International evidence on alternative models of the term structure of volatilities

The term structure of instantaneous volatilities (TSV) of forward rates for different monetary areas (euro, U.S. dollar and British pound) is examined using daily data from at‐the‐money cap markets. During the sample period (two and a half years), the TSV experienced severe changes both in level and shape. Two new functional forms of the instantaneous volatility of forward rates are proposed and tested within the LIBOR Market Model framework. Two other alternatives are calibrated and used as benchmarks to test the accuracy of the new models. The two new models provide more flexibility to adequately calibrate the observed cap prices, although this improved accuracy in replicating cap prices produces some instability in parameter estimates. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:653–683, 2009