The Fine-Structure of Volatility Feedback

26 Pages Posted: 11 Jun 2012

Date Written: June 11, 2012

Abstract

We attempt to unveil the fine structure of volatility feedback effects in the context of general quadratic autoregressive (QARCH) models, which assume that today's volatility can be expressed as a general quadratic form of the past daily returns. The standard ARCH or GARCH framework is recovered when the quadratic kernel is diagonal. The calibration of these models on US stock returns reveals several unexpected features. The off-diagonal (non ARCH) coefficients of the quadratic kernel are found to be highly significant both In-Sample and Out-of-Sample, but all these coefficients turn out to be one order of magnitude smaller than the diagonal elements. This confirms that daily returns play a special role in the volatility feedback mechanism, as postulated by ARCH models. The feedback kernel exhibits a surprisingly complex structure, incompatible with models proposed so far in the literature. Its spectral properties suggest the existence of volatility-neutral patterns of past returns. The diagonal part of the quadratic kernel is found to decay as a power-law of the lag, in line with the long-memory of volatility. Finally, QARCH models suggest some violations of Time Reversal Symmetry in financial time series, which are indeed observed empirically, although of much smaller amplitude than predicted. We speculate that a faithful volatility model should include both ARCH feedback effects and a stochastic component.

Keywords: volatility dynamics, GARCH models, endogenous feedback, time reversal invariance, stock markets

JEL Classification: G17, C13, C18, C32, C52

Suggested Citation

Chicheportiche, Rémy and Bouchaud, Jean-Philippe, The Fine-Structure of Volatility Feedback (June 11, 2012). Available at SSRN: https://ssrn.com/abstract=2081675 or http://dx.doi.org/10.2139/ssrn.2081675

Rémy Chicheportiche (Contact Author)

Ecole Centrale Paris ( email )

Paris
France

Jean-Philippe Bouchaud

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France
+33 1 49 49 59 20 (Phone)

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