Historical Yield Curve Scenarios Generation without Resorting to Variance Reduction Techniques

We propose a multivariate nonparametric technique for generating reliable scenarios and confidence intervals for the term structure of interest rates from historical data. The approach is based on a functional gradient descent (FGD) estimation of the conditional mean vector and the conditional volatility matrix of a multivariate interest rate series. The methodology is computationally feasible in large dimensions and avoids the use of variance reduction techniques like for instance principle components analysis. Moreover, it can account for a non-linear time series dependence of interest rates at all available maturities. Based on theestimated FGD terms structure dynamics we apply filtered historical simulation to compute out-of-sample term structure scenarios and confidence intervals. We apply our methodology to daily USD bond data and back-test its out-of-sample accuracy for forecasting horizons from 1 to 10 days. When compared with some further scenario generating technologies based on principal components, a multivariate CCC-GARCH model, or the exponential smoothing volatility forecasting technique used by the RiskMetricsTM approach, we find empirical evidence of a clearly higher predictive potential of FGD-based scenarios generating techniques. Specifically, at forecasting horizons of one day FGD provided accurate multivariateVaR computations for times to maturity between one month and thirty years. For longer horizons (i.e. ten days) accurate VaR predictions are obtained for times to maturity between roughly one and thirty years.