Modeling stock return distributions with a quantum harmonic oscillator

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.

Applying Quantum Mechanics for Extreme Value Prediction of VaR and ES in the ASEAN Stock Exchange

“…Economies 2021, 9, x FOR PEER REVIEW 9 of 16 quadrant of positive positions, which explains that returns are still moved. In this case, the high energy zone stands for the explanation of Bull market momentums (Ahn et al 2018;Ataullah et al 2008). Conversely, the fall of returns (Bear market momentum) is the negative quadrant-compared with the case of low energy with no evidence or information to push up.…”

Quantum Propensity in Economics

“…In the social version, the frequency can therefore be thought of as representing a linearised resistance to change. For something like a stock market, the frequency can be used to represent the speed of mean reversion of returns (Ahn et al, 2017), while the constant Z can be intepreted as a scaling factor.…”

“…Another difference between quantum and classical oscillators is that the former features discrete energy levels. The ground state, which again can be viewed as representing the potential for a transaction to occur, corresponds to the normal distribution, while the other states show more complicated distributions, and contribute the non-normal behavior also seen with markets (Ahn et al, 2017).…”

Quantum‐tative Finance

“…In fact, this has already been done. Ahn et al (2017) showed that a similar quantum oscillator model outperformed traditional stochastic process models for fitting historical price changes in the Financial Times Stock Exchange (FTSE) All-Share Index. The system was found to be in the ground state nearly all of the time, with the next two levels contributing the skewness and kurtosis that characterized the data.…”