Simplicial Persistence of Financial Markets: Filtering, Generative Processes and Structural Risk

Area of Science:

• Network science
• Financial econometrics
• Complex systems analysis

Background:

• Understanding the temporal dynamics of financial markets is crucial for assessing systemic risk.
• Traditional methods often fail to capture high-order structures in market evolution.
• Network analysis offers a powerful lens to study complex interdependencies.

Purpose of the Study:

• To introduce simplicial persistence as a novel measure for quantifying the time evolution of network motifs.
• To investigate the long-memory properties and decay regimes in financial market network structures.
• To characterize financial market efficiency and liquidity using network-based decay exponents.

Main Methods:

• Simplicial persistence was applied to networks derived from correlation filtering.
• Topological Minor Free Graph (TMFG) filtering and simple thresholding were used for network generation.
• Null models were employed to analyze the generative process and evolutionary constraints.
• Decay exponents of long-memory processes were calculated to characterize markets.

Main Results:

• A two-regime power-law decay was observed in the number of persistent simplicial complexes, indicating long memory.
• The TMFG method effectively identified high-order structures, outperforming thresholding methods.
• More liquid markets exhibited slower persistence decay compared to less liquid markets.
• This finding contrasts with the notion of efficient markets being purely random.

Conclusions:

• Simplicial persistence reveals predictable collective variable evolution in financial markets, even if individual dynamics are less predictable.
• Slower persistence decay in liquid markets may indicate higher systemic fragility to shocks.
• The study provides a new framework for characterizing financial market behavior and efficiency through network dynamics.