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Modeling Stock Return Distributions with A Quantum Harmonic Oscillator

by Kwangwon Ahn, Mu Young Choi*, Bingcun Dai, Sungbin Sohn, Biao Yang

ARTICLE | Europhysics Letters | Vol.120, 2017


Abstract


We propose a quantum harmonic oscillator as a model for the market force which draws a stock return from short-run fluctuations to the long-run equilibrium. Analyzing the Financial Times Stock Exchange (FTSE) All Share Index, we demonstrate that our model outperforms traditional stochastic process models, e.g., geometric Brownian motion and the Heston model, with smaller fitting errors and better goodness of fit statistics. The solution of the Schro¨dinger equation for the quantum harmonic oscillator shows that stock returns follow a mixed χ distribution, which describes Gaussian and non-Gaussian features of the stock return distribution. In addition, we provide an economic rationale of the physics concepts such as the eigenstate, eigenenergy, and angular frequency, which sheds light on the relationship between finance and econophysics literature.

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