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Volatility is a widely recognized measure of market risk. As volatility is not observed it has to be estimated from market prices, i.e., as the implied volatility from option prices. The volatility index VIX making volatility a tradeable asset in its own right is computed from near- and next-term put and call options on the S&P 500 with more than 23 days and less than 37 days to expiration and non-vanishing bid. In the present paper we quantify the information content of the constituents of the VIX about the volatility of the S&P 500 in terms of the Fisher information matrix. Assuming that observed option prices are centered on the theoretical price provided by Heston's model perturbed by additive Gaussian noise we relate their Fisher information matrix to the Greeks in the Heston model. We find that the prices of options contained in the VIX basket allow for reliable estimates of the volatility of the S&P 500 with negligible uncertainty as long as volatility is large enough. Interestingly, if volatility drops below a critical value of roughly 3%, inferences from option prices become imprecise because Vega, the derivative of a European option w.r.t. volatility, and thereby the Fisher information nearly vanishes.
Volatility clustering and fat tails are prominently observed in financial markets. Here, we analyze the underlying mechanisms of three agent-based models explaining these stylized facts in terms of market instabilities and compare them on empirical grounds. To this end, we first develop a general framework for detecting tail events in stock markets. In particular, we introduce Hawkes processes to automatically identify and date onsets of market turmoils which result in increased volatility. Second, we introduce three different indicators to predict those onsets. Each of the three indicators is derived from and tailored to one of the models, namely quantifying information content, critical slowing down or market risk perception. Finally, we apply our indicators to simulated and real market data. We find that all indicators reliably predict market events on simulated data and clearly distinguish the different models. In contrast, a systematic comparison on the stocks of the Forbes 500 companies shows a markedly lower performance. Overall, predicting the onset of market turmoils appears difficult, yet, over very short time horizons high or rising volatility exhibits some predictive power.