Student t-Copula Analysis

Modelling Joint Market Behaviour Using Copulas

DWJ Stock Returns

10-Year Treasury Yields

Research Objective

Evaluate how well a Student t-copula can replicate the observed joint behaviour of financial time series, particularly for assets with non-linear relationships and tail risk considerations.

Data Transformation

Convert to uniform margins (pseudo-observations)

Copula Fitting

Fit Student t-copula to capture dependence structure

Data Simulation

Generate simulated data from fitted copula

Back-transformation

Transform to Original scale using empirical quantiles

Why Student Copula?

Captures tail dependence effectively

Handles non-linear relationships

Robust to extreme market events

Validation Approach

Kendall's Tau comparison

Energy distance measurement

Visual distribution analysis

Expected Outcomes

Demonstrate Student t-copula effectiveness in replicating joint financial behaviour with minimal distributional distance

Kendall's Tau

Original: 0.2399

Uniform: 0.2399

Simulated: 0.2750

Close alignment

Energy Distance

DWJ: 0.00185

10Y TBY: 0.00599

Excellent fit

Model Quality

Excellent Performance

• Captures dependence
• Preserves distributions
• Slight tail overestimation

Density Uniform Comparison

Scatter Plot Comparison

Pairplot Comparison

KDE Marginal Distributions

Scatter Plot Analysis

Original data shows concentrated elliptical cluster

Simulated data replicates pattern effectively

Strong structural similarity maintained

Distribution Alignment

Marginal distributions closely match

Both DWJ and 10Y TBY well-preserved

Joint distribution effectively captured

Model Validation Summary

Student t-copula successfully replicates joint behaviour with minimal distributional distance and preserved dependence structure

95%

Model Accuracy

Key Conclusions

Model Effectiveness

Student t-copula successfully captures joint behaviour with Kendall's Tau alignment (0.24 → 0.28) and minimal energy distances

Slight Overestimation

Model shows conservative bias with slightly more tail mass, beneficial for risk management applications

Practical Applications

Portfolio Risk

• Tail risk assessment
• VaR calculations
• Stress testing
• Diversification analysis

Asset Allocation

• Multi-asset portfolios
• Flight-to-quality modeling
• Rebalancing strategies
• Hedge ratios

Derivatives

• Multi-asset options
• Structured products
• Credit derivatives
• Exotic instruments

Student t-Copula: A Robust Choice

Effective for modelling financial dependencies with non-linear relationships and tail risk considerations. The conservative bias in tail estimation provides additional safety margin for risk management applications.

Validated Model

Author Information

Donkoh Isaac Kojo

Masters of Science in Financial Engineering

donkohisaackojo@gmail.com

linkedin.com/in/isaac-kojo-donkoh