Identifying financial instability conditions using high frequency data

In this paper we study an indicator of financial instability which relies on the computation of the decay rate for the propagation of a given market shock. The rate of variation of an initial perturbation through time enable us to understand if such shock will be rapidly absorbed by the market or, on the opposite, it will have an amplifying instability effect. The indicator combines in a non-linear way volatility, leverage and covariance between leverage and price. It can be applied in a model-free way to high frequency financial market data, resulting into an early warning indicator of instability characterizing the financial time series under investigation. 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.