The Impact of Jumps in Volatility and Returns

Authors

  • Bjørn Eraker,

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    • Eraker is at the Economics Department, Duke University; Johannes is at the Graduate School of Business, Columbia University; and Polson is at the Graduate School of Business, University of Chicago. For helpful comments, we thank David Bates, Mike Chernov, Paul Conway, Anne Gron, Lars Hansen, an anonymous referee, and seminar participants at the 2001 Western Finance Assocation conference, Columbia, Duke, NYU, and Wharton. Rob Engle deserves special thanks for his discussion of the paper. All remaining errors are our own.
  • Michael Johannes,

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    • Eraker is at the Economics Department, Duke University; Johannes is at the Graduate School of Business, Columbia University; and Polson is at the Graduate School of Business, University of Chicago. For helpful comments, we thank David Bates, Mike Chernov, Paul Conway, Anne Gron, Lars Hansen, an anonymous referee, and seminar participants at the 2001 Western Finance Assocation conference, Columbia, Duke, NYU, and Wharton. Rob Engle deserves special thanks for his discussion of the paper. All remaining errors are our own.
  • Nicholas Polson

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    • Eraker is at the Economics Department, Duke University; Johannes is at the Graduate School of Business, Columbia University; and Polson is at the Graduate School of Business, University of Chicago. For helpful comments, we thank David Bates, Mike Chernov, Paul Conway, Anne Gron, Lars Hansen, an anonymous referee, and seminar participants at the 2001 Western Finance Assocation conference, Columbia, Duke, NYU, and Wharton. Rob Engle deserves special thanks for his discussion of the paper. All remaining errors are our own.

Abstract

This paper examines continuous-time stochastic volatility models incorporating jumps in returns and volatility. We develop a likelihood-based estimation strategy and provide estimates of parameters, spot volatility, jump times, and jump sizes using S&P 500 and Nasdaq 100 index returns. Estimates of jump times, jump sizes, and volatility are particularly useful for identifying the effects of these factors during periods of market stress, such as those in 1987, 1997, and 1998. Using formal and informal diagnostics, we find strong evidence for jumps in volatility and jumps in returns. Finally, we study how these factors and estimation risk impact option pricing.

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