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

Abstract

h i g h l i g h t s• 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. a b s t r a c tWe 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.

Quantum Brownian motion model for the stock market

“…The description of the price of a single stock based on quantum mechanics provides an instructive point of view to deal with dynamical problems in the stock market [21,29]. Under the quantum-mechanics-based description, one single stock i is described by a wave function |ψ i .…”

“…where ω i is the characteristic oscillating frequency of the stock [21,29]. The probability distribution of the ground state |ψ 0 (x, t)| 2 is not a Dirac-peak distribution function.…”

“…The interaction between the index and the stocks is purely linear. The influence of macroscopic external Table 1: Mapping between a quantum closed system and a single stock [21,29].…”

“…Recently, integration of quantum mechanics into finance has been seriously attempted. No sooner had path integral methods first been applied to options pricing successfully [20] than a series of financial analyses with concepts and tools from quantum mechanics used were launched [21][22][23][24][25][26][27][28][29]. Despite of the mathematical success of quantum-mechanics models for financial instruments, few studies have been tried to exploit quantum statistical dynamics relying on open-system concepts yet.…”

“…The criticism of applying multifractal analyses to intraday stock market indices [35], as an example, implies a lapse of concentration in overusing mathematical tools other than identifying instructive physical concepts for economics.In 1933, Frisch presented a damped harmonic oscillator model [36]. As one of the most influential models in dynamic economics, it presumes that on account of stock trading and its auxiliary expense, the price of a single stock should oscillate and dissipate to equilibrium like a damped harmonic oscillator while being impelled by time-varying information outside [29]. Notwithstanding its intuitive physical point of view, Frisch's model cannot explain why there always exists persistent fluctuations of the stock price [37].…”