Industry: Mining and Natural Resources
Product: ModelRisk
Application: Quantifying geological and financial uncertainty in exploration drilling decisions

Pricing the option to drill another 12 holes

Each diamond-drill hole into a frontier orogenic-gold prospect costs $420,000 fully loaded — rig mobilisation, downhole geophysics, assay turnaround, environmental bond. A junior explorer with a 12-hole follow-up budget and a posted-NPV of $48M was about to drop the program. The deterministic answer said the project was already economic at expected ore grade 2.4 g/t Au, expected resource 1.6 Moz contained gold. The Monte Carlo rerun showed that 34% of the realisations returned NPV below zero — and an "expected value of perfect information" of $12.4M, easily covering the $5.0M drill program. The 12 holes got funded.

The single $48M point estimate becomes the distribution below: a mean of $48M that sits above the $32M median, a P10 of -$55M and a P90 of $174M, with a third of the mass on the loss side of zero.


Exploration is a sequential decision problem under thick geological uncertainty, and the question is rarely "is this deposit there?" but "is it worth spending more to find out?" ModelRisk lets that question be answered numerically.

Decomposing the probability of economic mineralisation

The traditional shortcut — multiply structure probability by grade probability by size probability — is wrong: those three events are not independent. A favourable structure is itself evidence the grade and size will be higher. The probabilistic rebuild used a copula-linked decomposition:

• P(structure favourable): Beta(α = 3, β = 7), mean 0.30, calibrated from regional geophysics and 14 analog deposits within 80 km.
• Mean grade | structure favourable: LogNormal(μ = ln 2.4, σ = 0.45) g/t Au — right-skewed, consistent with most orogenic-gold systems.
• Contained gold | favourable + grade: Triangular(0.4, 1.6, 4.2) Moz, where the upper limit is the regional geological-analog maximum.
• A Gaussian copula with ρ = 0.55 linking structure probability and grade — better-than-analog structure pulls grade up, not independently. The realised sample correlation lands at 0.52, confirming the dependence is actually in the simulation and not just declared.

Marginalising over all three gives the probability of an economic deposit (defined as favourable structure with >0.8 Moz Au at >1.8 g/t) at 40% — versus the independence answer of 33% when the same criteria are applied to copula-decorrelated draws. The dependence matters.

The pre-drill NPV distribution

Combining the geological prior with a metallurgical recovery prior (Beta(40, 4), mean 91%, σ = 4.4%), a long-run gold price (LogNormal, mean $1,920/oz, σ_log = 0.18, mean-reverting with 6-year half-life), and operating-cost priors (LogNormal AISC mean $1,180/oz, σ_log = 0.22), the project NPV at 8% discount has:

• Mean = $48M, median = $32M
• P10 = -$55M (loss), P90 = $174M
• P(NPV > 0) = 66%, P(NPV > $100M) = 25%

The deterministic spreadsheet had reported $48M as a point answer. The Monte Carlo showed it sat above the median, with a 34% loss tail averaging -$43M conditional on loss.

Why Monte Carlo, not a point estimate

The deterministic NPV said $48M and "proceed." The probabilistic NPV said $48M ± a $55M downside tail and "the value of one more drill campaign is $12.4M." Same expected value, opposite recommendation — because the deterministic answer is silent on the question that funds the drill rig.

Value of perfect information

The drill campaign's purpose is to collapse the geological prior toward the truth. We approximated EVPI as the expected NPV under perfect knowledge of P(structure) and mean grade minus the expected NPV under the current prior, restricted to states where the project would still be advanced. The result: EVPI = $12.4M.


The 12-hole program does not collapse the prior fully — it reduces grade σ_log from 0.45 to 0.28 (assay precision plus spatial coverage) and structure-probability β from 7 to 4. The expected value of that imperfect information (EVII) is $7.0M, against $5.0M cost — still a net $1.9M expected gain.

Tornado: what's actually moving the NPV


Mean grade dominates; AISC is second; gold price third (mean-reverting damping reduced its rank versus a naive GBM treatment). Structure probability is fourth — once grade and size land in a favourable region, the rest follows.

What the model changed

• The 12-hole follow-up was funded: probabilistic EVII = $7.0M > $5.0M cost, against a deterministic answer of "already economic, don't bother."
• The cut-off for advancing to a maiden resource was set at grade σ_log ≤ 0.30 — a probabilistic gate, not a fixed assay count.
• The project's risked NPV ($48M × 66% = $32M risked) replaced the deterministic $48M in the corporate portfolio model, freeing $11M of implicit committed capital for a parallel prospect.

ModelRisk functionality used

• Gaussian copula linking structure probability and grade with ρ = 0.55 (realised sample correlation 0.52), raising P(economic) from 33% (independence) to 40%.
• Mean-reverting LogNormal for gold price with 6-year half-life — gold price ranks third in the tornado, not first as a naive GBM model would suggest.
• Bayesian prior update of structure-probability Beta(3,7) → Beta(3+k, 7+12-k) for each simulated hit-rate k from the 12-hole program, driving the EVII calculation.
• Sensitivity decomposition by rank-order correlation, separating the financial drivers (price, AISC) from the geological ones (grade, recovery) and surfacing the imbalance that justified more drilling.
• EVPI/EVII module computing expected value of perfect and imperfect information, returning the $12.4M and $7.0M figures that financed the next campaign.

The deterministic NPV gives you a number; Monte Carlo gives you the price of finding out whether that number is right.