Universal regimes for rates and inflation: the effect of local elasticity on market and counterparty risk

The dependence of interest rate volatility on the level of rates has both general macroeconomic significance and direct consequences on computing market risk metrics such as VAR, SVAR or ES, and counterparty credit risk modelling. Such dependence is investigated and viewed in terms of local elasticity. A new regime at low and negative rates with volatility independent of the level of the rates is found, and three other regimes reported by Deguillaume et al. (The nature of the dependence of the magnitude of rate moves on the rates levels: A universal relationship. Quant. Financ., 2013, 13(3), 351–367] are confirmed with more recent data and a larger pool of currencies. A preliminary study into the existence of regimes for break-even inflation is also conducted and indications of regimes are found. One of these regimes has no equivalence in interest rates; it exhibits negative elasticity slope which may imply a similar regime if rate levels also reach sufficiently negative values. The overall shape of inflation elasticity resembles a strangle payoff, and we hypothesise that this directly reflects markets’ response to macroeconomic policy of inflation targeting and also indirectly links such policy to the nominal rate regimes. We demonstrate that the incorporation of such regimes in market risk modelling improves its predictive capacity, and for counterparty risk modelling has significant impact on risk and regulatory calculations.