The science behind our quantitative market models

Our predictive models identify log-periodic patterns that precede major market shifts. Below we offer a short explanation of the nature of these patterns and how they are leveraged in our predictive modeling, specifically through the Log-Periodic Power Law (LPPL) type of models, and how they offer capital market professionals an ability to gain critical market foresights.

Unlike traditional models focusing on randomness and Brownian motion, we view markets as complex dynamical systems exhibiting critical phenomena and discrete scale invariance, similar to systems in statistical physics and complexity theory. This approach acknowledges the inherent complexity and feedback loops within financial markets, where investor behavior, macro environment changes, and external shocks interact in non-linear ways to produce emergent phenomena, such as bubbles and crashes.

Log-Periodic Patterns Preceding Market Crashes

Research consistently identifies log-periodic patterns as precursors to major market downturns. These patterns are characterized by accelerating oscillations in asset prices as markets approach a critical point. This observation suggests that financial markets exhibit specific signals that can be decoded to predict impending shifts.

The occurrence of log-periodic patterns is not confined to financial markets alone. A notable parallel has been drawn with the precursors to major earthquakes, where similar patterns have been observed. For example, Anifrani et al. [2] highlight this phenomenon, indicating a fundamental similarity in the behavior of seemingly disparate systems. Such findings support the hypothesis that both financial markets and natural systems share underlying principles that govern their behavior as they move towards critical points.

Phase Transition Phenomena and Financial Markets

Phase transitions, a key concept in thermodynamics, provide a compelling lens for viewing market dynamics. Just as matter undergoes a phase change (e.g., from solid to liquid) under certain conditions, financial markets exhibit transitional behaviors at critical points. The analogy extends to critical phenomena in general, where systems experience profound changes. This scientific perspective has established a theoretical foundation for understanding the transformations within financial markets as they approach points of significant change.

Building on the observations of log-periodic patterns and the analogy to phase transitions, Log-Periodic Power Law (LPPL) models have been refined to predict market critical points with remarkable precision. These models operate on the principle of discrete scale invariance, a concept that suggests patterns repeat across different scales. In the context of financial markets, this means that the signs of impending market shifts can be detected through the analysis of price movements over time, regardless of scale. The LPPL models capitalize on this principle to identify the log-periodic oscillations that signal an approaching market correction or rebound.

Real-time practical application

Our quantitative models are practical tools operating in real-time, precisely identifying critical market points. Unlike traditional market analysis, which often relies on historical data and linear projections, our LPPL-based model incorporates the complex dynamics of market behavior, offering a more nuanced and predictive insight into market trends.

The unique benefits for market professionals include:

  • Early Warning Signals: The ability to detect precursors to market downturns or rallies, allowing for proactive rather than reactive decision-making.
  • Risk Mitigation: Enhanced risk management through the identification of potential volatility, enabling better hedging strategies.
  • Investment Timing: The opportunity to optimize investment timing, potentially leading to higher returns by capitalizing on market corrections or avoiding downturns.

Examples of model output

As our model process live market price feeds, they compute nonlinear invariant properties that describe the system at a given point in time. When they detect patterns similar to past critical points, they flag these instances on a chart, signaling potential market tops or bottoms. These signals help market professionals make informed decisions.

lpp signal indicating top

An important point to make is that top and bottom signals do not promise retracement or rebound. They indicate that the trend that has been taking place until this point (where prices are displaying the power law divergence) is about to end. The forecast is a period of price sidewise movement or in some cases a retracement/rebound.

A Glossary

  • Discrete Scale Invariance: The property of a system where certain patterns repeat over different scales or sizes, observable in financial markets as recurring price patterns over time.
  • Critical Points (Critical Phenomena): Conditions under which a system undergoes a significant change in behavior or structure, analogous to the tipping points before market crashes or surges.
  • Thermodynamic Phase Transitions: The transformation of a system from one phase to another, such as liquid to gas, paralleled in financial markets by shifts from bull to bear markets or vice versa.
  • Log-periodic Fluctuations: Cyclical variations in a system that signal approaching critical points, seen in markets as repeating price patterns leading up to major trend changes.
  • Self-Organized Criticality: A system’s natural evolution into a critical state where a minor event can lead to significant, often disproportionate, changes. In financial markets, this concept helps explain how markets can remain seemingly stable for extended periods, only to be disrupted by sudden crashes or rallies triggered by seemingly small events or changes in investor sentiment.
  • Log-Periodic Power Law (LPPL): In 1996, two independent works [3,4] have proposed that critical phenomena would be possible scenarios for describing market crashes. More precisely, it has been proposed that a traded asset price increases as a power law decorated with a log-periodic oscillation. In the following years this approach has been further developed under a broad name of a LPPL Model.


Applying principles from critical phenomena and discrete scale invariance to financial markets marks a significant advancement in predictive modeling. By integrating this model into their analysis toolkit, market professionals can enhance their decision-making processes, leading to improved risk management and investment outcomes.


  1. Mandelbrot, B. B. (1963). The Variation of Certain Speculative Prices. Journal of Business, 36, 349-371.
  2. Anifrani, J.-C., Le Floc’H, C., Sornette, D., & Souillard, B. (1995). Universal Log-Periodic Correction to Renormalization Group Scaling for Rupture Stress Prediction From Acoustic Emissions. Journal de Physique I, 5(6), 631-638.
  3. Sornette, D., Johansen, A., & Bouchaud, J.-P. (1996). Stock Market Crashes, Precursors and Replicas. Journal de Physique I France, 6, 167-175.
  4. Feigenbaum, J. A., & Freund, P. G. O. (1996). Discrete Scale Invariance in Stock Markets Before Crashes. International Journal of Modern Physics B, 10(27), 3737-3745.