Arbitrage impact on the relationship between XRP price and correlation tensor spectra of transaction networks

ArXiv ID: 2405.00051 “View on arXiv”

Authors: Unknown

Abstract

The increasing use of cryptoassets for international remittances has proven to be faster and more cost-effective, particularly for migrants without access to traditional banking. However, the inherent volatility of cryptoasset prices, independent of blockchain-based remittance mechanisms, introduces potential risks during periods of high volatility. This study investigates the intricate dynamics between XRP price fluctuations across diverse crypto exchanges and the correlation of the largest singular values of the correlation tensor of XRP transaction networks. Particularly, we show the impact of arbitrage opportunities across different crypto exchanges on the relationship between XRP price and correlation tensor spectra of transaction networks. Distinct periods, non-bubble and bubble, showcase different characteristics in XRP price fluctuations. Establishing a connection between XRP price and transaction networks, we compute correlation tensors and singular values, emphasizing the significance of the largest singular value. Comparisons with reshuffled and Gaussian random correlation tensors validate the uniqueness of the empirical tensor. A set of simulated weekly XRP prices, resembling arbitrage opportunities across various crypto exchanges, further confirms the robustness of our findings. It reveals a pronounced anti-correlation during bubble periods and a non-significant correlation during non-bubble periods with the largest singular value, irrespective of price fluctuations across different crypto exchanges.

Keywords: cryptoassets, XRP, transaction networks, correlation tensor, arbitrage opportunities

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts like correlation tensors, double singular value decomposition, and random matrix theory, with significant LaTeX notation and derivations. It demonstrates empirical rigor by using real transaction and price data from multiple exchanges, conducting statistical tests, and validating findings with simulated data and comparisons to null models.

  flowchart TD
    A["Research Goal<br>Investigate arbitrage impact on the relationship<br>between XRP price & transaction network correlation spectra"] --> B["Data Collection<br>Real XRP transaction network data<br>Price data from diverse crypto exchanges"]
    
    B --> C["Methodology: Tensor Analysis<br>Compute correlation tensors of transaction networks<br>Extract largest singular values"]
    
    C --> D["Validation & Simulation<br>Compare with random/Gaussian tensors<br>Simulate arbitrage price scenarios"]
    
    D --> E["Analysis by Market Regime<br>Separate bubble vs non-bubble periods"]
    
    E --> F["Key Findings<br>Bubble: Strong anti-correlation<br>Non-bubble: Non-significant correlation<br>Robust across arbitrage scenarios"]
    
    style A fill:#e1f5e1
    style F fill:#fff3cd