MODEL 09 // Extreme Value Theory & Black Swan Risk

Pareto Fat-Tailed Peak-Over-Threshold (POT)

Applied Physics Catalogue
Governing Mathematical Equation
TVaRq(X)=αα−1xm(1−q)1/α,X=xmin⁡(1−U)−1/α\text{TVaR}_q(X) = \frac{\alpha}{\alpha - 1} \frac{x_m}{(1-q)^{1/\alpha}}, \quad X = x_{\min} (1 - U)^{-1/\alpha}

Systemic Risk Mechanism & Physics Formulation

Asymptotic tail loss quantification overriding Gaussian assumptions with fat-tailed Pareto distributions where 80% of damage stems from 1% of Black Swan events.

Key Technical Deliverables

>Tail Value-at-Risk (TVaR) Asymptotic Exceedance
>Heavy-Tailed Pareto Loss Index α Computation
>Extreme Value Theory (EVT) Black Swan Simulation