TITLE:
Forecasting Portfolio Market Risk Using Multivariate GARCH-Vine Copula Approach
AUTHORS:
Valentine Wanjiku Mwai, Cyprian Ondieki Omari, Simon Maina Mundia
KEYWORDS:
Portfolio Market Risk, Dependency Modelling, Backtesting, Multivariate GARCH, Constant Conditional Correlation, Dynamic Conditional Correlation, Regular Vine, D-Vine, C-Vine, S-Vine, Value at Risk, Expected Shortfall
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.15 No.4,
November
7,
2025
ABSTRACT: The global financial landscape is increasingly becoming interconnected, with financial markets exhibiting complex interdependencies. This increases the possibility of market risk spreading from one market to another, as market shocks often propagate across asset classes especially during periods of economic uncertainty. Failure to adequately capture the characteristics of univariate return series and the dependence structure between them, may lead to significant underestimation of the market risk forecasts. The standard multivariate Generalized Autoregressive Conditional Heteroskedasticity models assume that financial data follow a normal distribution, an assumption that fails to capture the heavy tails, skewness, and non-linear dependencies commonly observed in asset returns. Thus, this study models the dependency structures among a portfolio of financial asset classes and forecasts the Value-at-Risk and Expected Shortfall using multivariate Generalized Autoregressive Conditional Heteroskedasticity Vine Copula approach. The multivariate GARCH model captures the dynamic volatilities and conditional correlations among assets, then vine copulas are used to model the remaining non-linear and tail dependence relationships between the standardized residuals. The empirical results indicated that the financial return series exhibit complex dependence patterns that vary across asset classes and evolve over time, reflecting the diverse behaviors of financial markets under varying economic conditions. Among the models considered, the constant conditional correlation stationary vine copula demonstrates superior performance in dependence modelling. Backtesting results for one-day-ahead Value-at-Risk and Expected Shortfall indicate that constant conditional correlation vine copula models significantly outperformed the constant and dynamic conditional correlation models with normal and Student-t innovations over a one-day horizon. In contrast, dynamic conditional correlation vine copula models generally exhibit poor predictive accuracy and fail to meet key backtesting tests. Overall, the empirical findings of this study indicated that the constant conditional correlation regular vine copula offers the most reliable and precise framework for modelling and forecasting portfolio market risk.