Assessing the compensation for volatility risk implicit in interest rate derivatives

We use the risk neutral volatilities which market participants use to price dollar, euro and pound swaptions to the aim of assessing the size and the sign of the daily compensation for interest rate volatility risk between October 1998 and August 2006. The measurement of the unobservable volatility risk premium rests on a simple garch model, which generates the parameters of the volatility process under the physical measure and produces paths of future volatilities, whose averages represent the realized volatility forecasts. Results show that interest rate volatility has embodied a large — negative — compensation for volatility risk, in line with other studies focusing on different asset classes. We also document that the volatility risk premium has exhibited a term structure across the analyzed maturity spectrum and that it has changed through time, but much less than risk neutral volatilities. Compensation for volatility risk is positively related to risk neutral volatility, although the relation is not completely linear, and it is influenced, as expected, by the level of the short term rate and its realized volatility. Also a small but robust number of macroeconomic surprises affect compensation for volatility risk, with macroeconomic uncertainty in one country spilling over to other currencies. Estimates of the risk aversion coefficient computed over the same sample as the volatility risk premium suggest that (minus) the volatility risk premium can be almost directly read as risk aversion.