Didier Sornette: Endogenous vs Exogenous Crashes in Financial Markets

Abstract (Via ARXIV)

In a series of papers based on analogies with statistical physics models, we have proposed that most financial crashes are the climax of so-called log-periodic power law signatures (LPPS) associated with speculative bubbles [Sornette and Johansen, 1998, Johansen and Sornette, 1999, Johansen et al., 1999, Johansen et al., 1999, Sornette and Johansen, 2001]. In addition, a large body of empirical evidence supporting this proposition have been presented [Sornette et al., 1996, Sornette and Johansen, 1998, Johansen et al., 1999, Johansen and Sornette, 2000,Johansen and Sornette, 2001b, Sornette and Johansen, 2001]. Along a complementary line of research, we have established that, while the vast majority of drawdowns occurring on the major financial markets have a distribution which is well-described by a stretched exponential, the largest drawdowns are occurring with a significantly larger rate than predicted by extrapolating the bulk of the distribution and should thus be considered as outliers [Johansen and Sornette, 1998, Sornette and Johansen, 2001, Johansen and Sornette, 2001b, Johansen, 2002]. Here, these two lines of research are merged in a systematic way to offer a classification of crashes as either events of an endogenous origin associated with preceding speculative bubbles or as events of an exogenous origin associated with the markets response to external shocks.

We first perform an extended analysis of the distribution of drawdowns in the two leading exchange markets (US dollar against the Deutsmark and against the Yen), in the major world stock markets, in the U.S. and Japanese bond market and in the gold market, by introducing the concept of “coarse-grained drawdowns,” which allows for a certain degree of fuzziness in the definition of cumulative losses and improves on the statistics of our previous results. Then, for each identified outlier, we check whether LPPS are present and take the existence of LPPS as the qualifying signature for an endogenous crash: this is because a drawdown outlier is seen as the end of a speculative unsustainable accelerating bubble generated endogenously. In the absence of LPPS, we are able to identify what seems to have been the relevant historical event, i.e., a new piece of information of such magnitude and impact that it is seems reasonable to attribute the crash to it, in agreement with the standard view of the efficient market hypothesis. Such drawdown outliers are classified as having an exogenous origin. Globally over all the markets analyzed, we identify 49 outliers, of which 25 are classified as endogenous, 22 as exogeneous and 2 as associated with the Japanese anti-bubble. Restricting to the world market indices, we find 31 outliers, of which 19 are endogenous, 10 are exogenous and 2 are associated with the Japanese anti-bubble. The combination of the two proposed detection techniques, one for drawdown outliers and the second for LPPS, provides a novel and systematic taxonomy of crashes further subtantiating the importance of LPPS.

Conclusion Excerpted (Via Arxiv)

By combining the statistical evidence of two methods, that is, the analysis of financial data from the point of view of detecting (i) anomalous events seen as outliers to the parameterization (3) and (ii) accelerating log-periodic power laws quantified by eq.(1) with values of ω and z satisfying (2) qualifying endogenous speculative bubble, we have provided an objective test of the hypothesis that the largest negative markets moves are special and form two distinct populations. The exogenous crashes can be attributed to extraordinary important external perturbations and/or news impacting the market. The endogenous crashes can be seen as the natural deaths of self-organized self-reinforcing speculative bubbles giving rise to specific precursory signatures in the form of log-periodic power laws accelerating super-exponentially.

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22. October 2009 by Miguel Barbosa
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