Measuring multivariate maximal tail dependence

Battle Count: 79

The MTCM is relevant for quantitative trading primarily through its application to multivariate tail dependence modeling, which is critical for portfolio risk management, stress testing, and understanding joint extreme events across assets. The identification of off-diagonal stress directions is particularly useful for scenario analysis. However, the paper is primarily theoretical and focused on hydrological applications, with no direct trading strategy or financial market application demonstrated.

For specific copula families (Marshall-Olkin, Archimax, nested Archimedean with regularly varying generators), closed-form expressions make implementation straightforward. For general copulas, numerical optimization over the constraint set B (product of coordinates equals 1) is required, which involves constrained optimization in d dimensions. The reparametrization via logarithmic coordinates (x_j = log(b_j)) simplifies the constraint to a linear one. No reference implementation is provided.

The paper provides complete closed-form expressions for MTCM and its maximizer for several copula families (Marshall-Olkin, Archimax, nested Archimedean). All proofs are included in the appendix. The application uses publicly available data from Smith et al. (1990) and Tawn (1990). However, no code or software implementation is provided, and the general numerical optimization for arbitrary copulas is not detailed.