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

Abstract

We solved a stylized fact on a long memory process of volatility cluster phenomena by using Minkowski metric for GARCH(1,1) under assumption that price and time can not be separated. We provide a Yang-Mills equation in financial market and anomaly on superspace of time series data as a consequence of the proof from the general relativity theory. We used an original idea in Minkowski spacetime embedded in Kolmogorov space in time series data with behavior of traders. The result of this work is equivalent to the dark volatility or the hidden risk fear field induced by the interaction of the behavior of the trader in the financial market panic when the market crashed.

Relativistic Option Pricing

“…Tenreiro Machado (2014) applied relativity in financial time series, and Pincak and Kanjamapornkul (2018) used relativity in financial time series forecast models. Pincak and Kanjamapornkul (2018) considered a special Minkowski metric where price and time cannot be separated.…”