### Abstract

Actuaries manage risk, and asset price volatility is the most fundamental parameter in models of risk management. This study utilizes recent advances in econometric theory to decompose total asset price volatility into a smooth, continuous component and a discrete (jump) component. We analyze a data set that consists of high-frequency tick-by-tick data for all stocks in the S&P 100 Index, as well as similar futures contract data on three U.S. equity indexes and three U.S. Treasury securities during the period 1999-2005. We find that discrete jumps contribute between 15% and 25% of total asset risk for all equity index futures, and between 45% and 75% of total risk for Treasury bond futures. Jumps occur roughly once every five trading days for equity index futures, and slightly more frequently for Treasury bond futures. For the S&P 100 component stocks, on days when a jump occurs, the absolute jump is between 80% and 90% of the total absolute return for that day. We also demonstrate that, in the cross section of individual stocks, the average jump beta is significantly lower than the average continuous beta. Cross-correlations within the bond and stock markets are significantly higher on days when jumps occur, but stock-bond correlations are relatively constant regardless of whether or not a jump occurs. We conclude with a discussion of the implications of our findings for risk management.

Original language | English |
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Pages (from-to) | 76-91 |

Number of pages | 16 |

Journal | North American Actuarial Journal |

Volume | 11 |

Issue number | 4 |

State | Published - Oct 2007 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistics, Probability and Uncertainty
- Economics and Econometrics
- Statistics and Probability

### Cite this

*North American Actuarial Journal*,

*11*(4), 76-91.