Gold as an Implicit Call Option on Fiat Collapse: A Model-Driven Analysis

According to the methodology of Dixit and Pindyck (1994), gold contains an implicit call option on the collapse of the fiat system. The price dynamics St incorporate a Poisson jump process Nt: dSt/St = μdt + σdWt + (J-1)dNt, where Nt∼Poisson(λ) for the arrival of a systemic fiat crisis, and J is the jump amplitude (e.g., +300%). The value of the implicit option C_o is: C_o = S₀e^{-λT}Φ(d₁) – Ke^{-rT}Φ(d₂) + Σ_{k=1}^{∞} e^{-λT}(λT)^k/k! × Payoff_k. Even with a low λ (2% per year), the time value and asymmetry justify a structural allocation. This serves as a hedge against tail risk, validated by massive purchases from central banks (BRICS) via Steelldy Engine 3.8.