Matthias Leiss

Option-Implied Objective Measures of Market Risk

Foster and Hart (2009) introduce an objective measure of the riskiness of an asset that implies a bound on how much of one’s wealth is ‘safe’ to invest in the asset while (a.s.) guaranteeing no-bankruptcy in the long run. In this study, we translate the Foster-Hart measure from static and abstract gambles to dynamic and applied finance using nonparametric estimation of risk-neutral densities from S&P 500 call and put option prices covering 2003 to 2013. This exercise results in an option-implied market view of objective riskiness. The dynamics of the resulting ‘option-implied Foster-Hart bound’ are analyzed and assessed in light of well-known risk measures including value at risk, expected shortfall and risk-neutral volatility. The new measure is shown to be a significant predictor of ahead-return downturns. Furthermore, it is able to grasp more characteristics of the risk-neutral probability distributions than other measures, furthermore exhibiting predictive consistency. The robustness of the risk-neutral density estimation method is analyzed via a bootstrap.

Super-Exponential Bubbles and Expectations: Theory, Simulations and Empirics

Transient super-exponentiality is a well-known statistical regularity of financial markets and generally associated with unsustainable growth and bubbles. We contribute to the understanding of super-exponential dynamics by assessing it from two new angles. First, we introduce an agent-based model of super-exponential bubbles on a risky asset market with fundamentalist and chartist traders. We show analytically and by simulations, that their mutual interactions repeatedly generate super-exponentially growing prices. Moreover, we combine our agent-based model with the methodology of log-period power law singularities (LPPLS) often used for bubble econometrics. We introduce a third type of trader who employs the LPPLS framework to detect the existence of a bubble and invests accordingly, trying to ride the bubble while it lasts and to quit before the subsequent crash. We find that the presence of LPPLS traders increases market volatility. In part two, we construct risk-neutral return probability distributions from S&P 500 option prices over the decade 2003–2013. The data strongly suggests increasing option-implied return expectations prior to the crash of 2008, which translates into transient super-exponential growth expectations. Furthermore, we find evidence for a regime-change from an abnormal pre-crisis period to a “new normal” post-crisis. Granger-causality tests indicate that the Federal Reserve policy played a significant role in this transition.

Option-Implied Objective Measures of Market Risk with Leverage

Leverage has been shown to be procyclical and indicative of financial market risk. Here, we present a novel, inherently forward-looking way to estimate market leverage ratios based on derivative prices, option hedging, and the ‘operational’ riskiness measure by Foster and Hart (J Polit Econ 117(5):785–814, 2009). Furthermore, we report option-implied ‘optimal’ leverage levels inferred via the (Kelly, IRE Trans. Inf. Theory 2(3):185–189, 1956) criterion. The resulting measure of leverage exhibits strong procyclicality prior to the Global Financial Crisis of 2008. Finally, we find it to successfully predict large stock market downturns.