An Algorithmic Model Linking Military Force-Posture and Chokepoint Risk to Global Oil Prices

Executive summary

This report reconstructs a rigorous, modular “force‑posture → chokepoint/infrastructure risk → supply/flow impairment → price distribution” model for the global oil market across near‑term (0–12 months) and medium‑term (1–3 years) horizons in USD. The approach formalizes a decomposition between a structural baseline price (fundamentals) and a geopolitical/chokepoint risk premium (probability‑weighted tail risk), then specifies how force‑posture signals (e.g., rapid‑deployment forces) update scenario probabilities and expected physical impairments. [1]

The contemporary stress test for the model is the March 2026 Middle East war shock: the International Energy Agency (IEA) characterizes the crisis as the largest supply disruption in global oil market history, with flows through the Strait of Hormuz collapsing from ~20 mb/d pre‑war “to a trickle,” Gulf producers cutting output by at least ~10 mb/d, and global oil supply projected to plunge by ~8 mb/d in March (partly offset elsewhere). The IEA also states that member countries agreed on 11 March to make 400 million barrels available from emergency reserves, while prices experienced extreme swings (Brent futures near $120/bbl at the peak, later ~ $92/bbl “time of writing,” +$20/bbl for the month). [2]

Force‑posture matters because it changes the conditional probability of specific operational paths (e.g., seizure/denial of export hubs), which directly alters the market’s expected loss distribution. In March 2026 reporting, the U.S. Department of Defense[3] ordered deployment of thousands of paratroopers from the 82nd Airborne Division as the war with Iran[4] escalated; reporting also described Kharg Island as a focal option and a critical vulnerability for Iranian exports. [5]

Chokepoint and maritime‑risk inputs must be modeled explicitly. The U.S. Energy Information Administration[6] emphasizes that in 2024 the Strait of Hormuz carried ~20 mb/d (≈20% of global petroleum liquids consumption), with limited bypass capacity (about 2.6 mb/d potentially available via Saudi/UAE pipelines). [7] In March 2026, insurance and shipping frictions became a first‑order constraint: Reuters reported hull war‑risk premiums jumping from ~0.25% to as high as ~3% of vessel value in some cases (millions of dollars per voyage), while other reporting noted even higher extremes and a large stock of vessels trapped in the Gulf area—conditions that raise delivered costs, increase delays, and can themselves reduce effective supply. [8]

Historically, oil shocks show strong nonlinearities: large price responses relative to physical supply cuts, especially when disruptions are expected to escalate or persist. A canonical empirical anchor is that a 10% cut in world oil supplies from abrupt OPEC/Persian Gulf disruptions correlates with a ~35–43% rise in inflation‑adjusted crude prices. [9] Short‑run elasticities are central. In a structural framework, Kilian & Murphy estimate a median short‑run price elasticity of oil demand “in use” around −0.24 (68% bands −0.42 to −0.09) and note oil supply is nearly vertical on impact (~0.01–0.02). [10]

A calibrated, probability‑weighted model should output not a point forecast but a distribution and tail metrics (e.g., probability of >$120 or >$160). This report provides (i) a variable schema, (ii) a 1970‑present disruption table with sources, (iii) a model architecture (equations + pseudocode + mermaid flowchart), (iv) calibration/backtest examples using historical Brent spot data, and (v) a scenario ladder that shows how a $70 structural baseline can map to $80–90, $100–120, and $135–160+ under parameterized shock/buffer/elasticity/insurance regimes. [11]

Definitions and variable schema

This section defines a minimal but sufficient variable set to map (a) force‑posture and chokepoint states into (b) volume/flow impairments and (c) oil‑price outcomes. Variables are defined so they can be estimated daily and aggregated to weekly/monthly horizons.

Core price decomposition

Let:

P_obs(t) = observed benchmark oil price at time t (e.g., Brent spot or front‑month futures), USD/bbl. [12]
P_struct(t) = structural or fundamentals‑implied price (USD/bbl). Conceptually grounded in supply–demand balance, inventories, marginal barrel costs, and macro demand; operationally estimated via a structural model or reduced‑form baseline (see calibration section). [13]
Γ(t) = geopolitical + chokepoint + logistics risk premium (USD/bbl). This is the portion of price not explained by P_struct. [14]
ε_t = residual noise / model error.

ASCII math:

P_obs(t) = P_struct(t) + Γ(t) + ε_t

Force-posture and escalation signals

G(t) = geopolitical escalation factor (dimensionless index). Constructed from observable signals: troop deployments/alerts, naval asset movements, explicit threats/ultimatums, active strikes, and diplomatic off‑ramps. [15]
e = elasticity parameter(s). Because “elasticity” is overloaded, this report uses:
e_d_SR = short‑run price elasticity of oil demand (negative; magnitude |e_d_SR|). [10]
e_s_SR = short‑run price elasticity of oil supply (positive; very small on impact). [10]
e_d_MR, e_s_MR = medium‑run elasticities over 1–3 years (larger in magnitude than SR due to substitution/investment). [16]

Chokepoint and infrastructure constraint variables

C(t) = chokepoint/logistics constraint factor (dimensionless index), combining:
chokepoint status (open/contested/closed),
rerouting capacity utilization,
maritime insurance availability/cost,
shipping delays, and
port/storage constraints. [17]

Key embedded parameters:

Hormuz multiplier (m_H): nonlinear amplification (>1) capturing the fact that a chokepoint interruption creates delays and cost escalations beyond the nominal lost flow, especially when bypass capacity is small relative to normal through‑flow. Empirically motivated by the scale (≈20 mb/d) and limited bypass options (≈2.6 mb/d potentially available in disruption). [18]
Kharg concentration factor (k_Kharg): concentration multiplier for export disruption risk when a large share of a producer’s exports depends on a single hub. Reuters reports Kharg Island handles ~90% of Iranian oil exports and hosts major storage/terminal infrastructure, implying high single‑point fragility. [19]
time-to-repair (T_repair): distribution of repair/restoration time for damaged processing/export infrastructure (days–months). For example, after the 2019 Abqaiq attack, Saudi Aramco reported partial output quickly and expected full restoration by end‑September, implying a T_repair on the order of weeks for that incident. [20]
rerouting capacity (R_route): available pipeline/alternative export capacity (mb/d) that can bypass the chokepoint. EIA estimates ~2.6 mb/d potentially available via relevant Saudi/UAE pipelines in a disruption scenario (noting operational constraints). [7]
shipping delays (Δt_ship): additional transit time (days) due to rerouting, convoying, port congestion, or halted movement. These delays effectively reduce near‑term deliverable supply and raise working‑capital/storage needs. [18]
tanker insurance premium (π_ins): incremental war‑risk premium (USD per voyage or % hull value) that can be converted into USD/bbl shipping cost. Reuters reported hull war‑risk premiums jumping from ~0.25% to as high as ~3% of vessel value in early March 2026. [21]

Supply-loss, buffers, and scenario outputs

loss_i: gross supply or export loss component i (mb/d). Examples: (i) production shut‑ins, (ii) export terminal outages, (iii) refinery outages, (iv) sanctions‑driven export reductions. [22]
inventories (I): usable inventories (commercial + strategic), often best represented as days of cover and by location/quality (light vs heavy). EIA and the IEA both emphasize inventories as the first buffer in outages. [23]
spare capacity (S_spare): sustainable supply that can be brought online rapidly (mb/d). The IEA’s OMR defines sustainable capacity as able to be reached within 90 days and sustained; it gives country-level “effective spare capacity” estimates. [2]
P_scenario: scenario price outcome (distribution), USD/bbl.
Tail-risk metrics: e.g., P(P_scenario > 120), P(P_scenario > 160), VaR_95, CVaR_95.

Historical precedent and a sourced timeline of major oil disruptions since 1970

Historical shocks repeatedly show three patterns that matter for modeling:

Price responds to both realized supply loss and the risk of escalation (risk premium), especially for Persian Gulf disruptions. [24]
Inventories and spare capacity shape the peak and the persistence of price spikes. [25]
Logistics/insurance constraints can become binding, turning “flow problems” into “production shut‑ins,” as described by the IEA in March 2026 when storage filled and exports stalled. [26]

Major disruptions timeline (illustrative)

Sourced disruption table

The table below emphasizes (i) physical supply/flow impairment, (ii) price impact and volatility, and (iii) duration/persistence, using mostly primary/official and peer‑reviewed sources.

Episode	Date window	Mechanism	Quantified supply/flow impact	Price/volatility outcome (illustrative)	Duration notes	Sources
OAPEC embargo / 1973–74 shock	Oct 1973–Mar 1974	Embargo + production cuts	Supply disruption estimated ~7.8% of world production (drop measure used in Hamilton’s compiled shock list)	Oil price nearly quadrupled from ~$2.90/bbl to ~$11.65/bbl by Jan 1974	Embargo lifted Mar 1974; higher price regime persisted	[27]
Iranian Revolution / second oil shock	1978–1980 (shock concentrated 1979–80)	Revolution + precautionary demand/hoarding	Iranian output decline ~4.8 mb/d (≈7% of world prod at the time) by Jan 1979; shock list reports ~8.9% world‑production “drop”	Oil prices more than doubled between Apr 1979 and Apr 1980	Spike linked to both realized loss and fear of further disruptions	[28]
Iran–Iraq War (incl. early production losses)	1980–1981 (early shock)	War removes production temporarily; later replacement elsewhere	Combined loss of Iran+Iraq production about ~6% of world production (Hamilton narrative); shock list reports ~7.2% world‑production “drop”	Real oil price doubled between 1978 and 1981 (depending on price measure)	Initial shortfall made up elsewhere “within a few months” in Hamilton’s account	[29]
Tanker War insurance escalation (Kharg focus)	1984–1988	Attacks on shipping/terminals raise war risk & costs	Hull rates reached ~7.5% for Kharg after a May 1984 attack (insurance market example), illustrating how logistics can choke flows without total production loss	Higher freight/insurance costs; increased risk premium; set precedent for convoy/escort strategies	Demonstrates insurance as a transmission channel for price effects	[30]
Iraq invades Kuwait / Gulf Crisis	Aug 1990–1991	Production disruption + escalation fear	Peak lost production about ~4.3 mb/d combined Iraqi+Kuwaiti crude; shock list reports ~8.8% world‑production “drop”	Historical accounts document immediate price run‑up; (see backtest chart for Brent response)	Kuwait recovered faster than Iraq (sanctions/conflict impeded)	[31]
Venezuelan strike + Iraq War II run‑up	2002–2003	Strike + war uncertainty; temporary Iraqi loss	Hamilton reports Venezuelan strike eliminated ~2.1 mb/d (Dec 2002–Jan 2003) and US attack removed ~2.2 mb/d over Apr–Jul 2003	St. Louis Fed review describes a “war premium” often discussed at ~$5–$15/bbl around Iraq (illustrative framing)	Example of “buy the rumor / sell the news” dynamics	[32]
Arab Spring / Libya civil war disruption	2011	Civil conflict removes high‑value light sweet crude	EIA: production fell ~60–90%; IEA: 132 mb removed by end‑May; IEA coordinated 60 mb release (2 mb/d for 30 days)	Sustained tightness risk; quality mismatch amplified price effect beyond volumetric loss	IEA expected Libyan supplies largely off rest of 2011	[33]
Abqaiq–Khurais attacks	Sep 2019	Processing outage + risk repricing	EIA: Abqaiq reduced to ~2.0 mb/d vs est. 7.0 mb/d capacity; Khurais 1.2 mb/d shuttered for 24h	EIA: 12.7% daily Brent change was largest in 29 years; large intraday ranges; partial reversal as information arrived	Aramco expected full restoration by end‑Sep 2019; inventories buffered exports	[34]
Russia–Ukraine energy shock	2022–	War + sanctions/rerouting	IEA (Mar 2022) warned of material losses to Russian supply; ECB analysis highlights sharp initial price spike	ECB: oil prices rose sharply post invasion and later returned around pre‑invasion levels after ~8 weeks (contextual)	Medium‑term effects mediated by rerouting, demand response, policy	[35]
Red Sea/Bab al‑Mandeb disruptions	2023–2025	Attacks raise routing/insurance costs and shift flows	EIA notes 2024 disruptions around Bab al‑Mandeb led Aramco to route more crude overland via East‑West pipeline to Red Sea ports	Reuters: war‑risk premiums for Red Sea voyages rose to ~1% of ship value in Jan 2024 (illustrative cost channel)	Demonstrates persistent logistics premium without full supply loss	[36]
Middle East war / Hormuz shock	Feb–Mar 2026 (ongoing)	Chokepoint closure + infrastructure strikes + storage saturation	IEA: Hormuz flows plunge from ~20 mb/d to a trickle; Gulf producers cut at least ~10 mb/d; supply projected −8 mb/d in March; refineries shut; 400 mb emergency release	IEA: Brent futures near $120/bbl then ~ $92; high volatility; insurance/physical protection key to flow resumption	Outcomes depend crucially on duration of shipping disruption and infrastructure damage	[37]

Elasticities and key response parameters

Elasticities are not “one number.” They vary by horizon (SR vs MR), by whether inventories are treated explicitly, and by whether the model is structural or reduced‑form.

Short-run demand elasticity

In a structural oil market model incorporating inventories, Kilian & Murphy estimate:

median short‑run price elasticity of oil demand in production around −0.44, and
median short‑run price elasticity of oil demand in use around −0.24 (with 68% error bands roughly −0.42 to −0.09). [10]

For many tail‑risk calculations, the “demand in use” elasticity is the relevant stabilizer because it reflects substitution/demand response at the point of consumption and incorporates inventory behavior more realistically than zero‑elasticity conjectures. [10]

Short-run supply elasticity

Kilian & Murphy also emphasize that short‑run oil supply is near vertical, with their estimate on impact around 0.01–0.02. [10] This is why even moderate net disruptions can generate large price moves, particularly if buffers are constrained.

Medium-run elasticities and nonlinearities

Over 1–3 years, both demand and supply become more elastic due to substitution, efficiency, and investment responses; time‑varying evidence also suggests that macro context affects impulse responses (e.g., different eras exhibit different oil‑shock sensitivities). [38]

A useful empirical check on “effective elasticity” in crisis regimes is Huntington’s historical finding: a 10% cut in world oil supplies from abrupt OPEC/Persian Gulf disruptions correlates with ~35–43% increases in inflation‑adjusted crude prices—implicitly combining physical scarcity, escalation risk, and market frictions. [9]

Algorithmic model architecture

A robust model should be scenario‑based, because the mapping from posture to outcomes runs through discrete operational states (open vs contested vs closed chokepoint; limited vs extensive infrastructure damage; coordinated stock release vs delayed response). The goal is probability‑weighted distributions and tail metrics, not a single price.

Structural equations

1) Scenario probabilities: posture → probabilities

Let scenarios be s ∈ {0,1,2,...} (e.g., “status quo,” “partial disruption,” “major hub outage,” “chokepoint closure,” “closure + infrastructure loss”). Define a feature vector:

X(t) = [force posture score, strike intensity proxies, diplomatic signals, chokepoint status, insurance premium, inventory tightness, spare capacity, positioning z‑scores, …].

Use a softmax map:

score_s(t) = β_s · X(t)
π_s(t) = exp(score_s(t)) / Σ_k exp(score_k(t))

2) Physical impairment: scenario → net effective shortfall

Define:

L_s(t) = Σ_i loss_{i,s}(t) (gross loss, mb/d)
B_s(t) = offsets from buffers (mb/d) = spare capacity ramp + inventory draw rate + rerouting capacity actually usable − refinery/feedstock bottlenecks

Then:

ΔQ_s(t) = max(0, L_s(t) - B_s(t)) (mb/d)
d_s(t) = ΔQ_s(t) / Q_world(t) (fraction of global market)

3) Chokepoint/logistics premium: C(t)

Represent chokepoint closure and logistics constraints as a cost and delay shock:

shipping cost adders ($/bbl) from π_ins and freight,
and an “availability” reduction from Δt_ship (some barrels arrive late, effectively shrinking near‑term supply).

IEA explicitly highlighted that adequate insurance and physical protection are key to resuming flows through Hormuz, and that storage filling forces production cuts in the region—exactly the dynamic C(t) is meant to capture. [26]

4) Price mapping: net shortfall + elasticity

With constant‑elasticity demand as a first approximation:

Q = A * P^(-|e_d_SR|)
=> P_s,phys(t) = P_struct(t) * (1 / (1 - d_s(t)))^(1/|e_d_SR|)

Then add risk/logistics premium (one workable approach is multiplicative risk premium + additive shipping cost):

P_scenario_s(t) = P_s,phys(t) * (1 + RP_s(t)) + ShipCost_s(t)

where RP_s(t) is a scenario‑conditional risk premium component driven by escalation uncertainty and market microstructure.

5) Mixture distribution output

P_scenario(t) ~ mixture over s: Σ_s π_s(t) * Dist_s( P_scenario_s(t) )

Compute:

Expected price: E[P_scenario(t)]
Tail probability: Pr(P_scenario(t) > K)
VaR_α, CVaR_α

Pseudocode

INPUTS (daily/weekly):
P_obs, inventory levels (by region & quality), spare capacity,
chokepoint status (Hormuz/Bab al-Mandeb), R_route,
tanker insurance premium π_ins, shipping delays Δt_ship,
force posture signals (deployments, alerts), market positioning

STEP 1: Estimate/Update P_struct(t)
- baseline model (e.g., supply-demand balance + inventories + macro demand proxy)
- Kalman filter or rolling regression to update

STEP 2: Build feature vector X(t)
- posture score, chokepoint flags, insurance premium, inventories z-score, spare capacity, etc.

STEP 3: Update scenario probabilities π_s(t) = softmax(β_s·X(t))

STEP 4: For each scenario s:
- draw loss components loss_{i,s} (production shut-ins, export loss, refinery loss)
- compute buffers B_s (spare capacity ramp, inventory release, rerouting)
- compute d_s = max(0, L_s - B_s)/Q_world
- map to price using elasticity distribution + risk premium model + shipping cost

STEP 5: Aggregate to mixture distribution:
- P_scenario distribution via Monte Carlo
- output E[P], median, VaR/CVaR, exceedance probabilities

OUTPUTS:
- Probability-weighted price distribution
- Tail-risk metrics (Pr > 120, Pr > 160, VaR95, CVaR95)
- Attribution: physical vs logistics vs risk premium

Mermaid flowchart of model components

flowchart TD
A[Force-posture signals deployments, alerts, strikes, diplomacy] --> B[Geopolitical factor G(t) escalation & resolution scores]
C[Chokepoint status C(t) open/contested/closed rerouting capacity] --> D[Flow impairment model ΔQ_s(t)]
E[Inventories & spare capacity commercial + strategic + OPEC spare] --> D
F[Insurance & shipping frictions π_ins, freight, Δt_ship] --> D
B --> P[Scenario probabilities π_s(t)]
D --> M[Price mapping elasticity + risk premium]
P --> Z[Mixture distribution]
M --> Z
Z --> O[Outputs E[P], median, VaR/CVaR, Pr(P>K)]

Calibration, backtesting, and sensitivity analyses

This section shows how to (a) calibrate baseline mappings and (b) test predictive behavior using historical episodes with publicly available data.

Data used for the illustrative backtests

Brent spot price series: “Europe Brent Spot Price FOB (Dollars per Barrel)” from EIA’s historical data tables (daily). [39]
Event anchors (start dates) are chosen at the first trading day when the disruption became known/active (examples below), consistent with EIA’s discussion of intraday and daily responses to disruption news. [34]

Event-study backtest: how Brent behaved around shock onsets

The chart below indexes Brent to 100 at the pre‑event close and plots a −20 to +60 trading‑day window around several major disruption onsets (1990, 2003, 2011, 2019, 2022, and the early‑March 2026 war shock in the EIA series).

Brent event study

Interpretation highlights:

1990 Gulf Crisis shows a steep re‑pricing consistent with a large disruption and escalation fear. EIA documents a combined Iraq/Kuwait outage peaking around 4.3 mb/d, and Hamilton’s shock list frames the event as an ~8.8% world‑production drop. [40]
2003 Iraq invasion shows “sell the news” behavior in this event‑window setup—consistent with a resolving uncertainty channel and the idea that war risk can be priced in ahead of the event and unwind on realization. [41]
2019 Abqaiq produced an unusually large one‑day move and intraday range; EIA reports the 12.7% daily change was the largest in 29 years and details the temporary processing reduction. [34]
2026 shock reflects early‑March repricing; the IEA describes extreme volatility and a near‑halt in Hormuz movement, which is exactly the condition where chokepoint/logistics variables should dominate scenario selection and tails. [2]

A simple physical-mapping backtest: predicted vs observed peaks

As a deliberately conservative benchmark, map an assumed supply‑cut fraction d to a “no‑risk‑premium” predicted peak using constant‑elasticity demand with |e_d_SR|≈0.24 (Kilian & Murphy demand‑in‑use median). [10]

Backtest scatter

This diagnostic reveals systematic gaps:

Some events plot above the diagonal (observed > predicted), consistent with risk premium/logistics amplification dominating (e.g., early 2022, where expectations and policy uncertainty were large). [42]
Some events plot below the diagonal (observed < predicted), consistent with buffers and rapid restoration (inventories, spare capacity, and quick repairs) blunting the price path (e.g., Abqaiq where Aramco expected restoration within weeks and exports were supported by inventory draw). [43]

This is exactly why a complete model must treat inventories/spare capacity and time‑to‑repair as explicit state variables—not afterthoughts. [44]

Sensitivity analysis: why elasticity dominates “the $160 math”

Under constant‑elasticity demand (no risk premium, no shipping premium), the price response is:

P_new = P0 * (1 / (1 - d))^(1/|e|)

Sensitivity of price (P0 = $70) to net supply shortfall d and |e|:

| Net shortfall d | |e|=0.06 | |e|=0.10 | |e|=0.15 | |e|=0.24 | |e|=0.30 | |---:|---:|---:|---:|---:|---:| | 2% | 98.0 | 85.7 | 80.1 | 76.1 | 74.9 | | 4% | 138.2 | 105.3 | 91.9 | 83.0 | 80.2 | | 6% | 196.3 | 130.0 | 105.7 | 90.6 | 86.0 | | 8% | 281.0 | 161.1 | 122.0 | 99.1 | 92.4 | | 10% | 405.2 | 200.8 | 141.3 | 108.6 | 99.5 | | 12% | 589.4 | 251.3 | 164.1 | 119.2 | 107.2 |

Two implications:

If |e| is near ~0.24 (Kilian & Murphy median demand‑in‑use), even large net disruptions produce big but not infinite price moves. [10]
Tail outcomes like $160 become plausible when (i) net disruptions get into high single digits and/or (ii) the effective short‑run elasticity collapses in crisis microstructure (physical rationing, delayed response, refinery/feedstock constraints), and (iii) logistics/insurance choke flows. These dynamics are consistent with historical evidence that price responses can be large relative to cuts, especially for Persian Gulf disruptions. [45]

Scenario ladder: mapping a $70 structural baseline to $80–90, $100–120, and $135–160+

This section constructs three parameterized cases using the model logic. The purpose is not to assert a single forecast, but to show transparent arithmetic that connects assumptions to outcomes and to identify which assumptions do the work.

Shared notation

Let baseline structural price be:

P_struct = $70

Let the net shortfall fraction be:

d = (gross_loss - buffers) / Q_world
buffers = spare_ramp + inventory_release + rerouting - bottlenecks

Price mapping (physical channel):

P_phys = P_struct * (1 / (1 - d))^(1/|e_d_SR|)

Then add risk/logistics:

P_scenario = P_phys * (1 + rp) + ship_cost

Where:

rp = scenario risk premium rate (dimensionless),
ship_cost = insurance/freight/delay cost converted to $/bbl.

Case A: mild escalation / partial logistics friction → $80–90

Assume:

gross_loss ≈ 4% of global supply
buffers ≈ 2% (inventories + limited spare + rerouting)
net shortfall d = 0.02
|e_d_SR| = 0.24 (baseline structural estimate) [10]
rp ≈ 5%
ship_cost ≈ $2/bbl

ASCII math:

d = 0.02
P_phys = 70 * (1/0.98)^(1/0.24) ≈ 70 * 1.0878 ≈ 76
P_scenario ≈ 76*(1.05) + 2 ≈ 82

Interpretation: this is the regime of “stress but not panic,” often seen when flows are disrupted but buffers and rerouting prevent a sustained physical drawdown. The EIA’s chokepoint framing explains why even temporary delays can raise costs, but the effect is bounded when alternatives exist and inventories can bridge. [46]

Case B: severe stress / partial chokepoint impairment → $100–120 (with fat right tail)

Assume:

gross_loss ≈ 10%
buffers ≈ 3%
d = 0.07
|e_d_SR| = 0.24
rp ≈ 12%
ship_cost ≈ $6/bbl

d = 0.07
P_phys = 70 * (1/0.93)^(1/0.24)
≈ 70 * (1.0753)^(4.167) ≈ 70 * 1.35 ≈ 94.5
P_scenario ≈ 94.5*(1.12) + 6 ≈ 112.8

This resembles a world where the chokepoint is not fully closed but is “functionally impaired” (high insurance premiums, sporadic movement, storage filling), which is consistent with the IEA’s description that export‑oriented refineries shut as storage tops up and producers curtail output when ships cannot load. [26]

Case C: chokepoint closure + concentrated hub risk → $135–160+

This is the regime where force posture (and the implied operational path) matters most. Two empirical anchors motivate the structure of this case:

Hormuz is a critical chokepoint with ~20 mb/d flow scale and limited bypass options; disruption can rapidly become a global physical shortage, not just a risk premium. [18]
Kharg Island concentration is extreme (reported ~90% of Iranian exports), implying high fragility if a campaign targets or denies that hub. [19]

Assume:

gross_loss ≈ 12%
buffers ≈ 3%
d = 0.09
|e_d_SR| modestly more inelastic in crisis microstructure (e.g., 0.18–0.24 effective; inventories can help but logistics constraints bind)
rp ≈ 20–25% (escalation + duration uncertainty)
ship_cost ≈ $10–$15/bbl (insurance/freight/delay translation)

One illustrative arithmetic point:

d = 0.09
|e| = 0.20
P_phys = 70 * (1/0.91)^(1/0.20)
= 70 * (1.0989)^5 ≈ 70 * 1.60 ≈ 112
P_scenario ≈ 112*(1.25) + 12 ≈ 152

This is consistent with IEA language that duration of Hormuz disruption is decisive, and with reported war‑risk premium spikes that can impose de facto blockades even when physical passage is theoretically possible. [37]

Probability distributions for Cases A/B/C

The plot below shows illustrative Monte Carlo distributions (truncated display window), using uncertain gross losses, buffers, crisis‑shifted elasticities, risk premium rates, and shipping costs.

Scenario distributions

Illustrative tail interpretation (qualitative):

Case A places most probability mass in the ~$75–90 range (low tail beyond $120).
Case B centers around ~$100–130 with meaningful probability above $120 and a non‑trivial right tail (reflecting escalation uncertainty).
Case C shifts the center into the ~$130–160 zone with substantial probability mass above $160, representing “closure + concentrated infrastructure risk + insurance/friction constraints.”

The modeling rationale for fat tails is consistent with historical evidence that Gulf shocks are amplified by escalation risk and logistics constraints. [47]

Invalidation conditions, interventions, and data sources for implementation

Invalidation conditions (what breaks the $135–160+ path)

A high‑price tail scenario should be actively invalidated when any of the following are observed:

Verified restoration of chokepoint throughput (e.g., sustained tanker transits and loadings returning toward pre‑shock levels), because Hormuz flow scale is the core amplifier. [18]
Insurance and protection mechanisms normalize (war‑risk premiums collapse; escorted corridors credible), since insurance/availability can be the binding constraint even when the waterway is not physically blocked. [48]
Demonstrated spare capacity + inventory release + rerouting provide durable offsets, turning a gross shock into a smaller net shortfall (d falls). The IEA explicitly frames emergency releases as a buffer but only a stopgap if disruptions persist. [49]
Demand destruction becomes visible and durable (flight cancellations, industrial curtailments, product export restrictions). The IEA already quantified demand reductions tied to flight disruptions and product shortages in March–April 2026 relative to earlier expectations; this channel grows as prices rise. [2]

Policy and market interventions that alter outcomes

Interventions change outcomes primarily by increasing buffers B(t) or by lowering the duration probability of adverse scenarios:

Coordinated strategic stock draws: IEA’s coordinated emergency releases (e.g., 60 mb in 2011; 400 mb in March 2026) directly add to effective supply over a defined period. [50]
Physical protection / escorted corridors: can reduce π_ins and increase effective throughput, collapsing the logistics premium and preventing storage‑forced production cuts. [26]
Rerouting infrastructure use (pipelines bypassing chokepoints): EIA estimates some bypass capacity, but it is limited relative to Hormuz scale and may already be in use, limiting surge capability in crisis. [7]
Repair speed and redundancy: speed of restoration (e.g., Abqaiq 2019 timeframe) truncates T_repair and sharply reduces tail risk. [43]

Recommended data sources and APIs

A production implementation should avoid single‑source dependence and should separate open, official, and commercial/proprietary feeds.

Model input	Preferred data source type	Practical examples (non-exhaustive)	Notes
Benchmark prices P_obs	Official + exchange-derived	EIA historical Brent spot (daily), ICE settlement (for futures), front‑month curves	EIA daily Brent series supports long backtests. [12]
P_struct drivers	Official + macro	global demand proxies, OECD/IEA inventory reports, refinery runs	Structural baseline should be model-based, not hand-waved. [44]
Chokepoint flow scale	Official analytics	EIA chokepoint analyses (Hormuz flows, bypass capacity)	EIA provides key scale and bypass estimates. [7]
Inventories I(t)	Official	IEA OMR observed stocks; OECD cover days; government vs commercial splits	March 2026 OMR provides global observed stocks breakdown. [2]
Spare capacity S_spare	Official analytics	IEA OMR “sustainable capacity” and “effective spare capacity”	Use country-level series and ramp constraints. [2]
Insurance premium π_ins	Market reporting + brokers	Reuters insurance reports; London market statements	Convert % hull value to $/bbl via ship size/route assumptions. [51]
Shipping delays Δt_ship	AIS/port analytics	AIS-based providers (commercial) + official disruption notes	In crisis, delays create effective supply loss. [52]
Force posture features	Official statements + credible reporting	DOD announcements; major‑paper reporting; defense beat wires	Use parsimonious features (troops, readiness, strike tempo). [53]
Hub concentration (k_Kharg)	Market intelligence + reporting	Reuters on Kharg export shares + storage	Concentration is a structural fragility input. [19]

A note on claims that “force posture rewrites the oil equation”

The model implication is precise: force posture does not change oil prices directly—it changes the probability distribution over discrete outcomes (closure vs partial flow, hub denial vs intact infrastructure, rapid repair vs prolonged outage). When the threatened node is a chokepoint of ~20 mb/d scale with limited bypass capacity, or an export hub handling ~90% of a major producer’s exports, probability shifts can rationally produce large risk premia and fat‑tailed price distributions. [54]

[1] [2] [26] [37] [49] [52] https://www.iea.org/reports/oil-market-report-march-2026

https://www.iea.org/reports/oil-market-report-march-2026

[3] [4] [10] [13] [25] [44] https://www.cftc.gov/sites/default/files/idc/groups/public/%40swaps/documents/file/plstudy_28_cepr.pdf

https://www.cftc.gov/sites/default/files/idc/groups/public/%40swaps/documents/file/plstudy_28_cepr.pdf

[5] [6] [15] [53] https://www.reuters.com/world/middle-east/us-expected-send-thousands-soldiers-middle-east-sources-say-2026-03-24/

https://www.reuters.com/world/middle-east/us-expected-send-thousands-soldiers-middle-east-sources-say-2026-03-24/

[7] [17] [18] [36] [46] [54] https://www.eia.gov/todayinenergy/detail.php?id=65504

https://www.eia.gov/todayinenergy/detail.php?id=65504

[8] [21] [48] [51] https://www.reuters.com/world/middle-east/maritime-insurance-premiums-surge-iran-conflict-widens-2026-03-06/

https://www.reuters.com/world/middle-east/maritime-insurance-premiums-surge-iran-conflict-widens-2026-03-06/

[9] [24] [45] [47] https://www.sciencedirect.com/science/article/abs/pii/S0301421517308443

https://www.sciencedirect.com/science/article/abs/pii/S0301421517308443

[11] [12] [39] https://www.eia.gov/dnav/pet/hist/rbrtem.htm

https://www.eia.gov/dnav/pet/hist/rbrtem.htm

[14] [34] https://www.eia.gov/todayinenergy/detail.php?id=42675

https://www.eia.gov/todayinenergy/detail.php?id=42675

[16] [38] https://users.ugent.be/~gpeersma/gert_files/research/BP1_april11.pdf

https://users.ugent.be/~gpeersma/gert_files/research/BP1_april11.pdf

[19] https://www.reuters.com/business/energy/kharg-island-struck-by-us-is-key-hub-iran-oil-exports-2026-03-14/

https://www.reuters.com/business/energy/kharg-island-struck-by-us-is-key-hub-iran-oil-exports-2026-03-14/

[20] [23] [43] https://www.eia.gov/todayinenergy/detail.php?id=41413

https://www.eia.gov/todayinenergy/detail.php?id=41413

[22] [31] [40] https://www.eia.gov/todayinenergy/detail.php?id=730

https://www.eia.gov/todayinenergy/detail.php?id=730

[27] https://www.federalreservehistory.org/essays/oil-shock-of-1973-74

https://www.federalreservehistory.org/essays/oil-shock-of-1973-74

[28] https://www.federalreservehistory.org/essays/oil-shock-of-1978-79

https://www.federalreservehistory.org/essays/oil-shock-of-1978-79

[29] [32] https://econweb.ucsd.edu/~jhamilton/oil_history.pdf

https://econweb.ucsd.edu/~jhamilton/oil_history.pdf

[30] https://www.strausscenter.org/strait-of-hormuz-insurance-market/

https://www.strausscenter.org/strait-of-hormuz-insurance-market/

[33] https://www.eia.gov/todayinenergy/detail.php?id=390

https://www.eia.gov/todayinenergy/detail.php?id=390

[35] [42] https://www.eia.gov/todayinenergy/detail.php?id=51658

https://www.eia.gov/todayinenergy/detail.php?id=51658

[41] https://oxfordenergy.org/wpcms/wp-content/uploads/2010/11/SP1-TheFirstOil-WarImplicationsoftheGulfCrisisintheOilMarket-LArcheretal-1990.pdf

https://oxfordenergy.org/wpcms/wp-content/uploads/2010/11/SP1-TheFirstOil-WarImplicationsoftheGulfCrisisintheOilMarket-LArcheretal-1990.pdf

[50] https://www.iea.org/news/iea-makes-60-million-barrels-of-oil-available-to-market-to-offset-libyan-disruption

https://www.iea.org/news/iea-makes-60-million-barrels-of-oil-available-to-market-to-offset-libyan-disruption