The Impact of Jumps in Volatility and Returns
Michael S. Johannes
Columbia Business School - Finance and Economics
University of Wisconsin - Madison - Department of Finance, Investment and Banking
University of Chicago - Booth School of Business
November 1, 2000
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.
Number of Pages in PDF File: 47
Keywords: Jumps, Stochastic Volatility, Continuous-Time Econometrics, Option Pricing, Market Stress
Date posted: January 1, 2001
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