Quantum spatial-periodic harmonic model for daily price-limited stock markets

• The price of a price-limited stock is presumed oscillating and damping in a spatial-periodic harmonic oscillator potential well.
• There is negative non-linear relation between the volatility and trading volume of a stock.
• Price limit will abnormally increase volatility if within a certain regime of trading volume.

We investigate the behaviors of stocks in daily price-limited stock markets by purposing a quantum spatial-periodic harmonic model. The stock price is considered to be oscillating and damping in a quantum spatial-periodic harmonic oscillator potential well. A complicated non-linear relation including inter-band positive correlation and intra-band negative correlation between the volatility and trading volume of a stock is numerically derived with the energy band structure of the model concerned. The effectiveness of price limit is re-examined, with some observed characteristics of price-limited stock markets in China studied by applying our quantum model.