Realizing stock market crashes: stochastic cusp catastrophe model of returns under the time-varying volatility
This paper develops a two-step estimation methodology, which allows us to apply catastrophe theory to stock market returns with time-varying volatility and model stock market crashes. Utilizing high frequency data, we estimate the daily realized volatility from the returns in the first step and use stochastic cusp catastrophe on data normalized by the estimated volatility in the second step to study possible discontinuities in markets. We support our methodology by simulations where we also discuss the importance of stochastic noise and volatility in deterministic cusp catastrophe model. The methodology is empirically tested on almost 27 years of U.S. stock market evolution covering several important recessions and crisis periods. Due to the very long sample period we also develop a rolling estimation approach and we find that while in the first half of the period stock markets showed marks of bifurcations, in the second half catastrophe theory was not able to confirm this behavior. Results suggest that the proposed methodology provides an important shift in application of catastrophe theory to stock markets.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Shaffer, Sherrill, 1991.
"Structural shifts and the volatility of chaotic markets,"
Journal of Economic Behavior & Organization,
Elsevier, vol. 15(2), pages 201-214, March.
- Sherrill Shaffer, 1988. "Structural shifts and the volatility of chaotic markets," Working Papers 88-17, Federal Reserve Bank of Philadelphia.
- Tim Bollerslev, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
EERI Research Paper Series
EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
- Cobb, Loren, 1980. "Estimation Theory for the Cusp Catastrophe Model," MPRA Paper 37548, University Library of Munich, Germany, revised 05 Jun 2010.
- Ho, Thomas S Y & Saunders, Anthony, 1980. " A Catastrophe Model of Bank Failure," Journal of Finance, American Finance Association, vol. 35(5), pages 1189-1207, December.
- Levy, Moshe, 2008. "Stock market crashes as social phase transitions," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 137-155, January.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001.
"Modeling and Forecasting Realized Volatility,"
NBER Working Papers
8160, National Bureau of Economic Research, Inc.
- Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2003.
"A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data,"
NBER Working Papers
10111, National Bureau of Economic Research, Inc.
- Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
- Gerard Gennotte and Hayne Leland., 1989.
"Market Liquidity, Hedging and Crashes,"
Research Program in Finance Working Papers
RPF-192, University of California at Berkeley.
- Zeeman, E. C., 1974. "On the unstable behaviour of stock exchanges," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 39-49, March.
- Raoul Grasman & Han L.J. van der Maas & Eric-Jan Wagenmakers, . "Fitting the Cusp Catastrophe in R: A cusp Package Primer," Journal of Statistical Software, American Statistical Association, vol. 32(i08).
- Lux, Thomas & Marchesi, Michele, 2002. "Journal of economic behavior and organization: special issue on heterogeneous interacting agents in financial markets," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 143-147, October.
- Balasko, Yves, 1978. "Economic Equilibrium and Catastrophe Theory: An Introduction," Econometrica, Econometric Society, vol. 46(3), pages 557-69, May.
- Barlevy, Gadi & Veronesi, Pietro, 2003.
"Rational panics and stock market crashes,"
Journal of Economic Theory,
Elsevier, vol. 110(2), pages 234-263, June.
- Rosser Jr., J. Barkley, 2007. "The rise and fall of catastrophe theory applications in economics: Was the baby thrown out with the bathwater?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3255-3280, October.
- Levy, Moshe & Levy, Haim & Solomon, Sorin, 1994. "A microscopic model of the stock market : Cycles, booms, and crashes," Economics Letters, Elsevier, vol. 45(1), pages 103-111, May.
- Sornette, Didier & Johansen, Anders, 1998. "A hierarchical model of financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 581-598.
- Fischer, Edwin O & Jammernegg, Werner, 1986. "Empirical Investigation of a Catastrophe Theory Extension of the Phillips Curve," The Review of Economics and Statistics, MIT Press, vol. 68(1), pages 9-17, February.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1302.7036. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
If references are entirely missing, you can add them using this form.