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The Nelsen 13 Copula for Dependence Modeling and Sampling

Code Stratmill research code

Summary

This module implements the bivariate Nelsen 13 copula, a tool for modeling dependence between two uniform variables. It provides the copula cumulative distribution and density, a conditional distribution, random pair generation, and a parameter estimator based on Kendall's tau. These functions can support dependence modeling in quantitative finance, including work that requires joint rather than independent return behavior.

Sampling starts with independent uniform inputs and numerically inverts a conditional probability function to construct a dependent pair. The parameter estimate numerically integrates a generator-based expression for Kendall's tau, then solves for the parameter that matches the observed sample statistic. The implementation documents a nonnegative parameter range in the constructor and a narrower range for pair generation, while the estimator searches a bounded interval. It offers analytical distribution formulas alongside numerical root finding and integration; the excerpt does not explain calibration validation, boundary handling, or how to select this family against alternatives. Users should check parameter validity and numerical behavior for their intended data and applications.

Key ideas

  • The Nelsen 13 copula represents dependence between two uniform random variables.
  • Its cumulative distribution, density, and conditional distribution are calculated analytically.
  • Pair sampling uses numerical inversion of a conditional probability function.
  • The parameter can be estimated by matching model Kendall's tau to a sample tau.
  • The implementation's numerical thresholds and parameter bounds warrant validation for a particular use case.

Tags

StatisticsDerivatives pricingRisk management

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