Frank Copula Sampling, Density, and Kendall Tau Calibration

Summary

This document describes a bivariate Frank copula implementation for modeling dependence between two uniform variables. It provides methods to sample paired observations, calculate the copula density and cumulative distribution, and evaluate a conditional probability. The sampling procedure transforms independent uniform draws into dependent pairs using the copula parameter.

It also explains how to estimate the Frank parameter from sample Kendall tau: numerically evaluate a relation involving the Debye function and solve for the parameter with a root finder. The document supplies analytical expressions and implementation details, but no empirical results or model comparisons. The parameter is expected to be nonzero, and numerical behavior near zero or at extreme values is not discussed. As a code module, it is a technical reference rather than a complete trading strategy; use in market analysis would require fitting, validation, and assessment of whether the chosen dependence structure matches the data.

Key ideas

• The Frank copula models dependence between two uniform variables through a single parameter.
• Sampling transforms independent uniform draws into paired observations with Frank dependence.
• The module provides density, cumulative distribution, and conditional probability calculations.
• Kendall tau can be mapped to the copula parameter by numerically solving an equation involving the Debye function.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.