This study investigates the lead-lag relationship between the price movements of VIX futures and VIX index levels. As a proxy for the futures, the front month VIX futures contract is used. A Johansen cointegration approach with a vector error correction model and Granger causality analysis are...

We study the pricing of shocks to uncertainty and volatility using a novel and wide-ranging set of options contracts. If uncertainty shocks are viewed as bad by investors, portfolios that hedge them should earn negative premia. Empirically, however, such portfolios have historically earned...

We study the pricing of uncertainty shocks using a wide-ranging set of options that reveal premia for macroeconomic risks. Portfolios hedging macro uncertainty have historically earned zero or even significantly positive returns, while those exposed to the realization of large shocks have earned...

We document a transaction level invariance relation among concurrent activity variables in the S&P 500 futures market: return volatility per transaction is proportional to the inverse of the squared expected trade size. It captures the time series behavior extremely well. Even more strikingly,...

Ex-ante estimates of the volatility premium embedded in VIX futures, known as the VIX premium, fall or stay flat when ex-ante measures of risk rise. This is not an artifact of mismeasurement: 1) Ex-ante premiums reliably predict ex-post returns to VIX futures with a coefficient near one, and 2)...