The Nasdaq crash of April 2000: Yet another example of log-periodicity in a speculative bubble ending in a crash

The presence of log-periodic structures before and after stock market crashes is considered to be an imprint of an intrinsic discrete scale invariance (DSI) in this complex system. The fractal framework of the theory leaves open the possibility of observing self-similar log-periodic structures at different time scales. In the present work we analyze the daily closures of three of the most important indices worldwide since 2000: the DAX for Germany and the Nasdaq100 and the S&...

A phenomenon of the financial log-periodicity is discussed and the characteristics that amplify its predictive potential are elaborated. The principal one is self-similarity that obeys across all the time scales. Furthermore the same preferred scaling factor appears to provide the most consistent description of the market dynamics on all these scales both in the bull as well as in the bear market phases and is common to all the major markets. These ingredients set very desira...

We define a financial bubble as a period of unsustainable growth, when the price of an asset increases ever more quickly, in a series of accelerating phases of corrections and rebounds. More technically, during a bubble phase, the price follows a faster-than-exponential power law growth process, often accompanied by log-periodic oscillations. This dynamic ends abruptly in a change of regime that may be a crash or a substantial correction. Because they leave such specific trac...

Keeping a basic tenet of economic theory, rational expectations, we model the nonlinear positive feedback between agents in the stock market as an interplay between nonlinearity and multiplicative noise. The derived hyperbolic stochastic finite-time singularity formula transforms a Gaussian white noise into a rich time series possessing all the stylized facts of empirical prices, as well as accelerated speculative bubbles preceding crashes. We use the formula to invert the tw...

We document a well-developed log-periodic power-law antibubble in China's stock market, which started in August 2001. We argue that the current stock market antibubble is sustained by a contemporary active unsustainable real-estate bubble in China. The characteristic parameters of the antibubble have exhibited remarkable stability over one year (Oct. 2002-Oct. 2003). Many tests, including predictability over different horizons and time periods, confirm the high significance o...

A number of papers claim that a Log Periodic Power Law (LPPL) fitted to financial market bubbles that precede large market falls or 'crashes', contain parameters that are confined within certain ranges. The mechanism that has been claimed as underlying the LPPL, is based on influence percolation and a martingale condition. This paper examines these claims and the robustness of the LPPL for capturing large falls in the Hang Seng stock market index, over a 30-year period, inclu...

By combining (i) the economic theory of rational expectation bubbles, (ii) behavioral finance on imitation and herding of investors and traders and (iii) the mathematical and statistical physics of bifurcations and phase transitions, the log-periodic power law model has been developed as a flexible tool to detect bubbles. The LPPL model considers the faster-than-exponential (power law with finite-time singularity) increase in asset prices decorated by accelerating oscillation...

We propose that large stock market crashes are analogous to critical points studied in statistical physics with log-periodic correction to scaling. We extend our previous renormalization group model of stock market prices prior to and after crashes [D. Sornette et al., J.Phys.I France 6, 167, 1996] by including the first non-linear correction. This predicts the existence of a log-frequency shift over time in the log-periodic oscillations prior to a crash. This is tested on th...

By combining (i) the economic theory of rational expectation bubbles, (ii) behavioral finance on imitation and herding of investors and traders and (iii) the mathematical and statistical physics of bifurcations and phase transitions, the log-periodic power law (LPPL) model has been developed as a flexible tool to detect bubbles. The LPPL model considers the faster-than-exponential (power law with finite-time singularity) increase in asset prices decorated by accelerating osci...

In a recent comment (Johansen A 2003 An alternative view, Quant. Finance 3: C6-C7, cond-mat/0302141), Anders Johansen has criticized our methodology and has questioned several of our results published in [Sornette D and Zhou W-X 2002 The US 2000-2002 market descent: how much longer and deeper? Quant. Finance 2: 468-81, cond-mat/0209065] and in our two consequent preprints [cond-mat/0212010, physics/0301023]. In the present reply, we clarify the issues on (i) the analogy betwe...