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Encyclopedia of Financial Models, 3 Volume Set by Frank J. Fabozzi

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The Active-Passive Decomposition Model for MBS

ALEXANDER LEVIN, PhD

Director, Financial Engineering, Andrew Davidson & Co., Inc.

Abstract: Even a simple mortgage pass-through is a path-dependent financial instrument, valuation of which depends on prepayment “burnout.” The burnout is caused by observed or unobserved heterogeneity of borrowers; as a result, a mortgage pool's composition changes in the presence of refinancing incentives. An attractive modeling approach for dealing with this is to split a mortgage pool into mutually exclusive “active” and “passive” groups. Not only does such a method explain the burnout, it effectively decomposes the path-dependent valuation problem into two easy-to-solve path-independent ones. The method is faster than the traditional Monte Carlo sampling approach while delivering the full set of interest rate risk measures at no additional cost of computing time. The method can be applied to an attractive prepayment model specification where the speed is a function of the pool's objective price, and not an interest rate. This makes universal refinancing modeling feasible as the same curve or curves can apply to both fixed- and adjustable-rate mortgages.

The active-passive decomposition (APD) method of mortgage-backed securities (MBS) modeling and valuation was introduced in Levin (2001, 2002, 2003). An efficient alternative to brute-force Monte Carlo simulation, the APD method splits a mortgage pass-through into two path-independent components, ...

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