Modeling stock return distributions with a quantum harmonic oscillator

¹ Graduate School of Future Strategy, Korea Advanced Institute of Science and Technology - Daejeon 34141, Korea
² Department of Physics and Astronomy and Center for Theoretical Physics, Seoul National University Seoul 08826, Korea
³ Saïd Business School, University of Oxford - Oxford OX1 1HP, UK
⁴ HSBC Business School, Peking University - Shenzhen 518055, PRC
⁵ Bocconi University - Milano 20100, Italy

^(a) mychoi@snu.ac.kr

Received: 11 October 2017
Accepted: 8 January 2018

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. The stochastic equation governing our model is transformed into a Schrödinger equation, the solution of which features “quantized” eigenfunctions. Consequently, stock returns follow a mixed χ distribution, which describes Gaussian and non-Gaussian features. Analyzing the Financial Times Stock Exchange (FTSE) All Share Index, we demonstrate that our model outperforms traditional stochastic process models, e.g., the geometric Brownian motion and the Heston model, with smaller fitting errors and better goodness-of-fit statistics. In addition, making use of analogy, 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.