Our new method shares some features with its predecessors, the PORC model developed by Bear Sterns [1997] and the work of Oren Cheyette [1996]. AD&Co has developed two mathematically equivalent models that produce the prOAS valuation.

Method 1: Explicit risk accounting
Suppose we consider one valuation risk factor, call it x. This can be an uncertain parameter or a stochastic process. According to the CAPM, every instrument exposed to this factor should be given an additional return proportional to the price volatility caused by the factor volatility, s. The coefficient of this proportionality is called price of risk, let us denote it as p. Therefore,

Return compensation for bearing a risk = ps(dP/dx) (1)

This term should be added to the expected return for any investment period and for any level of interest rates. Explicit accounting of the derivative of price P with respect to factor x is possible in special cases only. For example, the PORC model interprets x as a random parameter, the overall prepay multiple; the needed derivative is then found by stressing x and measuring new (stressed) prices using several sets of Monte-Carlo runs. The PORC method can barely handle a situation when factor x is dynamic. For example, the turnover rate is known and documented today, but may be uncertain in the future.

AD&Co.'s active-passive decomposition (APD) model (Levin [2003]) allows for extending the application of the direct risk accounting. The APD method splits the MBS collateral into two parts differing in refinancing propensity, active and passive. This split explains the burnout effect by decomposing the path-dependent, heterogeneous collateral into two path-independent, homogenous pieces that can be valued using a quick backward induction instead of Monte-Carlo. APD also allows for computing the price's derivative, dP/dx , at every pricing node of a finite difference grid or a probability tree. In particular, one can measure the risk for every investment period and every level of rates.

Despite its rich and informative outcome, the explicit risk accounting method has limited practical application because taking the direct measure of dP/dx is not always feasible. For example, it can't be used for CMOs when the risk factor, or factors, are dynamic processes because prices and their derivatives can't be computed in the future. However, for active-passive decomposed pass-throughs, the explicit risk accounting is an efficient method. AD&Co. has successfully implemented APD in a new valuation system, available for trial online. Please ask Ilda or Rob for the access. >>>