Super-Exponential Growth Expectations and the Global Financial Crisis

Abstract

We construct risk-neutral return probability distributions from S&P 500 options data over the decade 2003 to 2013, separable into pre-crisis, crisis and post-crisis regimes. The pre-crisis period is characterized by increasing realized and, especially, option-implied returns. This translates into transient unsustainable price growth that may be identified as a bubble. Granger tests detect causality running from option-implied returns to Treasury Bill yields in the pre-crisis regime with a lag of a few days, and the other way round during the post-crisis regime with much longer lags (50 to 200 days). This suggests a transition from an abnormal regime preceding the crisis to a "new normal" post-crisis. The difference between realized and option-implied returns remains roughly constant prior to the crisis but diverges in the post-crisis phase, which may be interpreted as an increase of the representative investor's risk aversion.

Bitcoin Bubble Trouble

“…If we have -1<b<0 , we define ρ(q) ≡ 1 for q a ≤-b. The case -1<b<0 results in a finite-time singularity with super-exponential growth as in Johansen and Sornette (2010) and as confirmed in a model-independent analysis of real stock market data by Leiss et al (2015) and in equity markets by Yan et al (2012). This is because, when the denominator in (9) is <1, the corresponding numerator can attain the value of the denominator with finite mispricing and thus in finite time.…”

Bubbles as Violations of Efficient Time-Scales

“…Brock, as cited in Veres (2013), defines bubbles as "a monotonically increasing sequence of prices." Hüsler et al (2013) and Leiss et al (2015) cite super-exponential growth rates 6 as the hallmark of a bubble. This chimes 3 Quoted in Cassidy (2010).…”

A simple mechanism for financial bubbles: time-varying momentum horizon

“…Previous models developed by our group implementing the concept of positive feedbacks to characterize bubbles have emphasized mostly the influence of past prices level on future returns [Sornette and Andersen, 2002;Lin and Sornette, 2013;Hüsler et al, 2013;Corsi and Sornette, 2014;Lin et al, 2014;Sornette and Cauwels, 2015a] and the reinforcing role of social influence of the price formation process [Kaizoji et al, 2015]. The role of a nonlinear response to momentum [Ide and Sornette, 2002] has been suggested to be at the origin of the super-exponential price growth characterising bubbles [Sornette and Cauwels, 2015a;Leiss et al, 2015] and also as a model of hyperinflation [Sornette et al, 2003]. Here, we take a different route by constructing the simplest continuous price process whose expected returns and volatility are functions of momentum only.…”