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Essays on variance risk, jump risk and options information

Jian Du, University of Massachusetts Amherst


Both volatility and the tail of the stock return distribution are impacted by discontinuities ("large jumps") in the stock price process. In the first chapter, "The Tail in the Volatility Index"1, we construct model-free volatility and tail indexes in a manner that clearly distinguishes one from the other. Our tail index measures time-variation in jump intensity, and is constructed non-parametrically from the identical set of 30-day index options used to construct a volatility index. We use the indexes to examine the economic importance of volatility and the tail in predicting market returns over 1996–2011. We find that discontinuities predict market returns through both potential channels, volatility and tail risk, respectively. In the second chapter, "The Pricing of Market Risks in Equity Options: Evidence From Individual Variance Risk Premiums", I examine the pricing of market level risks in equity options by studying the model-free individual variance risk premiums (VRP) constructed from options and stocks data. I document significant empirical findings that a positive market equity risk premium, a negative market variance risk premium, and a negative market jump risk premium are priced in the cross-section of individual VRPs. The results are robust after controlling for firm-level variables, including firm size, book-to-market ratio, momentum, stock illiquidity, idiosyncratic volatility and options trading volume. I propose a non-parametric way to decompose the individual VRPs into three components: the common unexplained component, the systematic exposure component, and the idiosyncratic component. I find that the (conditional) common unexplained component is significantly negative and time varying, and it strongly predicts future 6-month to 2-year stock market return and future 3-month to 2-year growth of economic activities. My findings support a missing risk factor story and suggest that the cross-section of individual VRPs can be understood as risk premiums rather than mispricing. In the last chapter, "Option Trading Activities and the Future Stock Returns", I present empirical finding that the trading activities in equity options market contain information about future stock movement. I test two variables of options trading activities, the aggregate options trading volume (volume) and the call-put ratio from options volume (C/P). Stocks with low volume outperform stocks with high volume; stocks with high C/P outperform stocks with low C/P. The predictability is strong with both economical and statistical significance; it is present when I track future stock returns from one week up to two months. I find stronger predictability for stocks with lower liquidity in the equities market. The results are robust when I control for firm size, firm book-to-market ratio, previous stock return and previous stock variance, or when I control for the effect of earnings announcements. Considering that the volume and C/P are publicly observable, my results question the market efficiency across options market and equities market. 1The first chapter, "The Tail in the Volatility Index", is co-authored with Nikunj Kapadia.

Subject Area


Recommended Citation

Du, Jian, "Essays on variance risk, jump risk and options information" (2012). Doctoral Dissertations Available from Proquest. AAI3545919.