How Do the Volatilities of Rates Depend on Their Level? The “Universal Relationship” Revisited

Abstract

We present a straightforward extension valid in the current negative-rate regime of the “universal relationship” uncovered in De Guillaume, Rebonato, and Pogudin (2013) between the level of rates and their volatility. We also provide an explanation of the origin of this relationship by showing the existence of two sharply distinct regimes for the volatility of real rates as a function of real rate levels, and by linking periods of high inflation with periods of high real rates. Finally, we provide evidence that the “volatility of volatility” also displays a “universal” behavior, with a significant linear dependence on the level of rates (and of the volatility itself).

TOPICS: Fixed income and structured finance, volatility measures, quantitative methods, statistical methods, developed markets

Key Findings

• ▪ The universal relationship, across currencies and tenors, between volatilities and the level of rates first presented in De Guillaume, Rebonato, and Pogudin (2013) also applies to the extremely-low-rate environment of the last decade, and we present a simple extension of the relationship to handle the case of negative rates.

• ▪ We explain the origin of this relationship by showing the existence of two sharply distinct regimes for the volatility of real rates as a function of real rate levels, and by linking periods of high inflation with periods of high real rates.

• ▪ We show that the “volatility of volatility” also displays a “universal” behaviour, with a significant linear dependence on the level of rates (and of the volatility itself).