Detection of financial bubbles using a log‐periodic power law singularity (LPPLS) model

This article provides a systematic review of the theoretical and empirical academic literature on the development and extension of the log‐periodic power law singularity (LPPLS) model, which is also known as the Johansen–Ledoit–Sornette (JLS) model or log‐periodic power law (LPPL) model. Developed at the interface of financial economics, behavioral finance and statistical physics, the LPPLS model provides a flexible and quantitative framework for detecting financial bubbles and crashes by capturing two salient empirical characteristics of price trajectories in speculative bubble regimes: the faster‐than‐exponential growth of price leading to unsustainable growth ending with a finite crash‐time and the accelerating log‐periodic oscillations. We also demonstrate the LPPLS model by detecting the recent bubble status of the S&P 500 index between April 2020 and December 2022, during which the S&P 500 index reaches its all‐time peak at the end of 2021. We find that the strong corrections of the S&P 500 index starting from January 2022 stem from the increasingly systemic instability of the stock market itself, while the well‐known external shocks, such as the decades‐high inflation, aggressive monetary policy tightening by the Federal Reserve, and the impact of the Russia/Ukraine war, may serve as sparks. This article is categorized under: Applications of Computational Statistics > Computational Finance Algorithms and Computational Methods > Computational Complexity Statistical Models > Nonlinear Models Daily LPPLS confidence indicator for positive bubbles is shown in red and negative bubbles in green (right scale) along with the S&P 500 index in blue (left scale), from 4/1/2020 to 12/30/2022.