Risk analysis in the brazilian stock market: copula-APARCH modeling for value-at-risk

Area of Science:

• Quantitative Finance
• Financial Risk Management
• Econometrics

Background:

• Risk management is crucial in financial analysis to assess potential investment losses.
• Understanding the dependence structure of assets is key for accurate risk assessment.
• Pairs trading strategies on the Brazilian Stock Exchange (B3) were analyzed.

Purpose of the Study:

• To quantify the dependence structure of selected Brazilian stocks using bivariate static conditional copulas.
• To estimate the Value-at-Risk (VaR) for pairs trading portfolios.
• To evaluate the impact of different copula functions on VaR estimation.

Main Methods:

• Application of bivariate static conditional copulas to model asset dependencies.
• Utilized the copula-APARCH approach with Normal, T-student, and Joe-Clayton copula functions.
• Analysis focused on pairs trading portfolios composed of B3, Gerdau, Magazine Luiza, and Petrobras stocks.

Main Results:

• Identified significant patterns of dependence, particularly at the extremes of the distribution.
• Copula form showed limited relevance for Value-at-Risk (VaR) estimation across most portfolios.
• Fitted models provided conservative risk measures for 5% and 1% significance levels.

Conclusions:

• Bivariate static conditional copulas effectively capture extreme dependence in financial markets.
• The chosen copula functions yield significant and conservative VaR estimates for risk management.
• The methodology supports robust risk aggregation and financial decision-making.