Paper #59

System Reliability Analysis of Correlated Multi-Asset Stop-Loss Positions Using FORM, Ditlevsen Bounds, and Sobol Attribution

Bassem Saassouh

Presenting author: Bassem Saassouh

Session: O10

Abstract

Standard per-asset risk tools do not aggregate correlated failures into a single system-level breach probability with design-point scenarios and factor attribution. This paper formulates the multi-asset stop-loss problem as a six-dimensional series-system reliability problem at the terminal horizon. Three correlated loss shocks and three uncertain volatilities enter through the Nataf transformation. FORM locates the component design points and Ditlevsen bounds bracket the system failure probability. On an illustrative Gold--Silver--Bitcoin case study at a one-week horizon, FORM-based inclusion--exclusion gives 0.228 against Monte Carlo 0.223. The assumed correlation reduces the union probability by 4.8 percentage points relative to independence. Failures cluster rather than become universally less likely. A Sobol decomposition attributes about 55 percent of Silver's stop-breach variance to a latent factor aligned with Gold's shock. The three volatility uncertainties together contribute below 1 percent of system-margin variance.