“Speculative Influence Network” during financial bubbles: application to Chinese stock markets

We introduce the Speculative Influence Network (SIN) to decipher the causal relationships between sectors (and/or firms) during financial bubbles. The SIN is constructed in two steps. First, we develop a Hidden Markov Model (HMM) of regime-switching between a normal market phase represented by a geometric Brownian motion and a bubble regime represented by the stochastic super-exponential Sornette and Andersen (Int J Mod Phys C 13(2):171–188, 2002) bubble model. The calibration of the HMM provides the probability at each time for a given security to be in the bubble regime. Conditional on two assets being qualified in the bubble regime, we then use the transfer entropy to quantify the influence of the returns of one asset i onto another asset j, from which we introduce the adjacency matrix of the SIN among securities. We apply our technology to the Chinese stock market during the period 2005–2008, during which a normal phase was followed by a spectacular bubble ending in a massive correction. We introduce the Net Speculative Influence Intensity variable as the difference between the transfer entropies from i to j and from j to i, which is used in a series of rank ordered regressions to predict the maximum loss (%MaxLoss) endured during the crash. The sectors that influenced other sectors the most are found to have the largest losses. There is some predictability obtained by using the transfer entropy involving industrial sectors to explain the %MaxLoss of financial institutions but not vice versa. We also show that the bubble state variable calibrated on the Chinese market data corresponds well to the regimes when the market exhibits a strong price acceleration followed by clear change of price regimes. Our results suggest that SIN may contribute significant skill to the development of general linkage-based systemic risks measures and early warning metrics.