2024/06/21 by Issey Sukeda, Sukeda, Issey, Tomonari Sei +1
Computer Science · Economics, Econometrics and Finance · #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Numerical Methods and Algorithms
paper · pdf · doi:10.48550/arxiv.2406.14814
openalex publication_date 2024/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In dependence modeling, various copulas have been utilized. Among them, the Frank copula has been one of the most typical choices due to its simplicity. In this work, we demonstrate that the Frank copula is the minimum information copula under fixed Kendall's τ (MICK), both theoretically and numerically. First, we explain that both MICK and the Frank density follow the hyperbolic Liouville equation. Moreover, we show that the copula density satisfying the Liouville equation is uniquely the Frank copula. Our result asserts that selecting the Frank copula as an appropriate copula model is equivalent to using Kendall's τ as the sole available information about the true distribution, based on the entropy maximization principle.