Inferring Volatility from the Yield Curve

Abstract

In this paper, we assess how to recover the volatility of interest rates in the euro area money market, on the sole basis of the zero-coupon yield curve. Our primary result is that there exists an empirical regularity (linking rates and volatility) that takes a relatively simple mathematical form. We also show that the existence of such regularity cannot be explained by a reasoning based on the hypothesis of absence of opportunities of arbitrage since a continuous-time arbitrage-free model may produce instances of curves that are consistent with a continuum of level of volatilities. We exhibit an example for this.