Assessing the Compensation for Volatility Risk Implicit in Interest Rate Derivatives

Volatilities implied from interest rate swaptions are used to assess the size and the sign of the compensation for volatility risk, for dollar, euro and pound rates at a daily frequency, between October 1998 and August 2006. The measurement of the volatility risk premium rests on a simple model according to which variance forecasts are generated under the objective probability measure. Results show that especially between September 2001 and mid-2003 dollar implieds were embodying a large - negative - compensation for volatility risk, a component which was smaller in absolute terms - but not relative to the level of the respective implied volatilities - for the other two currencies. While the negative compensation for volatility risk is in line with previous studies focusing on other asset classes, we also document that it exhibits a term structure, more evident for dollar and euro rates than for pound rates. The volatility risk premium is strongly changing through time but much less than implied volatilities. Estimates of risk aversion based on the physical skewness and kurtosis of interest rate changes suggest that (minus) the volatility risk premium can almost directly be read as risk aversion, as its proportionality with such risk aversion measure is about 0.8. Also, compensation for volatility risk is positively related to expected volatility, although the relation is not completely linear. Daily compensation for volatility risk is influenced, as expected, by the level of the short term rate and its volatility as well as by a small but robust number of macroeconomic surprises. The latter induce more sizeable changes on compensation for volatility risk of dollar rates than of euro or pound rates