The Impact of Jumps in Volatility and Returns

47 Pages Posted: 1 Jan 2001  

Michael S. Johannes

Columbia Business School - Finance and Economics

Bjorn Eraker

University of Wisconsin - Madison - Department of Finance, Investment and Banking

Nick Polson

University of Chicago - Booth School of Business

Multiple version iconThere are 2 versions of this paper

Date Written: November 1, 2000

Abstract

This paper examines a class of continuous-time models that incorporate jumps in returns and volatility, in addition to diffusive stochastic volatility. We develop a likelihood-based estimation strategy and provide estimates of model parameters, spot volatility, jump times and jump sizes using both S&P 500
and Nasdaq 100 index returns. Estimates of jumps times, jump sizes and volatility are particularly useful for disentangling the dynamic effects of these factors during periods of market stress, such as those in 1987, 1997 and 1998. Using both
formal and informal diagnostics, we find strong evidence for jumps in volatility, even after accounting for jumps in returns. We use implied volatility curves computed from option prices to judge the economic differences between the models. Finally, we
evaluate the impact of estimation risk on option prices and find that the uncertainty in estimating the parameters and the spot volatility has important, though very different, effects on option prices.

Keywords: Jumps, Stochastic Volatility, Continuous-Time Econometrics, Option Pricing, Market Stress

Suggested Citation

Johannes, Michael S. and Eraker, Bjorn and Polson, Nick, The Impact of Jumps in Volatility and Returns (November 1, 2000). Available at SSRN: https://ssrn.com/abstract=249764 or http://dx.doi.org/10.2139/ssrn.249764

Michael Slater Johannes (Contact Author)

Columbia Business School - Finance and Economics ( email )

3022 Broadway
New York, NY 10027
United States

Bjorn Eraker

University of Wisconsin - Madison - Department of Finance, Investment and Banking ( email )

975 University Avenue
Madison, WI 53706
United States

Nick Polson

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States
773-702-7513 (Phone)
773-702-0458 (Fax)

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