The MSR valuation puzzle can be solved within the option-adjusted valuation
(OAV) framework. Most market makers are aware of the concept of volatility
and adjust static valuation measures (such as yield) accordingly.
Where does volatility come from?
The best way to incorporate volatility into the MSR valuation framework
is to design an OAV system that is calibrated to the swaption market.
The at-the-money volatility quotes can be translated into an internal
model's parameters, such as the short-rate volatility and mean reversion.
The observed volatility skew (volatility dependency on strike) can be
captured by selecting the "right" term structure model itself.
For example, normal distribution is widely perceived today as the most
suitable model for swap rates, therefore, the model of Hull and White
can be employed. We highly recommend using this model with a time-dependent
volatility function that can be calibrated to expiration terms ranging
from 3 months to 10 years. The underlying swap rate maturity terms can
be selected to best represent mortgage indices. The next exhibit compares
static valuation with a true OAV model.