The New Variation Method of Volatility Risk Premium

Integrated implied volatility is an expected quadratic variation that can be de-rived from European option prices under the risk neutral measure, whereas integrated realized volatility is a historical quadratic variation that can be derived from high-frequency ex-post stock returns under the physical measure. Earlier studies used the difference as the volatility risk premium and showed the premium was negative for buy-ers of options in most periods. Their method, however, has a filtration inconsistency problem when we evaluate an expected risk premium. This problem results from the difference of the filtration required for the computation of the two volatility estimates. We proposes a new method of evaluating the expected risk premium with consistent filtration. In our method, the premium is identified as the gap between the current integrated implied volatility and the integrated volatility estimated by a time series model of realized volatilities. We calculate the premium under the condition that the one-day realized volatility obeys either the Heston model or the ARFIMAX model. We found the premium based on our method correlates with market risk indicators, such as Citi Macro Risk Index or iTraxx Japan, more strongly than those based on the earlier works. This indicates our proposed measure of expected volatility risk premium reflects the market sentiment well and it is a valid indicator for the market risk aver-sion. As a byproduct, we can quantify the probability where the realized volatility goes below the implied volatility. This probability might also be an indicator for market’s volatility risk aversion.