The Curious Case of Backward Short Rates

In this paper, we discuss how to discretize continuous-time short rate models in order to properly handle backward-looking interest rate derivatives. We show that the popular discretization approaches are based on forward-looking one-period rates, making them intrinsically ill-suited to deal with backward-looking rates. We propose a simple backward discretization approach that is beneficial when dealing with both backward-looking and forward-looking interest rate derivatives.