Risk estimation of CSI 300 index spot and futures in China from a new perspective

We investigate the statistical behavior and application in risk estimation of recurrence intervals between high-frequency returns that are either larger than a given positive threshold or smaller than a negative threshold for the stock index and stock index futures markets in China. By studying the probability density function of recurrence intervals, we find symmetric profiles for both the positive and negative occurrence thresholds, which can be fitted with stretched exponential functions. The probability density function further scales with the mean interval as the unified functional form for different thresholds. We further study the dependence of the conditional probability density function and the scaled mean condition recurrence interval on the previous recurrence interval, and demonstrate the existence of short memory in recurrence intervals. The result from detrended fluctuation analysis exhibits long-term correlations, where the detrended fluctuation function decays as an exponential function, with an exponent between 0.5 and 1. Based on the results of the analysis of recurrence intervals, we construct a hazard function and define a loss probability in order to evaluate risk in financial markets. To our surprise, a crossover is found in the loss probability plot of the stock index and its futures market, which sheds light on the issue of value at risk (VaR) overestimation (underestimation) based on recurrence interval analysis of complex financial markets. The study would enable one to improve risk estimation and is useful for management of risks in financial markets.