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Valuation Commentary - February '07
ARMed with Backward Induction and Risk-Neutrality
by Alex Levin
The new AD&Co prepayment model for ARMs (version 5.2) applies principles and design views proven successful for the fixed-rate MBS. In particular, we have extended the active-passive decomposition (APD) approach, which splits the path-dependent collateral into two path-independent pieces. Valuation via two quick and accurate backward induction steps becomes possible; it replaces the traditional Monte-Carlo altogether. This method greatly facilitates constructing a so-called risk-neutral prepayment model, a process we term “risk-neutral calibration.” To revisit the method, read the Divide and Conquer trilogy [Levin (2004)], or its condensed version published by the Summer 2005 Journal of Portfolio Management [Levin and Davidson (2005)]. The method attributes the existence of OAS to prepay model risk and introduces prOAS, a measure of excess return after both interest rate risk and prepay model risk are hedged out. The AD&Co prepayment model may have a physical form (that results in an OAS) or a risk-neutral form resulting in prOAS. Only changes in prepay tunings differentiate one from another.
The backward induction method and prepay risk-neutrality are functionally unrelated. However, risk-neutral calibration is a time-consuming iterative process. To simplify, if N is the number of risk-neutral tunings, M is the number of benchmark instruments, and L is the number of required iterations, then the total number of OAS to Price conversions will be equal to M times N times L, and usually counts in hundreds or even thousands. The process at AD&Co became feasible courtesy of the APD collateral structure powered by the backward induction. Until now, we have been restricted to fixed rate collateral in our attempt to develop risk-neutral prepayment views. The time has come to extend.
Backward Induction for ARMs
Splitting collateral into active (fast) and passive (slow) groups solves the problem of path-dependence only for fixed-rate pools. Indeed, when prepayment burnout is, by far, the strongest source of path-dependence, the APD is sufficient. ARMs have other path-dependent features associated with discrete coupon resets. When valuing an ARM backwards, we can’t assess its interest cashflow, simply because we are lacking information about its last reset.
