Statistical correlation properties of the SHIBOR interbank lending market

The purpose of this paper is to investigate the statistical correlation properties of the Shanghai Interbank Offered Rate (SHIBOR) interbank lending market.

The authors apply methods of correlation analysis, random matrix theory (RMT) and minimum spanning tree (MST) to investigate the correlation properties of Chinese interbank lending market and analyze how the SHIBOR panel banks behave in different market periods.

First, the largest eigenvalue λ ₁ is the index to describe the market mode of the whole market when all banks behavior collectively and λ ₁/N is a good estimator of the average correlation <C> of the correlation matrix. Second, notably, the authors find the “market mode” is weakened in two crises periods of 2008 stock market crash and 2009 Global Financial Crisis. This is significantly different from other market where the “market mode” is normally strengthened in crises periods. Third, the authors subtract the contribution of λ ₁, the second and third eigenvalue, λ ₂ and λ ₃, will fall outside of the predicted interval. And both λ ₂ and λ ₃ are getting times larger in the crises periods than in “Non-Crisis” period. Fourth, and in the MST analysis, the authors find again that the average distances of the MST are the times larger in crises periods than in “Non-Crisis” period and the second largest eigenvalue is a good estimator of the average distance of the MST.

According to the best knowledge, this paper is the first work on the study of the statistical properties of an interbank lending market using quotation level data of panel banks, which allows us to analyze the properties of the interest rate formation and how all panel banks behavior in different periods. This work is also the first study on the SHIBOR market using econophysics methods of correlation analysis, RMT and MST.