Significance of log-periodic precursors to financial crashes

By Didier Sornette, Anders Johansen. 2001

227 citations recorded by the source corpus.

We clarify the status of log-periodicity associated with speculative bubbles preceding financial crashes. In particular, we address Feigenbaum's criticism ([A article="1469-7688/1/3/306"] Feigenbaum J A 2001 Quantitative Finance 1 346-60 [/A]) and show how it can be refuted. Feigenbaum's main result is as follows: 'the hypothesis that the log-periodic component is present in the data cannot be rejected at the 95% confidence level when using all the data prior to the 1987 crash; however, it can be rejected by removing the last year of data' (e.g. by removing 15% of the data closest to the critical point). We stress that it is naive to analyse a critical point phenomenon, i.e., a power-law divergence, reliably by removing the most important part of the data closest to the critical point. We also present the history of log-periodicity in the present context explaining its essential features and why it may be important. We offer an extension of the rational expectation bubble model for general and arbitrary risk-aversion within the general stochastic discount factor theory. We suggest guidelines for the use of log-periodicity and explain how to develop and interpret statistical tests of log-periodicity. We discuss the issue of prediction based on our results and the evidence of outliers in the distribution of drawdowns. New statistical tests demonstrate that the 1% to 10% quantile of the largest events of the population of drawdowns of the NASDAQ composite index and of the Dow Jones Industrial Average index belong to a distribution significantly different from the rest of the population. This suggests that very large drawdowns may result from an amplification mechanism that may make them more predictable.

Subfields: Computational Theory and Mathematics, Economics and Econometrics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/1fd8ffd1d38976144693688f7d43e8671a79b1d0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Didier Sornette
2. Vladimir Filimonov
3. Dimitrije Marković
4. Claudius Gros
5. Wei‐Xing Zhou
6. Anders Johansen

In Economics and Econometrics

1. Didier Sornette
2. Wei‐Xing Zhou
3. Ryan Woodard
4. Vladimir Filimonov
5. Anders Johansen
6. Wanfeng Yan
7. Dimitrije Marković
8. Claudius Gros

In Management Science and Operations Research

1. Didier Sornette
2. Vladimir Filimonov
3. Dimitrije Marković
4. Claudius Gros
5. Wei‐Xing Zhou
6. Anders Johansen

Citations in the corpus

• Shocks, Crashes and Bubbles in Financial Markets (2010, background): “…as well as emergent markets present the following characteristics (Johansen et al., 1999; Johansen and Sornette, 1999; Johansen et al., 2000; Sornette and Johansen, 2001): (i) a super-exponential overall acceleration of the price quantified by a power law in the time to the end of the…”
• Clarifications to questions and criticisms on the Johansen–Ledoit–Sornette financial bubble model (2011, result): “And they note that many of the case studies reported in Johansen and Sornette [36] and in Sornette and Johansen [62] have their LPPL fits that exhibit a negative slope some of the time.”
• Is there a real-estate bubble in the US? (2005, background): “Gh, 89.90.+n”
• A Stable and Robust Calibration Scheme of the Log-Periodic Power Law Model (2011, methodology): “The determination of the global minimum requires using some metaheuristic methods such as taboo search [6, 8] or genetic algorithm [9].”
• Dragon-Kings, Black Swans and the Prediction of Crises (2009, background): “Reproduced from Sornette and Johansen [32].”
• Critical Market Crashes (2003, unknown): “…already been used in practice and is investigated by our co-workers and us as well as several others, academics and most-of-all practitioners (see Sornette and Johansen, 2001, and Johansen and Sornette, 2002, for a recent review and assessment and Zhou and Sornette, 2002a, b, c for nonparametric…”
• Power laws and Self-Organized Criticality in Theory and Nature (2013, methodology): “Johansen and Sornette [80] used the existence of a log-periodic precursors as an indicator for an impending material failure, and Sornette and Johansen [152] applied similar methods for the prediction of bursts of financial bubbles, that is, market crashes.”