Using the right implied volatility quotes in times of low interest rates: An empirical analysis across different currencies

Negative rates directly impact the pricing and quoting of debt instruments, both guided by underlying rate models grounded in the assumption of nonnegative rates. In this paper, we calibrate three short-rate models - Hull-White, shift-extended Cox-Ingersoll-Ross, and shift-extended squared Gaussian - to negative rates environment. We use different market quotation methods for swaptions including Black, Bachelier, and shifted log-normal volatilities quoted for different currencies, specifically EUR, USD, GBP, and JPY. Our results suggest that the models studied can be effectively recalibrated in negative interest rate environments and that both existing and new quotation conventions are able to produce adequate calibration results.