Practical Copula Application Example: Analysis of Daily Returns in Shanghai and Shenzhen Stock Markets

Copula Application Example: Analysis of Daily Returns in Shanghai and Shenzhen Stock Markets

In the field of financial risk management, Copula models have gained significant attention due to their ability to flexibly capture nonlinear dependencies between variables. The following presents an analytical framework for implementing a bivariate Copula model using daily return data from Shanghai and Shenzhen stock markets.

This example implements a complete modeling workflow through MATLAB programming. The process begins with preprocessing daily return data from the CSI 300 Index and Shanghai Composite Index, involving steps such as calculating logarithmic returns and standardization procedures using MATLAB's financial toolbox functions. Subsequently, through marginal distribution fitting, the optimal distribution forms for both return series are determined, with common choices including normal distribution, t-distribution, and others evaluated using distribution fitting techniques.

During the Copula function selection phase, the implementation typically compares the fitting performance of several commonly used Copula functions, such as Gaussian Copula, t-Copula, Clayton Copula, and Gumbel Copula. Each Copula function exhibits different capabilities in characterizing tail dependencies, requiring selection of the most appropriate type based on actual data characteristics through comparative goodness-of-fit metrics.

Model validation constitutes a critical component of Copula applications. This example employs multiple statistical methods to verify the goodness-of-fit of Copula functions, including Kolmogorov-Smirnov tests and Akaike Information Criterion evaluation. By comparing test results across different Copula functions, the optimal model specification can be determined through systematic model selection algorithms.

The ultimately established Copula model accurately describes the correlation structure between Shanghai and Shenzhen stock markets, particularly demonstrating enhanced capability in capturing linkage effects during extreme market conditions. This type of analysis holds significant reference value for financial practices such as portfolio risk control and derivative pricing applications.

The MATLAB program implementation encompasses complete workflow stages including data import procedures, parameter estimation algorithms, and model validation tests, designed with flexibility to adapt to various financial data analysis requirements. By modifying input data and parameter settings, this program framework can be readily applied to correlation analysis in other market contexts through configurable parameter interfaces.