Q. Does an interest rate model selection matter for valuing MBS?
A. Yes, it does. For example, lognormality extends interest rate sensitivity [hence, Option Adjusted Duration (OAD)] for most MBS owning to the proportional volatility specification. When rates rise, MBS loses twice – due to higher rates and due to inflated volatility. For TBA pass-throughs, one should expect a 0.3-0.5 yr OAD difference between normality and lognormality.

Q. Isn’t a two-factor model always better than a single-factor model for MBS pricing?
A. Curiously enough, most MBS will be valued in a close range once a model is calibrated to the same set of swap rates and swaption volatilities. This paradox is explained by the nature of our (and others’) prepay model that simulates refinancing decisions as a series of European options.

We found that CMO tranches that are much shorter or much longer than their collateral will be valued differently. As a rule, two-factor rate modeling adds value for short tranches and subtracts it for long tranches. The same applies to inverse floaters. Some other instruments such as capped amortizing floaters are affected as well.

Q. Why does AD&Co recommend using swaptions, not caps, for volatility calibration?
A. Because jumps in short LIBOR rates are priced in caps. For the same variance, the jump process leads to smaller values of at-the-money (ATM) options than diffusion. That is why the short-dated caps look visibly cheaper on the Black-Scholes volatility scale than long-dated caps (cap hump) or even short-dated swaptions. Since all AD&Co rate models are diffusive ones, using caps will depress the short rate volatility and understate prepay option value. This comment applies to most existing MBS valuation models in general.

Q. AD&Co’s system uses ATM swaptions for volatility calibration. What about the skew?
A. The skew is controlled solely by the model selection itself. For example, when selecting a lognormal model, a user produces no skew. A normal model leads to a pronounced volatility skew that is approximately described by the inverse square-root function. Hence, we don’t load OTM or ITM volatilities when calibrating; we “measure” the skew first and then recommend a model.

 

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