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Report
The Law of One Price in Equity Volatility Markets
This paper documents law of one price violations in equity volatility markets. While tightly linked by no-arbitrage restrictions, the prices of VIX futures exhibit significant deviations relative to their option-implied upper bounds. Static arbitrage opportunities occur when the prices of VIX futures violate their bounds. The deviations widen during periods of market stress and predict the returns of VIX futures. A relative value trading strategy based on the deviation measure earns a large Sharpe ratio and economically significant alpha-to-margin. There is evidence that systematic risk and ...
Working Paper
The Effects of Asymmetric Volatility and Jumps on the Pricing of VIX Derivatives
This paper proposes a new collection of affine jump-diffusion models for the valuation of VIX derivatives. The models have two distinctive features. First, we allow for a positive correlation between changes in the VIX and in its stochastic volatility to accommodate asymmetric volatility. Second, upward and downward jumps in the VIX are separately modeled to accommodate the possibility that investors react differently to good and bad surprises. Using the VIX futures and options data from July 2006 through January 2013, we find conclusive evidence for the benefits of including both asymmetric ...
Discussion Paper
The Law of One Price in Equity Volatility Markets
Can option traders take a square root? Surprisingly, maybe not. This post shows that VIX futures prices exhibit significant deviations from their option-implied upper bounds—the square root of variance swap forward rates—thus violating the law of one price, a fundamental concept in economics and finance. The deviations widen during periods of market stress and predict the returns of VIX futures. Just as the stock market struggles with multiplication, the equity volatility market appears unable to take a square root at times.
Discussion Paper
Equity Volatility Term Premia
Investors can buy volatility hedges on the stock market using variance swaps or VIX futures. One motivation for hedging volatility is its negative relationship with the stock market. When volatility increases, stock returns tend to decline contemporaneously, a result known as the leverage effect. In this post, we measure the cost of volatility hedging by decomposing the prices of variance swaps and VIX futures into volatility forecasts and estimates of expected returns (“equity volatility term premia”) from January 1996 to June 2020.
Report
Equity Volatility Term Premia
This paper estimates the term-structure of volatility risk premia for the stock market. Realized variance term premia are increasing in systematic risk and predict variance swap returns. Implied volatility term premia are decreasing in risk initially, but then increase at a lag, predicting VIX futures returns. By modeling the logarithm of realized variance, the paper derives a closed-form relationship between the prices of variance swaps and VIX futures. The model provides accurate pricing and highlights periods of dislocation between the index options and VIX futures markets. Term premia ...