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.

We aim to provide an algorithm to predict the distribution of the critical times of financial bubbles employing a log-periodic power law. Our approach consists of a constrained genetic algorithm and an improved price gyration method, which generates an initial population of parameters using historical data for the genetic algorithm. The key enhancements of price gyration algorithm are (i) different window sizes for peak detection and (ii) a distance-based weighting approach for peak selection. Our results show a significant improvement in the prediction of financial crashes. The diagnostic analysis further demonstrates the accuracy, efficiency, and stability of our predictions.

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