[Paper Review] A permutation Information Theory tour through different interest rate maturities: the Libor case

Bariviera, Aurelio F., Guercio, M. Belen+2 more|arXiv (Cornell University)|Sep 1, 2015

Complex Systems and Time Series Analysis31 citations

TL;DR

This paper applies permutation information theory—specifically permutation Shannon entropy and Fisher information—to detect anomalies in Libor rates across seven maturities and four currencies (GBP, EUR, CHF, JPY) from 2001 to 2015. It identifies a significant, sustained loss of informational efficiency in 1M, 2M, and 3M maturities (2006–2012), particularly in GBP and CHF, which correlates with known manipulation, suggesting the method serves as a real-time market oversight tool for detecting structural shifts in financial time series.

ABSTRACT

This paper analyzes Libor interest rates for seven different maturities and referred to operations in British Pounds, Euro, Swiss Francs and Japanese Yen, during the period years 2001 to 2015. The analysis is performed by means of two quantifiers derived from Information Theory: the permutation Shannon entropy and the permutation Fisher information measure. An anomalous behavior in the Libor is detected in all currencies except Euro during the years 2006--2012. The stochastic switch is more severe in 1, 2 and 3 months maturities. Given the special mechanism of Libor setting, we conjecture that the behavior could have been produced by the manipulation that was uncovered by financial authorities. We argue that our methodology is pertinent as a market overseeing instrument.

Motivation & Objective

• To detect structural changes in Libor time series dynamics using information-theoretic quantifiers.
• To assess whether deviations from informational efficiency in Libor rates could signal manipulation.
• To develop a real-time monitoring tool for financial market integrity using local and global information measures.
• To evaluate the robustness of Libor as a benchmark rate across multiple currencies and maturities.
• To provide a quantitative, early-warning framework for regulators to detect market distress or manipulation.

Proposed method

• Uses permutation Shannon entropy and permutation Fisher information to quantify stochastic dynamics of Libor time series.
• Applies the Bandt-Pompe probability distribution with embedding dimension D=4 and time delay τ=1 to extract permutation patterns.
• Constructs an efficiency index E[P] = H[P] − F[P] bounded between -1 and 1, where high E indicates high randomness and low determinism.
• Employs a sliding window approach to compute E[P] over time, enabling local analysis of dynamical shifts.
• Visualizes results via color maps in the Shannon-Fisher plane, with color intensity reflecting informational efficiency.
• Defines 'inefficient' regions as H < 0.75 and F > 0.3, and 'efficient' regions as H > 0.75 and F < 0.3 for statistical comparison.

Experimental results

Research questions

• RQ1 Did Libor rates exhibit anomalous dynamical behavior during the 2006–2012 period, particularly in short maturities?
• RQ2 To what extent do permutation entropy and Fisher information detect structural shifts in Libor time series across different currencies?
• RQ3 Can the proposed efficiency index reliably identify periods of reduced informational efficiency consistent with market manipulation?
• RQ4 How does the informational efficiency of Libor vary across maturities (O/N to 12M) and currencies (GBP, EUR, CHF, JPY)?
• RQ5 Is the method capable of serving as a real-time early-warning system for market manipulation or systemic distress?

Key findings

• The 1M, 2M, and 3M maturities in GBP and CHF exhibited a pronounced loss of informational efficiency from 2006 to 2012, with 3M showing the most severe deviation.
• In GBP, 1M, 2M, and 3M maturities dropped to 33–39% efficient windows (H > 0.75, F < 0.3), indicating strong deterministic behavior.
• The Euro market showed a milder decline in efficiency, with 1M and 2M maturities remaining above 50% efficient windows, suggesting less manipulation.
• The Japanese Yen market displayed the lowest overall efficiency, with 1M and 2M maturities only 29–35% efficient, indicating persistent structural anomalies.
• The 6M and 12M maturities in all currencies maintained higher efficiency levels, especially in GBP and EUR, suggesting they were less affected by manipulation.
• A recovery in informational efficiency was observed post-2013, particularly in GBP and CHF, aligning with the end of the manipulation period.