Short-Rate Models in a Negative Rates Regime: A Calibration Across Currencies

Abstract

Over the past few years, central banks around the world have implemented aggressive expansionary monetary policy regimes to combat the global recession. As a result, rates have fallen sharply, and in some cases have entered unprecedented negative territory. Negative rates directly impact the pricing and quoting of debt instruments, both guided by underlying rate models grounded in the assumption of nonnegative rates. To reevaluate both processes, Russo and Fabozzi (2017) recalibrate three short-rate models -- Hull-White, shift-extended Cox-Ingersoll-Ross, and shift-extended squared Gaussian -- that guide the pricing of rate derivatives using EUR swaption prices quoted under three market quotation styles. The market quotation methods examined include Black, Bachelier, and shifted log-normal; while Black is the market standard, the latter two have recently stemmed from a need to account for negative rates. This thesis seeks to extend the study to other currencies, specifically USD, GBP, and JPY, as the negative rates regime extends globally and models must be adapted specifically to each currency. The goal is twofold: 1) to analyze relative errors in calibration across market quotes, thereby determining the robustness of each convention in calibration, and 2) to derive the optimal value of model parameters. Our results are promising, and coincide with those of Russo and Fabozzi. The new parameters are derived with relatively similar errors across all quotation styles, suggesting that the models can be effectively recalibrated under negative rates and that both existing and new quotation conventions are able to produce adequate calibration results.