Quantum Harmonic Oscillator Model of Index Fund Return Distributions
By Harry
This project uses the quantum harmonic oscillator to model past return distributions of the S&P 500 index fund. Quantum harmonic oscillators have a restoring force that pulls the system back to equilibrium, similar to how stock prices revert to their mean. In quantum models, energy levels take on specific values, which can better capture the discrete nature of transactions and price changes in the stock market. Stock prices change in discrete steps due to individual transactions. Each trade can be seen as moving the stock price from one “energy level” to another. Due to its energy levels, quantum oscillation can help with more accurate modeling. Moreover, quantum oscillations are described by wave functions which can give probability distributions to measure for a particular position. The added variability in quantum oscillations can tell more about volatility and better model non normal distributions of stock price. Modeling the stock market using quantum oscillations can be useful for companies and businesses at large for their investments. This includes allowing for better investing such as more accurate financial analysis that can better predict market interactions and changes. This could lead to more effective use of financial tools and better risk management through short and long term investments. Quantum oscillations for stock markets can also lead to interdisciplinary applications such as combining physics with data and economics. This can provide experts and students with a comprehensive understanding of market dynamics and advanced modeling techniques.