Neither “Normal” nor “Lognormal”: Modeling Interest Rates across All Regimes

We introduce a simple approach to managing portfolio interest rate risk that is consistent and performs well across different interest rate regimes, including when interest rates are low or even negative. Inspired by Fischer Black, this approach uses a novel “inverse-call transformation” methodology to convert interest rates into “shadow rates.” We show that this methodology is more appropriate than the standard “normal” and “lognormal” models for forecasting and managing the distribution of the profits and losses of portfolios affected by the term structure of interest rates, producing more reliable forecasts and thus risk estimates for purposes of both internal and regulatory risk management.