Valuation Commentary

A New Member of AD&Co: The Two-factor Gaussian Term Structure, Part II
by Alex Levin

Last month we introduced a two-factor Gaussian model, the latest addition to AD&Co's suite of term structures. I pledged to touch on an intriguing and practically important question: what financial instruments are valued differently when moving from a single-factor view to the two-factor view? Since a correctly calibrated two-factor model simulates the rate collection in a much more realistic and accurate fashion than any single-factor model, it seems at first glance that two- or more-factor modeling may reveal values and risks way beyond the primitive picture drawn by any single-factor model.

As paradoxical as it may sound, though it's easy to perceive an instrument as mis-valued by a single-factor model, most MBS by types and an absolute majority of them by outstanding volume, will not be valued materially differently if we switch the business regimen to the use of the two-factor model. Whereas some instruments and exotic options certainly require two- or more-factor modeling, we see the most important role of this new model in assessing the interest rate risk, not in finding today's value (or OAS).

Common Perception of MBS
During my career I have asked a number of practitioners about the "2-factor versus 1-factor" dilemma. The most common ("collective") answer was as such: the value of the embedded prepayment option depends on the correlation between a long rate that drives the prepay speed and the short rate that is used for discounting (see Kazarian et al [1998], or Belbase [2000]). Hence, the use of a realistic two-factor model should deflate the prepay option and increase the value of MBS.

What is Wrong with the Common Perception?
If the common perception were right, it would affect European options too. Consider, for example, a European swaption. The exercise is triggered by the long coupon rate; the discounting is done using an arbitrage-free sequence of the short rates, yet its price is known and independent of the rate model selection. Levin [2001] has given a simple argument reminiscent to the classic Black-Scholes setting that should we model the prepay option as a sequence of European pay-offs on a single long rate and fix volatility of this rate beforehand, we won't find material dependence on the model specification for most MBS. This statement seems surprisingly robust: it holds true even if we relax stiff assumptions. >>>