Options on crude oil futures are the most actively traded commodity options. We develop a class of computationally … efficient discrete-time jump models that allow for closed-form option valuation, and we use crude oil futures and options data … crucial for modeling crude oil futures and futures options, and we find evidence in favor of time-varying jump intensities …

Ex-ante estimates of the volatility premium embedded in VIX futures, known as the VIX premium, fall or stay flat when …-post returns to VIX futures with a coefficient near one, and 2) Falling ex-ante premiums predict increasing ex-post market and … investment risk, creating profitable trading opportunities. Falling hedging demand helps explain this behavior, as premiums and …

The illiquidity of long-maturity options has made it difficult to study the term structures of option spanning …

, and products, including variance swaps, straddles, and VIX futures. In addition, the paper derives a closed …-form relationship between the prices of variance swaps and VIX futures. While tightly linked, VIX futures exhibit deviations of varying … and their relationship to VIX futures' return predictability. …

hedging errors. In the empirical application, we synthesize the prices of the variance contract on S&P 500 index over the …

-of-volatility measures, identified model-free from options data as the VIX and VVIX indices, respectively, are only weakly related to each …