turnover can be viewed as additive sources of prepayments (AD&Co’s model also includes cashout refinancing and credit cure). The difference between the actual housing turnover (or refinancing) and the one computed by the model is the risk factor. We only regard systematic model errors, i.e. a model bias (inevitable oscillations are diversified over time and not priced by the market).
Errors of prepay modeling exhibit properties of both random processes and random parameters. There is no doubt that uncertainty in prepayment modeling grows over a time horizon subject to some bounds (after all, SMMs can’t exceed 1.0 and be below 0.0). However, empirical models can often exhibit a bias that already exists at time zero because they are calibrated to historical data. For example, the AD&Co.prepayment model calibrated to a long historical time period overstates the turnover speed for 2007. In order to construct the risk-neutral dynamics for a factor that exhibits both an uncertain starting level and day-by-day small changes, we will change its starting value and add a drift. Each of these two steps can have different s ’s.
Tuning the Knobs
Adding user-controlled drifts to prepay model factors is certainly possible. We demonstrated this in ValueNet, our first WEB-based valuation system. However, for our production OAS system that clients license, we decided to take a shortcut and restrict the user interference with tuning the existing prepayment knobs. This solution effectively exercises a simplified viewpoint on prepayment model risk: we interpret refinancing and turnover scale as random parameters, not random processes. The intuition behind this decision appealed to mere practicality.
