Over the weekend, Xerxes did a premium post about bitcoin, and in the comments section, The Wizard made mention of something I had never heard of called the Sornette LLPL. I did a bit of poking around and thought I’d share some information for everyone’s mutual benefit.
“Sornette LLPL power law ascent” refers to the work of Swiss geophysicist and financial economist Didier Sornette, who developed the Log-Periodic Power Law (LPPL) model to diagnose and predict financial bubbles and subsequent market crashes. The “power law ascent” is a key characteristic of the LPPL model, describing the faster-than-exponential growth in asset prices leading up to a critical point (the peak or crash time).
The LPPL Model Explained
- Super-Exponential Growth: A core feature of the LPPL model is the identification of “super-exponential” or power law growth in asset prices during the formation of a speculative bubble. Unlike normal exponential growth, where the growth rate is constant, in a bubble, the growth rate itself accelerates over time due to positive feedback loops and investor herding behavior.
- Log-Periodic Oscillations: This accelerated price path is “decorated” with accelerating oscillations in prices as the market approaches the critical point (crash date). These oscillations capture how market sentiment escalates and becomes increasingly unstable before a potential reversal.
- Finite-Time Singularity: The model predicts a finite-time singularity (
𝑡𝑐), which is the theoretical time at which the price growth becomes infinite, marking the most probable time for a crash or a major regime change (e.g., transition to a plateau or slow decay) to occur.
- Mechanism: The underlying theory posits that the hierarchical interactions and imitation behavior among rational and irrational investors create collective self-organization, leading to these characteristic patterns.
Didier Sornette and his team at the ETH Zurich’s Financial Crisis Observatory have applied the LPPL model to diagnose bubbles in various markets and predict critical transitions. The model is used as an early warning signal system for potential imminent market reversals.
For further information, you can explore resources such as Sornette’s book Why Stock Markets Crash or the research papers available on the Social Science Research Network (SSRN) and the ETH Zurich website.
