Pricing Geopolitical Risk: Closed-Form Valuation of Futures and Options on the GPR Index

On July 31, 2026, the European Central Bank (ECB) published the results of its thematic reverse stress test on geopolitical risk, in which 110 directly supervised banks identified scenarios severe enough to deplete CET1 capital by 300 bps. The exercise delivered narratives but not probabilities: without a market price of geopolitical risk, it has no quantitative anchor. This article closes that gap by applying the Grünbichler–Longstaff (1996) square-root, mean-reverting state-variable model directly to the Caldara–Iacoviello Geopolitical Risk (GPR) index, yielding closed-form prices for GPR futures and European options. Exact maximum-likelihood estimation on the monthly series from 1985 to June 2026 delivers a mean-reversion half-life of about two months toward a long-run mean of approximately 104, with the Feller condition satisfied with substantial slack, so the non-central chi-square pricing structure applies without modification. Applied to the ECB exercise, the framework converts the supervisory threshold into a tail-probability statement. Under the physical measure, the 12-month exceedance probability is approximately 12%—the answer a historical-simulation stress test would report. Under the risk-neutral measure it lies between 29% and 79% across the range of the market price of geopolitical risk motivated by analogy to inflation-swap risk premia—a bandwidth that is wide precisely because no traded GPR instrument yet identifies this parameter. Because the modeling techniques are deliberately standard, the article’s contribution is the practical layer: specification tests grounding the process choice in the data, confidence intervals around the physical anchor, a sensitivity analysis over the loss-channel mapping, and an explicit model-risk map organized for supervisory validation. The wedge between the physical probability and the risk-neutral band is the geopolitical risk premium, and a single observed transaction price on a cash-settled GPR contract—exchange-listed in the VSTOXX/VIX mold or OTC in the inflation-swap mold—would collapse the bandwidth to a point.