Clarifications to questions and criticisms on the Johansen–Ledoit–Sornette financial bubble model

Abstract

The Johansen-Ledoit-Sornette (JLS) model of rational expectation bubbles with finite-time singular crash hazard rates has been developed to describe the dynamics of financial bubbles and crashes. It has been applied successfully to a large variety of financial bubbles in many different markets. Having been developed over a decade ago, the JLS model has been studied, analyzed, used and criticized by several researchers. Much of this discussion is helpful for advancing the research. However, several serious misconceptions seem to be present within this literature both on theoretical and empirical aspects. Several of these problems stem from the fast evolution of the literature on the JLS model and related works. In the hope of removing possible misunderstanding and of catalyzing useful future developments, we summarize these common questions and criticisms concerning the JLS model and synthesize the current state of the art and existing best practice.

Financial Bubbles: Mechanisms and Diagnostics

“…This is illustrated in Figure 8, in which a positive bubble pattern can be seen in the S&P500 in the years before, and a negative bubble pattern in the period during the crisis. Calibrating this model and its siblings developed in our group is not easy [19]. Extreme care should be exercised to prevent over-fitting (when a good apparent fit is the result of mere chance) and obtain robust calibrations.…”

Super-Exponential Growth Expectations and the Global Financial Crisis

“…Consequently, the condition of no-arbitrage translates into a proportionality between the crash hazard rate and the instantaneous conditional return: as the return increases, the crash hazard rate grows and a crash eventually breaks the price unsustainable ascension. See Sornette et al (2013) for a recent review of many of these models.…”

World Financial 2014-2016 Market Bubbles: Oil Negative - US Dollar Positive

“…These parameters are subject to the following constraints as proposed by Sornette et al [39]: 0 < m < 1, 6 ≤ ω ≤ 13, B < 0, |C| < 1, t ≤ t c .…”