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Tails, Fears and Risk Premia

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  • Tim Bollerslev

    (Department of Economics, Duke University, Durham and CREATES)

  • Viktor Todorov

    (Department of Finance, Kellogg School of Management, Northwestern University)

Abstract

We show that the compensation for rare events accounts for a large fraction of the equity and variance risk premia in the S&P 500 market index. The probability of rare events vary significantly over time, increasing in periods of high market volatility, but the risk premium for tail events cannot solely be explained by the level of the volatility. Our empirical investigations are essentially model-free. We estimate the expected values of the tails under the statistical probability measure from "medium" size jumps in high-frequency intraday prices and an extreme value theory approximation for the corresponding jump tail density. Our estimates for the risk-neutral expectations are based on short maturity out-of-the money options and new model-free option implied variation measures explicitly designed to separate the tail probabilities. At a general level, our results suggest that any satisfactory equilibrium based asset pricing model must be able to generate large and time-varying compensations for fears of disasters.

Suggested Citation

  • Tim Bollerslev & Viktor Todorov, 2009. "Tails, Fears and Risk Premia," CREATES Research Papers 2009-26, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2009-26
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    More about this item

    Keywords

    rare events; jumps; high-frequency data; options; fears; extreme value theory; equity risk premium; variance risk premium;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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