D-Brane solutions under market panic

TL;DR

This paper models stock market dynamics using a relativistic quantum mechanics framework, representing prices as spinor particles on a curved geometric space to incorporate market volatility and arbitrage opportunities.

Contribution

It introduces a novel geometric quantum approach to financial markets, linking market shocks to relativistic effects and curvature in a brane-world model.

Findings

Spherical brane models recover classical Black-Scholes behavior.

Full brane-world scenarios describe non-equilibrium market dynamics.

Arbitrage opportunities are linked to Riemann curvature in the model.

Abstract

The relativistic quantum mechanic approach is used to develop a stock market dynamics. The relativistic is conceptional here as the meaning of big external volatility or volatility shock on a financial market. We used a differential geometry approach with the parallel transport of the prices to obtain a direct shift of the stock price movement. The prices are represented here as electrons with different spin orientation. Up and down orientations of the spin particle are likened here as an increase or a decrease of stock prices. The paralel transport of stock prices is enriched about Riemann curvature which describes some arbitrage opportunities in the market. To solve the stock-price dynamics, we used the Dirac equation for bispinors on the spherical brane-world. We found that when a spherical brane is abbreviated to the disk on the equator, we converge to the ideal behaviour of financial market where Black Scholes as well as semi-classical equations are sufficient. Full spherical brane-world scenarios can descibe a non-equilibrium market behaviour were all arbitrage opportunities as well as transaction costs are take into account.