Seminar| Institute of Mathematical Sciences
Time: Monday, July 13th, 2026,10:30-11:30
Location: IMS RS408
Speaker: Mortaza Baky Haskuee, Fields Institute for Research in Mathematical Sciences
Abstract:Financial risk management traditionally relies on linear correlation and Gaussian assumptions to model asset dependencies. However, during periods of market stress or euphoria, the relationships among financial institutions become distinctly nonlinear, characterized by tail dependence—where extreme returns in one asset systematically coincide with extreme returns in another—and spillover risk, where shocks propagate asymmetrically across interconnected entities. Conventional models often fail to capture these features, leading to underestimation of portfolio risk and systemic vulnerability.
This talk addresses these challenges by applying a copula GARCH framework to model the dependence structure among six major Canadian banks. Copulas are particularly suited to this task because they separate marginal dynamics (modeled via GARCH to capture volatility clustering and leptokurtosis) from the joint dependence structure, allowing flexible modeling of nonlinear linkages. Unlike correlation, copulas capture the full dependence surface, including asymmetric tail behavior: upper tail dependence (co-movement during rallies) and lower tail dependence (joint crashes). This capability is essential for quantifying spillover risk, as contagion often manifests precisely in the tails.
Empirically, we estimate normal and Student-t marginals alongside five copula families—Gaussian, t, Clayton, Frank, and Gumbel—on 6,822 daily returns from BMO, BNS, CIBC, NBC, RBC, and TD over the period 2000-2019. We use information criteria to choose best fitted copula model. The Gumbel copula, which captures upper tail dependence, is selected for some bank pairs, revealing substantial co-movement during market upswings. Conversely, some banks exhibit weaker dependence, suggesting a differentiated spillover profile. The t-copula consistently outperforms the Gaussian copula, confirming that tail dependence is a persistent feature of Canadian bank interdependencies. By explicitly modeling nonlinearities and tail asymmetries, the copula GARCH approach provides a more accurate assessment of spillover risk, with direct implications for portfolio diversification, systemic risk monitoring, and regulatory stress testing.