A Practical Stochastic Model for Projecting Nominal Interest Rates in a Monte Carlo Setting

Abstract

We present a real-world stochastic projection of nominal interest rate curves intended to integrate with Monte Carlo economic scenario generators. The model projects three time-varying parameters arising from a singular value decomposition of transformed historic interest rates, rather than modelling tenor points directly. A key feature is that we devise an empirically-motivated, rather than an assumed convenient form, transform function to apply to interest rates before performing the decomposition. This choice reflects an observed relationship between the volatility and level of interest rates. The resulting time-varying parameters, which we call time components, are projected as mean-reverting arithmetic random walks with mean reversion strength calibrated to historic behaviour. The drift of the model is adjusted so that the mean average of discount factors across simulations is in line with initial market-implied expectations. This adjustment preserves the required relationship between the level and the volatility of interest rates.