Value at Risk for Interest Rate-Dependent Securities

Abstract

Value at risk (VaR) may be calculated for interest rate-dependent securities using an extension of a non-parametric estimator. The method here uses a two-dimensional kernel with adjustable bandwidth to model the risk as it changes with the level of interest rates. Since the variance, skewness, kurtosis, and higher moments of the distribution of interest rate changes are allowed to vary non-parametrically with the level of rates, the model produces dynamically changing boundaries of risk for VaR that are based only on the data and are independent of a modeler's choices. These VaR bounds are shown to be significantly better measures by a variety of criteria. The hit rates using the model presented here are generally more accurate than a GARCH specification in backtesting.