VIX futures are exchange-traded contracts on a future volatility index (VIX) level derived from a basket of S&P 500 (SPX) stock index options. The authors posit a stochastic variance model of VIX time evolution, and develop an expression for VIX futures. Free parameters are estimated from market data over the past few years. It is found that the model with parameters estimated from the whole period from 1990 to 2005 overprices the futures contracts by 16-44%. But the discrepancy is dramatically reduced to 2-12% if the parameters are estimated from the most recent one-year period.

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In this study we empirically study the variance term structure using volatility index (VIX) futures market. We first derive a new pricing framework for VIX futures, which is convenient to study variance term structure dynamics. We construct five models and use Kalman filter and maximum likelihood method for model estimations and comparisons. We provide evidence that a third factor is statistically significant for variance term structure dynamics. We find that our parameter estimates are robust and helpful to shed light on economic significance of variance factor model.

What predicts returns on assets with “hard‐to‐value” fundamentals such as Bitcoin and stocks in new industries? We are the first to propose an equilibrium model that shows how technical analysis can arise endogenously via rational learning, providing a theoretical foundation for using technical analysis in practice. We document that ratios of prices to their moving averages forecast daily Bitcoin returns in and out of sample. Trading strategies based on these ratios generate an economically significant alpha and Sharpe ratio gains relative to a buy‐and‐hold position. Similar results hold for small‐cap, young‐firm, and low analyst‐coverage stocks as well as NASDAQ stocks during the dotcom era.