### Abstract

This article provides a data-driven analysis of the volatility risk premium, using tools from high-frequency finance and Big Data analytics. We argue that the volatility risk premium, loosely defined as the difference between realized and implied volatility, can best be understood when viewed as a systematically priced bias. We first use ultra-high-frequency transaction data on SPDRs and a novel approach for estimating integrated volatility on the frequency domain to compute realized volatility. From that we subtract the daily VIX, our measure of implied volatility, to construct a time series of the volatility risk premium. To identify the factors behind the volatility risk premium as a priced bias, we decompose it into magnitude and direction. We find compelling evidence that the magnitude of the deviation of the realized volatility from implied volatility represents supply and demand imbalances in the market for hedging tail risk. It is difficult to conclusively accept the hypothesis that the direction or sign of the volatility risk premium reflects expectations about future levels of volatility. However, evidence supports the hypothesis that the sign of the volatility risk premium is indicative of gains or losses on a delta-hedged portfolio.

Original language | English (US) |
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Pages (from-to) | 519-535 |

Number of pages | 17 |

Journal | Journal of Business and Economic Statistics |

Volume | 34 |

Issue number | 4 |

DOIs | |

State | Published - Oct 1 2016 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Social Sciences (miscellaneous)
- Economics and Econometrics
- Statistics, Probability and Uncertainty

### Keywords

- Big Data risk analytics
- Fourier transform
- Integrated volatility
- Microstructure noise
- Tail risk
- Ultra-high-frequency data
- Volatility risk premium

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## Cite this

*Journal of Business and Economic Statistics*,

*34*(4), 519-535. https://doi.org/10.1080/07350015.2016.1152968