Volatility Jumps

26 Pages Posted: 31 Jul 2008

Date Written: May 6, 2008

Abstract

The paper undertakes a non-parametric analysis of the very high frequency movements in stock market volatility using very finely sampled data on the S&P VIX index compiled by the CBOE. The data suggest that stock market volatility is best described as a pure jump process without a continuous component. The finding stands in contrast to nonparametric results, reported here and elsewhere, that the stock price itself is not a pure jump process but rather contains a continuous martingale component. The jumps in stock volatility are found to be so active that this discredits many recently proposed stochastic volatility models, including the classic affine model with compound Poisson jumps that is widely used in financial modeling and practice. Additional empirical work presents strong evidence for many common jumps, or co-jumps, in both the stock price and stock volatility.

Keywords: Stochastic volatility, activity index, Blumenthal-Getoor index, jumps, VIX index, jump risk premium

JEL Classification: C22, C51, C52, G12, G13, G14

Suggested Citation

Todorov, Viktor and Tauchen, George E., Volatility Jumps (May 6, 2008). Economic Research Initiatives at Duke (ERID) Working Paper No. 3, Available at SSRN: https://ssrn.com/abstract=1188509 or http://dx.doi.org/10.2139/ssrn.1188509

Viktor Todorov

Northwestern University ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

George E. Tauchen (Contact Author)

Duke University - Economics Group ( email )

Box 90097
221 Social Sciences
Durham, NC 27708-0097
United States
919-660-1812 (Phone)
919-684-8974 (Fax)

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