Quantum Economics and the Black-Scholes model
The Black-Scholes model is a formula used in finance to calculate the theoretical price of a financial option. Black, Scholes and Merton developed it in the 1970s. The model is based on the assumption that the price of a financial asset follows a log-normal stochastic process and considers factors such as the price of the underlying asset, the interest rate, the volatility of the investment and the time to expiration of the option. The resulting formula allows investors to determine the fair value of an option and thus make the right decision.
A relevant aspect of the traditional model is that the resulting volatility is a constant quantity. However, when looking at historical data, what actually happens is that if you plot volatility against price change, you do not get a horizontal line but a curve that resembles a smile. The greater the change in price, both towards higher and lower values, the higher the volatility. This empirical reality escapes the traditional Black-Scholes model1.
There are, however, models based on quantum probability theory that offer more accurate predictions of the real behaviour of volatility. This is the case, for example, with the quantum harmonic oscillator 2, which naturally reproduces financial statistics. In particular, in what regards volatility, it allows to modify the Black-Scholes model that generates more accurate predictions. Moreover, this new point of view makes it possible to reinterpret economics and finance from the point of view of quantum physics.
In short, quantum theory offers new tools of great potential. Only time will tell the extent of the impact of quantum theory on economics and finance.
[1] Orrell, D., & Richards, L. (2023). Keep on smiling: Market imbalance, option pricing, and the volatility smile.
[2]Orrell, D. (2022). A Quantum Oscillator Model of Stock Markets. Available at SSRN 3941518
