Interest Rates—Normal or Lognormal?

Abstract

Interest rates do not behave as if they follow a lognormal interest rate distribution, as is typically assumed in option-adjusted spread models, but rather behave with non-linear rate directionality. Incorporating this directionality allows for a robust description of the term structure of volatility, and allows skewness to occur naturally. The typical lognormal distribution will result in fixed-rate durations that are too long and cap values that are too high. Correlation between interest rates and volatility and mortgage spreads means that the negative convexity of mortgage instruments as measured by OAS models is overstated. The directionality of mortgage spreads can be incorporated into regression-based relative value models to make them even more powerful.