Identifying financial instability conditions using high frequency data

We study an indicator of financial instability based on the computation of the decay rate for the propagation of a given market shock. The rate of variation through time of an initial perturbation of the price process enables us to understand if such a shock will be rapidly absorbed or, on the contrary, it will be amplified by the market. The indicator combines non-linearly volatility, leverage and covariance between leverage and price and is model-free. It provides an early warning indicator of instability for a given high frequency financial time series. A new consistency theorem for the estimator of each component of the proposed indicator is proved. The properties of the indicator are investigated numerically under the CEV model and empirically using tick-by-tick data of the S&P 500 index futures.