D-brane solutions under market panic

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.Keywords: relativistic quantum approach, stock market panic, financial brane-world, dirac equation, curvature as a arbitrage * pincak@saske.sk

GARCH(1,1) Model of the Financial Market with the Minkowski Metric

“…The problem comes from the classical financial mathematics. We just want to perform fundamental investigations to find an adequate stochastic processes matching the real financial time series data [21] without considering the market microstructure with the underlying orderbook [22] of the financial market scaling [23] and the hidden structure of the financial market as a D-brane [24] with extradimensions [25]. The financial time series data in the moment of the financial market crashed [26] are typical experimental results which we have for the complex systems [27].…”