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.

Option-Implied Objective Measures of Market Risk

“…Arrow 1971;Friend and Blume 1975;Singleton 1982, 1984;Epstein and Zin 1991;Normandin and St-Amour 1998). In the spirit of Foster and Hart (2009), and in the light of recent findings (Leiss et al, 2015) that indicate changing risk attitudes over time as a result of events such as the Global Financial Crisis, for example, we restrain from making somewhat arbitrary assumptions on the utility of a representative agent and pursue directly with option-implied quantities instead.…”

“…For our purposes, the relatively new approach by Figlewski (2010), as adapted in the recent study (Leiss et al, 2015), turns out to be most suited in order to get as much information out of the data as regard extreme events. It combines a 4 th -order polynomial interpolation of data points in implied volatility space with appended generalized extreme value (GEV) tails beyond the range of observed strikes.…”

“…Allowing for non-standard features such as bimodality and fat tails will be of advantage for analyzing the highly different regimes around the Global Financial Crisis of 2008. We refer the interested reader to Leiss et al (2015), who discuss in detail the properties of RNDs during and around the Financial Crisis (see also Figlewski 2010;Birru and Figlewski 2012).…”

“…The original operationalization by Foster and Hart (2009) has recently been generalized to our setting by Riedel and Hellmann (2015) and Hellmann and Riedel (2015). To get most information out of the options data, our estimation of the underlying risk-neutral densities (RNDs) is done nonparametrically from S&P 500 call and put options prices using a variant of the method by Figlewski (2010) introduced in (Leiss et al, 2015).…”

Early Warning Signals of Financial Crises with Multi-Scale Quantile Regressions of Log-Periodic Power Law Singularities

“…One of the practical problems of bubble identification is that the fundamental value is not directly observable and is roughly estimated within a factor of 2 [10], typically. Based on the analyses of many historical bubbles, the studies [1][2][3]11] have documented that there are transient regimes during which the price growth rate (return) grows itself, which translates into a super-exponential time dynamics. Such a procyclical process involving positive feedbacks, which can be of many types, such as option hedging, portfolio insurance strategies, margin requirements, as well as the imitation and herding behavior in psychology.…”