GARCH(1,1) model of the financial market with the Minkowski metric

TL;DR

This paper introduces a novel GARCH(1,1) model incorporating Minkowski metric to analyze long memory volatility clusters in financial markets, linking concepts from physics to finance.

Contribution

It presents a new approach using Minkowski spacetime in GARCH modeling, deriving a Yang-Mills equation and revealing a hidden risk field related to trader behavior.

Findings

Model captures long memory and volatility clustering.

Identifies a dark volatility or hidden risk field.

Links market panic to physical theories.

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.