Generalization of the BTK Theory to the Case of Finite Quasiparticle Lifetimes

A generalization to the BTK theory is developed based on the fact that the quasiparticle lifetime is finite as a result of the damping caused by the interactions. For this purpose, appropriate self-energy expressions and wave functions are inserted into the strong coupling version of the Bogoliubov equations and subsequently, the coherence factors are computed. By applying the suitable boundary conditions to the case of a normal-superconducting interface, the probability current densities for the Andreev reflection, the normal reflection, the transmission without branch crossing and the transmission with branch crossing are determined. Accordingly the electric current and the differential conductance curves are calculated numerically for Nb, Pb, and Pb0.9Bi0.1 alloy. The generalization of the BTK theory by including the phenomenological damping parameter is critically examined. The observed differences between our approach and the phenomenological approach are investigated by the numerical analysis.

Volume-Synchronized Probability of Informed Trading (VPIN), Market Volatility, and High-Frequency Liquidity

We assess the predictive ability of three VPIN metrics on the basis of two highly volatile market events of China, and examine the association between VPIN and toxic-induced volatility through conditional probability analysis and multiple regression. We examine the dynamic relationship on VPIN and high-frequency liquidity using Vector Auto-Regression models, Granger Causality tests, and impulse response analysis. Our results suggest that Bulk Volume VPIN has the best risk-warning effect among major VPIN metrics. VPIN has a positive association with market volatility induced by toxic information flow. Most importantly, we document a positive feedback effect between VPIN and high-frequency liquidity, where a negative liquidity shock boosts up VPIN, which, in turn, leads to further liquidity drain. Our study provides empirical evidence that reflects an intrinsic game between informed traders and market makers when facing toxic information in the high-frequency trading world.