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The historically low interest rates experienced in 2003 have exposed some serious problems in the typical interest rate models, especially as applied to evaluating mortgage securities. This is serious, as many investors rely heavily on option-adjusted spread models to make asset allocation decisions between mortgages and other instruments, as well as relative value decisions within the mortgage market.
In this article we discuss the distortions in OAS modeling. We show in the first part that it is wrong to assume, as most models do, an interest rate process based on a lognormal interest rate distribution (volatility measured in percentages is constant). Basically, interest rates do not behave as if they follow a lognormal distribution. In fact, they behave with a non-linear rate directionality. Incorporating this directionality allows for a very robust description of the term structure of volatility, as well as for skewness to occur naturally.
We then apply those results, showing that using a typical lognormal distribution means that at low rate levels such as those prevailing in mid-2003, rates will be too high along high rate paths.
The practical implications of this analysis are that lognormal models result in fixed-rate durations that are too long and caps that are valued way too high, making floaters appear to be misleadingly rich in OAS models.
In the second part of the article, we model mortgage current-coupon rates. We show that the correlation between interest rates and volatility and mortgage spreads means that the negative convexity of mortgage instruments, as measured by OAS models, is overstated. Beyond the OAS modeling of mortgages, we discuss incorporation of the directionality of mortgage spreads into our favorite regression-based relative value models to make them even more powerful.
Our conclusion: Investors need to think long and hard about how they use OAS numbers in portfolio management.
I. OAS MODELING
Typically, OAS numbers are calculated using a Monte Carlo simulation that captures a bond's performance over a range of scenarios. In Monte Carlo simulation, a large number of interest rate paths are chosen from an interest rate distribution centered on forward rates. Cash flows for the mortgage securities are determined using a prepayment model, which gives prepayment rates at each node along each path. The OAS is the spread at...