Author:

Keywords:

Comonotonicity, systemic risk, correlation, VIX volatility index

Abstract:

We introduce a new and easy to calculate measure for systemic risk in financial markets. This measure is baptized the Herd Behavior Index (HIX). It is model-independent and forward looking, based on observed option data. In order to determine the degree of systemic risk or herd behavior in a financial market one should compare the observed market situation with the extreme (theoretical) situation under which the whole system is driven by a single factor. The Herd Behavior Index (HIX) is defined as the ratio of an option-based estimate of the risk-neutral variance of the market index and an option-based estimate of the corresponding variance of this extreme market situation. Using the theory of comonotonicity, the extreme situation can easily be backed out of the observed option quotes. The HIX can be determined for any market index provided an appropriate series of vanilla options is traded on this index as well as on its components. As an illustration, we determine historical values of the 30-days implied Herd Behavior Index for the Dow Jones Industrial Average, covering the period January 2003 to October 2009.