Regime-dependent price dynamics in critical mineral project valuation: a stochastic comparison of a CMSRI-driven threshold autoregressive framework and Geometric Brownian Motion

The valuation of critical mineral projects under uncertainty remains anchored to deterministic Discounted Cash Flow and Geometric Brownian Motion frameworks, which impose constant volatility and log-normal price assumptions poorly suited to regime-dependent commodity markets. This study specifies a Critical Mineral Systemic Risk Index Threshold Autoregressive (CMSRI-TAR) model and compares it with GBM inside a common Monte Carlo project engine, applied to the Dolphin Tungsten Project on King Island, Tasmania, over a 14-year mine life. Using 10,000 paired paths under Common Random Numbers, CMSRI-TAR yields a narrower and less adverse NPV distribution than GBM, with CVaR 95% estimates separated by approximately A$39.5 million. None of the three directional hypotheses is supported. The divergence reflects two properties of the estimated specification rather than any demonstrated forecasting advantage: the high-CMSRI regime carries a positive intercept and covers four-fifths of the sample, and negative autoregressive coefficients in both regimes slow the growth of log-price variance relative to a random walk. Because no out-of-sample evaluation is reported, the analysis establishes that the choice of price process is consequential for project-level tail risk, but not which process better represents tungsten prices. Critical mineral projects such as tungsten mines are usually valued with models that assume prices move randomly with constant volatility. This research shows that the choice of price model materially changes the risk profile of a project. Applied to the Dolphin Tungsten Project in Australia, a model in which prices respond to a systemic risk index produces a narrower range of project values and a smaller downside than the conventional model, with a difference of about A$39.5 million in expected loss under adverse conditions. The findings indicate that investors, lenders, and policymakers should justify their price model explicitly, because this choice can shift financing terms and investment decisions for critical mineral projects.