Generating Historically‐Based Stress Scenarios Using Parsimonious Factorization

We describe an empirical approach to generating plausible historically‐based interest rate shocks, which can be applied to any market environment and readily linked to movements in other key risk factors. Our approach is based upon yield curve parameterization and requires a parsimonious yet flexible factorization model. In the process of selecting a model, we evaluate three variants of the Nelson‐Siegel approach to yield curve approximation and find that, in the current low interest rate environment, a 5‐factor parameterization developed by Bjork and Christensen (1999) is best suited for accurately translating historical interest rate movements into plausible, current period shocks. Using the Bjork‐Christensen model, we parameterize a time series of historical yield curves and measure interest rate shocks as the historical change in each of the model's factors. We then demonstrate how to add these parameterized shocks to any market environment, while retaining positive rates and plausible credit spreads. Given a set of shocked interest rate curves, joint risk factor movements are calculated based upon historical, reduced form dependencies