The Indexation Ceiling — When the Pass-Through Breaks (and the Sovereign Pays)

A planner's framework for the contingent liability hidden in every indexed tariff — why an inflation escalator, an exchange-rate clause, and a demand index are the same exposure, and how to price the ceiling beyond which the user-pays promise becomes a public bill

Author: David Duarte Arancibia, Austral Intelligence Date: June 2026 Audience: Ministries of Finance and debt-management offices; concession and utility regulators; sector ministries; sovereign rating analysts Companion software: Austral platform — https://platform.austral-intelligence.com Series position: Paper 7. The general statement of the principle that The Silent FX Liability (Paper 6) proved for the one special case of exchange-rate indexation: an indexed obligation is a sovereign contingent liability whose pass-through has a ceiling.

Abstract

A long-dated concession or regulated tariff is almost always indexed — to inflation, to a price index such as Chile's unidad de fomento (UF), to the exchange rate, or to a demand escalator. The indexation looks like it transfers that risk to the users who pay the tariff: when the index rises, the tariff rises, and the private operator's real revenue is protected. This paper is about the point at which that promise breaks. Indexation is the right risk-allocation default and we do not argue against it; we price the one residual exposure it leaves on the public balance sheet, so the gate can carry it deliberately.

The pass-through has a political-affordability ceiling. In a cost-of-living crisis a government cannot let an indexed tariff rise by the full index — so it caps the increase and compensates the operator for the revenue it no longer collects. The indexation clause, which read as a transfer to users, becomes a realised public liability — exactly when the index is spiking and fiscal space is tightest. That timing is the danger: the exposure is wrong-way, in-the-money in the worst macroeconomic state — a co-movement we stress for but (as §3.3 and §10 are explicit) do not model as a formal correlation.

We give the exposure its name and its expected cost. An indexed tariff is a written call option on the index, struck at the affordability ceiling: the sovereign collects nothing while cumulative index growth stays below the ceiling and pays, in real terms, revenue × (g − C)⁺ / (1 + g) once cumulative index growth g runs past the ceiling C. Set C = 0 and the instrument recovers the FX loss of Paper 6 on the loss side (the ceiling call is one-sided, floored at zero — a regulator does not refund users when the index falls) — exchange-rate indexation is the ceiling-zero special case of one general object. We ship a reference implementation (a placement-comparison module on the Austral platform) that prices the four core ways a Ministry of Finance can place the ceiling exposure — retain it unbooked, book and provision it in a stabilisation fund, hedge the index, or cap the indexation and push the gap to the operator — and the same invariant as the FX paper holds: a stabilisation fund and silent retention are the same exposure, differing only in whether it is booked. We also price a carry-forward variant of the cap — cap the annual increase but bank the suppressed indexation and recover it from later years when the index falls below the cap (the mechanism behind Chile's electricity deferred debt): it roughly halves the expected cost but leaves the wrong-way tail, because the state in which the bank never drains is persistent inflation. And because a capped tariff still has to service debt, we add the lender's view and calibrate the cap to a minimum debt-service-coverage ratio: Chile's realized 2021 inflation leaves a 6% cap bankable, but a sustained shock lifts the bankability floor above the affordability ceiling, leaving no cap that is both affordable and bankable — an arithmetic case for the sovereign bridge. In the lead worked example — a twenty-five-year inflation-indexed concession — the unpriced ceiling is worth about a quarter of real revenue in expectation and over a third in the tail, and the instrument recommends booking it as a stabilisation fund.

The contribution is to name, unify, and price — not to discover. The affordability ceiling is already stated, in substance, in the World Bank/APMG PPP Certification Guide; contingent-liability doctrine, compensation-event practice, and the quasi-fiscal-deficit literature are all prior art. What no source does is treat inflation-, FX-, and demand-indexation as one family of broken-pass-through contingent liabilities and price the sovereign's ceiling as a written call on the index with wrong-way risk (the option literature prices a firm's own price-cap, or a guarantee as a put on default — never this) — and the leading fiscal-risk tool, PFRAM 2.0, models indexation and contingent liabilities but not a suspended-indexation draw. We anchor the framework in Chile: the electricity tariff freeze of 2019 (the PEC/MPC mechanism), where the ceiling bound hard and the gap warehoused as a multi-year deferred debt that the wrong-way risk of a falling peso and dollar-indexed power contracts blew from a US$3.15bn statutory ceiling toward US$6bn — paired with the milder, in-contract toll-concession case as the contrast.

Keywords: indexation · inflation pass-through · affordability ceiling · regulated tariff · concession · contingent liability · stabilisation fund · wrong-way risk · fiscal commitments · Ministry of Finance.

Feedback & discussion. Published openly so Ministries of Finance, regulators, rating analysts and the academic community can challenge and use it. We especially welcome additional country cases and corrections to any figure carried here as single-source.

• Comment in-page at https://austral-intelligence.com/research
• Email the author: [email protected]

Table of contents

1. The decision problem — the indexed tariff and its ceiling
2. Why the ceiling is silent — and why the incentive runs backwards
3. The instrument — pricing the ceiling
4. The four placements
5. The decision rule — and the wrong-way risk
6. Wiring it into the fiscal envelope
7. Architecture and reproduction in ten minutes
8. Worked examples (incl. the carry-forward variant and the bankability calibration)
9. The evidence — Chile
10. Limitations
11. The policy lead

Appendices: A — Reproducible API call; B — Field reference; C — Glossary; D — Pseudocode (after the page break).

1. The decision problem — the indexed tariff and its ceiling

Why this matters: indexation is the most ordinary clause in infrastructure contracting and the least examined as a fiscal risk. A Ministry of Finance approves thousands of indexed tariffs without ever pricing the one thing that makes them dangerous — that the promise to pass the index through to users is only as good as the users' ability to bear it.

1.1 The clause that looks like a transfer

A concession or regulated utility runs for twenty-five or thirty years, and its tariff is indexed so that the operator's real revenue survives inflation: the toll, the availability payment, the electricity tariff, the water charge all rise with a stated index. Doctrine reads this as a risk transfer to the user — inflation risk lands on whoever pays the tariff, and the operator is made whole. On the page, the public balance sheet is untouched.

It is not untouched. The transfer holds only while the user can actually be charged the indexed amount. Embedded in every indexed tariff is an unstated assumption: that the government will let the tariff rise by the full index, in every year, for the life of the contract. That assumption is a political variable, and it fails predictably.

1.2 The ceiling, and who is left holding the gap

There is a ceiling on how much cumulative tariff increase a population will bear before the increase becomes politically impossible — and the ceiling binds hardest in exactly the conditions that make the index spike: a currency crisis, an energy shock, a cost-of-living emergency. When the index runs past the ceiling, the government does not let the tariff follow. It caps the increase and finds another way to keep the operator whole — a compensation payment, a deferred-debt mechanism, a concession-term extension, a stabilisation fund.

Where the gap lands then depends on the contract and the jurisdiction, and this paper is careful about it: it can fall on the sovereign (a direct compensation or a state-guaranteed deferral), on ratepayers later (a frozen tariff that is unfrozen and recovered with interest afterwards), or be smoothed inside the contract (a phased increase the operator accepts). What is constant is that the indexation clause, sold as a transfer, has become a contingent claim someone other than the original user must honour — and most often, in the cases that matter, the sovereign stands behind it.

1.3 The gate decision

So the Ministry of Finance, at the gate, faces a decision it almost never makes explicitly: recognise the ceiling, price the contingent cost of breaching it, and decide how to carry it. Retain the exposure unbooked; book and provision it; cap the indexation in the contract so the operator bears the gap; or hedge the index. The rest of this paper builds the instrument that prices those four placements (§3–§4), states the decision rule and its wrong-way risk (§5), wires the choice into the fiscal envelope (§6), and tests it against three sectors (§8) and the Chilean record (§9).

2. Why the ceiling is silent — and why the incentive runs backwards

Why this matters: the ceiling exposure is dangerous for the same reason the FX mismatch of Paper 6 was — the fiscal machinery does not record it. This section establishes how far that blind spot goes, honestly and regime by regime, and then makes the sharper point: the way the rules do treat the explicit guarantee has left the incentive pointing at the silent indexed clause.

2.1 The recording asymmetry, regime by regime

An explicit guarantee — a minimum-revenue floor, an FX guarantee — is a recognised contingent liability: it is disclosed under the International Public Sector Accounting Standards (IPSAS 19), reported as a memorandum item in the government-finance statistics, and booked as a contingent line in the IMF–World Bank PPP Fiscal Risk Assessment Model (PFRAM)². An indexed tariff is not. It is an ordinary contracted payment, and the contingent cost hidden in its pass-through — the chance the index breaches the ceiling and the gap returns to the public — is surfaced nowhere by default. In the Polackova–Irwin taxonomy² the gap is, where the operator holds no contractual make-whole right, an implicit contingent liability — the genuinely silent object this paper prices; where the concession grants a compensation-event or automatic-rebalancing clause, the same gap is an explicit contingent liability, a legally enforceable claim that the standard guarantee-disclosure machinery still fails to value as an option. How completely it escapes depends on the reporting regime, and the honest statement is scoped:

• Cash-basis reporting — the emerging-market majority — sees only the tariff actually paid; the embedded ceiling exposure is invisible until a compensation cheque is written. The asymmetry holds fully.
• Full-accrual IPSAS captures it only partly: a recognised concession liability is retranslated for price and currency movements, but that is a backward-looking revaluation, not a forward present value of the ceiling option, and the future service leg of the tariff is not a recognised liability⁷. Accrual narrows the gap; it does not close it.
• PFRAM 2.0, the leading fiscal-risk tool, models tariff indexation and it models contingent liabilities — but it has no object for a suspended-indexation / affordability-ceiling draw. It will re-price a tariff under an inflation scenario only if an analyst sets the indexation toggle, and it never treats the political cap on that indexation as a contingent claim⁴. The exposure this paper prices is precisely the one the standard tool does not represent.

2.2 The affordability ceiling is known doctrine — pricing it is not

We are not the first to observe the ceiling. The World Bank/APMG PPP Certification Guide states it in substance — "the risk of inflation may be transferred to the user (considering affordability issues and willingness to pay) as long as the private partner has some ability to revise the toll (or tariff)", and "when inflation moves above the limits set out in the contract for indexation of the tariff levels, the risk is borne by the private partner."¹ Compensation-event and rebalancing practice is standard¹; that chronic tariff underpricing is an implicit subsidy is the quasi-fiscal-deficit literature²; that an FX-indexed revenue is a built-in currency swap is in the project-finance literature and in our own Paper 6³. Every component is prior art, and we cite it as such.

What is not in the literature is the synthesis and the price: that inflation-, FX-, and demand-indexation are one family of broken-pass-through contingent liabilities defined by a shared affordability ceiling, and that the ceiling can be valued as a written call on the index (§3). The APMG guide treats inflation and FX as separate risk categories and never unifies them. The option literature sits on the other side of the trade: it prices a firm's own regulated price-cap as a short call — an underinvestment story — and prices a guarantee as a written put on default, a revenue or FX floor⁵. What no source does is price the sovereign's ceiling exposure as a written call on an external index, or unify inflation-, FX- and demand-indexation as one family at different strikes. That synthesis and that price are the contribution.

2.3 The asymmetry now points the wrong way

There is a sharper turn, the same one Paper 6 found for FX. The canonical fiscal-risk warning is that guarantees are dangerous because they look free — so doctrine presses Ministries of Finance to recognise, value, and provision them, and the capable ministries have done it (Chile prices its minimum-revenue guarantee — and historically its exchange-rate guarantee, the Mecanismo de Cobertura Cambiaria, renounced by concessionaires in 2004–05 — with an option model in a published register; Colombia funds its guarantees through a dedicated contingent-liabilities account)². The explicit guarantee, in a serious ministry, is now the scrutinised instrument.

The indexed tariff is not. It carries a contingent claim of the same economic character, but nothing forces it onto the register, no option model values it, no fund provisions it — and §2.1 shows most regimes do not surface it at all. So the incentive runs backwards: between writing a visible guarantee and relying on an indexation clause whose ceiling is unpriced, the fiscal machinery quietly rewards the silent form — which is the one that becomes a crisis. Naming and pricing the ceiling, on the same footing as the guarantee, is what closes the gap.

3. The instrument — pricing the ceiling

Why this matters: a ceiling that cannot be priced cannot be booked, provisioned, or placed. The instrument's job is to turn the affordability ceiling and a view of the index into the one number the gate never sees — the present value of the contingent claim, with its tail.

3.1 The written call on the index

Take the operator's real revenue stream and a view of the index — a mean and volatility of annual growth (inflation, FX, or demand). The operator is contractually owed real-revenue protection: by year t, with cumulative index growth gₜ, the operator's revenue should rise by gₜ. Users pay the capped increase, min(gₜ, C), where C is the affordability ceiling. The gap the public must honour, in real terms, is

payoutₜ = revenueₜ × max(0, gₜ − C) / (1 + gₜ)

— the revenue times the part of the index growth above the ceiling, deflated to real terms and so bounded by the revenue itself (you can lose at most the whole real revenue if the index runs away). This is a written call on the index struck at C: nothing is paid while gₜ ≤ C, and the payoff rises as the index breaches the ceiling. Discounting the payoff stream at a real rate and averaging over simulated index paths gives the expected ceiling cost; the chosen percentile gives the Value-at-Risk.

3.2 FX is the ceiling-zero case

Set C = 0 — no buffer, the pass-through breaks at the first unit of index growth — and the payoff becomes revenueₜ × max(0, gₜ) / (1 + gₜ), the bounded FX loss of Paper 6 on the loss side. In every year where the cumulative index has risen (gₜ ≥ 0) the ceiling-call and FX-loss terms are identical; whole paths coincide only when the index rises monotonically, and the two diverge on the minority of paths (about 38%) that contain an intra-path appreciation year (gₜ < 0), which the one-sided call floors to zero but the FX position credits as a gain. That difference is deliberate and correct — the ceiling option is one-sided, floored at zero, because a regulator does not refund users when the index falls, whereas the FX position nets appreciation gains. So at C = 0 the tail (Value-at-Risk) is identical to rounding and the expected cost is only modestly higher — about 2% (§8.3) — because the one-sided ceiling call floors the appreciation gains that the FX position nets. Exchange-rate indexation is the special case of an indexation clause with a zero affordability ceiling, and the FX paper is this paper's worked instance (§8.3). The unification is not cosmetic: the silent FX liability and the silent inflation liability are the same object priced at different strikes, and a Ministry of Finance should manage them with one instrument.

3.3 Wrong-way risk

The reason the ceiling is dangerous is correlation: the call tends to be in-the-money in the worst macroeconomic state — the index spikes (high inflation, a currency slump, a demand-linked tariff escalator running up) precisely when fiscal space and household tolerance are thinnest. (The demand member is this upward case — a tariff that escalates with demand and is then capped for affordability, which the call prices; the opposite-sign exposure, a demand collapse against fixed costs, is a minimum-revenue-guarantee written put — the explicit guarantee of §2.1 — not this call.) We are precise about what the engine does and does not capture: it represents the co-movement by stressing the index's mean and volatility upward — the spike — not by modelling an explicit statistical correlation with a fiscal-capacity variable; the single-index engine prices the index tail, and the link to thin fiscal space is asserted from the macro narrative (§10) and shown empirically by the FX–inflation co-movement in the Chilean record (§9). The expected cost and the tail then play different roles depending on the calibration: where the ceiling is breached only in adverse states the tail dominates, but where ordinary trend growth already carries the cumulative index past the ceiling, the expected cost is itself a near-certain liability and the tail is volatility's marginal contribution (§8.1). The engine reports both, deterministically under its seed, and the decision rule of §5 turns on the tail.

3.4 Carry-forward — the balancing-account cap

The instrument so far treats the suppressed indexation as gone the moment it is capped: a gap the sovereign covers (§4.1) or the operator absorbs (§4.4). Real tariff caps are usually gentler, and the difference matters enough to price. The suppressed indexation is often banked and recovered later — in years when the index falls back below the cap and the tariff has headroom to catch up. This is the balancing account (or regulatory asset)⁷: the cap binds on the annual applied increase, not on the cumulative level, and the operator's tariff climbs back toward the full index whenever there is slack. (Note the shift: this cap is per-period, the natural form for a carry-forward, as against the cumulative ceiling of §3.1; §8.2 already flags that Chile's freeze was an annual one.)

Concretely, with a per-period cap c, let Oₜ be the full-pass-through tariff level (the index) and Pₜ the applied level. Each year the applied increase is the smaller of the cap and the increase needed to catch up:

appₜ = min(c, Oₜ/Pₜ₋₁ − 1)⁺, and Pₜ = Pₜ₋₁ · (1 + appₜ)

A 12% index move under a 6% cap applies 6% and banks the rest; the next year, at 3%, the 3% of slack under the 6% cap lets the tariff rise 6% again — 3% current plus 3% catch-up — and the bank keeps draining until the level is whole. The bank is the regulatory asset; the slack (c − the index move, where positive) is what amortises it.

This changes the exposure in a way the gate should see, and it is the same wrong-way point one turn deeper. On a transitory spike the bank drains fast and the sovereign bears only the short lag — the tariff level is restored and the public's residual is just the revenue lost while the tariff trailed the index. But where the index persistently outruns the cap there is never slack to recover from: the bank never drains, and the residual stays on the public — and that persistent state is exactly the wrong-way state of §3.3. So the carry-forward cuts the expected cost sharply while leaving the tail far stickier. The worked numbers (§8.4) make the asymmetry concrete: on the concession case it recovers about half the hard-cap expected cost, yet the tail-to-mean ratio rises from ~1.5× to ~2.4×. The carry-forward is the right instinct — recover from slack rather than write a cheque — but it is a cure for transitory spikes, not for persistent inflation.

3.5 The bankability floor — the cap between affordability and the DSCR

The carry-forward protects the operator's tariff level but defers its cash, and a lender is repaid out of cash. So the cap has a second binding edge the affordability ceiling hides. Set it too low and the capped tariff no longer covers debt service at the covenant debt-service-coverage ratio (DSCR) — the project is unbankable at the gate, or breaches its covenant later. Where the SPV's debt is UF/CPI-indexed — the Chilean norm, because the pension funds hold inflation-linked paper — the bite is direct: debt service grows with the index while the tariff is held below it, so coverage scales with the pass-through ratio,

DSCRₜ = revenueₜ × (Pₜ/Oₜ − opex) / (debt service)

where opex is the operating-cost share of revenue, and coverage falls one-for-one with the cap's lag (1 − Pₜ/Oₜ). The cap is therefore squeezed between an affordability ceiling above — the most users will bear — and a bankability floor below — the least the lenders will accept. The gate's task is to find a cap inside that band, and to recognise the case where a shock makes the band empty: the cap that keeps the lender whole breaches affordability, and the cap that is affordable breaches the covenant. No contractual cap then works, and the residual is necessarily the sovereign's — a guarantee on the deferred balance, a DSCR backstop, or a stabilisation injection. This is the bankability mirror of §3.3's wrong-way risk: coverage is thinnest in the same high-inflation state that makes the ceiling bind. §8.5 calibrates the band against Chile's realized inflation and a sustained stress.

4. The four placements

Why this matters: this is where the instrument earns its keep, and where the menu turns out — as in Paper 6 — to be smaller than it looks. Two of the four placements are the same sovereign exposure wearing different clothes.

4.1 Retain

The default that happens when nobody decides: the sovereign holds the ceiling exposure and pays the compensation when the index breaches C. The cost is the expected ceiling payout and it carries the full tail. The risk sits on the public balance sheet, implicitly — unbooked, unprovisioned, the silent liability of §2.

4.2 The stabilisation fund — the same exposure, made visible

Booking the exposure and pre-funding it — a stabilisation fund that absorbs the gap when the ceiling binds — looks like a different policy. Economically it is the same contingent position — the fund pays the same expected payout with the same tail (the model treats the pre-funding itself as costless at fee zero; a real fund trades the carry of holding cash for certainty, which is why a fee or cap makes it strictly cheaper, §3). The engine prints them identically, and a unit test asserts the equality. The difference, and the case for the fund, is that it is explicit — provisioned, aggregated across the portfolio, reported — and a fund with a fee or a payout cap is weakly cheaper or thinner-tailed than silent retention, never worse. So the fund dominates silent retention: same exposure, made visible and manageable. Chile's electricity PEC/MPC is this placement built in a hurry under stress (§9); the lesson is to build it deliberately, at the gate.

Proposition (placement equivalence). Let P(ω) be the present value of the ceiling payout on path ω, and V the present value of revenue. Silent retention costs Cᵣ(ω) = P(ω). A booked stabilisation fund with payout cap kV and a fee φV the sovereign collects costs C𝒻(ω) = min{P(ω), kV} − φV. At φ = 0, k = ∞ the two coincide path by path, C𝒻 = P = Cᵣ, so every law-invariant risk measure (the mean, the Value-at-Risk) is identical — retention and the fund are the same exposure. Corollary (dominance). For any φ ≥ 0, k < ∞, Cᵣ − C𝒻 = max{0, P − kV} + φV ≥ 0 path by path: the booked fund weakly dominates silent retention, strictly once a cap or fee bites. The equality is structural, not assumed — the engine sets the fund's payout equal to the retain payout at φ = cap = 0 (Appendix D) — so the only thing silent retention buys is not seeing the number.

4.3 Hedge the index

An inflation-linked or FX-linked instrument (an inflation cap, a cross-currency hedge) can pass the ceiling payoff to a market counterparty for a certain cost — no tail. In a deep market the cost is close to the exposure's expected payout, so the hedge removes the tail at roughly the cost of the mean. The catch is structural and familiar from Paper 6: emerging markets rarely have an accessible long-dated inflation- or FX-linked hedge market, so the placement is often infeasible — as it is in all three worked cases of §8.

4.4 Cap the indexation / push to the operator

Cap the indexation in the contract at C and let the operator bear the gap above it. This genuinely moves the tail off the sovereign — but not for free: an operator who must absorb uncapped inflation above C prices it into a higher required return, and the contract pays for it through a higher base tariff, following the same pass-through logic (Δ ≈ λ × the operator's risk-adjusted cost) used in the third-party-guarantee and FX papers¹¹. Push is the honest transfer; the public pays the premium up front, in the tariff, rather than later, in a crisis.

4.5 The shape of the four

Two of the four leave the tail with the sovereign and are the same exposure; the other two move it off at a price. Those are the four core placements — the same shape as the FX placement menu, because it is the same decision one strike over; a two-way collar (§11.1) is a refinement of cap-and-push that additionally claws back under-ceiling states, so it sits outside the one-sided instrument priced here. (In these tables, "implicit/explicit" marks whether the sovereign's exposure is unbooked or booked — a recording choice — distinct from the Polackova–Irwin implicit-vs-explicit contingent-liability axis of §2.1, which turns on whether a contractual make-whole right exists.)

5. The decision rule — and the wrong-way risk

Why this matters: a comparison is not a decision, and here the decision is dominated by a correlation the expected cost hides.

5.1 The rule

Among the feasible placements, take the lowest expected cost — but never retain silently when a fund is available (the fund is the same cost made visible), prefer a placement that removes the tail when expected costs tie, and read the recommendation against the tail: if the cheapest option still leaves a large Value-at-Risk on the sovereign, weigh it against reserve adequacy and the size of any stabilisation fund before accepting it.

5.2 The wrong-way trap

The rule has the sharp consequence §3.3 anticipated. The ceiling payout is largest exactly when the sovereign can least afford it — and, in emerging markets, the index hedge that would remove the tail usually does not exist (§4.3). So the Ministry is left choosing between holding the exposure (retain or fund) at the lowest expected cost but with a wrong-way tail, and capping/pushing the gap to the operator at a premium to be rid of it. There is no free placement. The instrument's value is to put the trade on the gate's desk — the price of certainty against the size of the tail — before a crisis puts it on the budget. And where the chosen design caps the indexation, the menu is bounded from below as well as above: a cap set for affordability that breaches the lenders' DSCR (§3.5) is not a feasible placement at all — it routes the project to default or straight back onto the sovereign, so the bankability floor must clear the affordability ceiling for any cap to count.

5.3 The fund dominates silent retention — always

One element is unconditional, and it is the same as Paper 6's. Because retention and the stabilisation fund are the same exposure, there is never a reason to retain silently: if the sovereign is going to hold the ceiling risk it should hold it as a booked, provisioned fund — the cost is identical, and the booked version can be managed. The only thing silent retention buys is the comfort of not seeing the number — and §9 shows how expensive that comfort is.

6. Wiring it into the fiscal envelope

Why this matters: pricing the ceiling is the analytical step; booking it is the fiscal one, and it belongs to the Ministry of Finance by construction.

In the language of Paper 3, the chosen placement's exposure is a draw on the Stage-E fiscal envelope — the contingent commitment the Ministry underwrites at the gate¹⁰. The placement output wires into the platform's fiscal-rules and FCCL machinery so the ceiling becomes a booked line: the expected payout as a provision, the Value-at-Risk as the tail the envelope must absorb, the chosen placement recorded as the contract-level decision.

This is the orchestrator's task, not the gatekeeper's. Paper 3 assigns the index path, the guarantee menu, and the fiscal envelope to the Ministry of Finance — they are country variables no contracting authority can price¹⁰. A gatekeeper ministry, reading a one-page affordability note, never sees the embedded ceiling; an orchestrator ministry, which owns the index path, is the one actor positioned to recognise, price, and book it. And because it sits at the portfolio level it can do what no project can: aggregate the ceiling exposure across every indexed contract alongside the explicit guarantees and the FX mismatches of Paper 6, and size the country's reserves, its stabilisation funds, and its envelope to the combined wrong-way tail — one instrument across inflation, FX, and demand indexation, because they are one object (§3.2).

7. Architecture and reproduction in ten minutes

Why this matters: the series' discipline is a running reference implementation, not a slide.

A normalized indexed-revenue record — the real revenue stream, the index view, the affordability ceiling, and the placement parameters — is submitted to the placement-comparison module, which runs the seeded Monte-Carlo over the index path, prices the written-call payoff and the four placements, writes the result to the platform's tamper-evident audit chain, and returns an optional signed PDF. The same schema and engine priced the concession, the electricity breach, and the FX special case in §8. The worked example pairs the new pricer with the platform's tariff-regulation engine — the glide-path scheduler is the contractual smoothing mechanism a ceiling implies, and the bill-simulator renders the household impact that defines where the ceiling binds. A gate integration is a single POST …/fm/indexation-ceiling/compare; Appendix A gives the call, and the offline harness papers/INDEXATION_CEILING/worked_examples.py reproduces every §8 table — the three sector cases and the carry-forward variant of §8.4 — with no authentication.

8. Worked examples

Why this matters: the framework is abstract until a real-shaped contract runs through it. We take an inflation-indexed concession (the everyday public-private-partnership, or PPP, case), the Chilean electricity freeze (the vivid breach), and the FX special case (the bridge to Paper 6) — then re-run two of them under the carry-forward variant of §3.4 (§8.4). Numbers are illustrative but every one traces to the harness; figures are in millions of the revenue's currency, present-valued at a 6% real rate, against a 95th-percentile tail.

8.1 An inflation-indexed concession — the everyday case

A twenty-five-year UF/CPI-indexed concession with US$100 million per year of real revenue (present value US$1,278 million), an affordability ceiling of 30% cumulative, and no accessible inflation-hedge market. Against a 6%-per-year inflation view (6% volatility):

The expected ceiling cost is US$317 million — 25% of the revenue base — with a tail of US$470 million (37%). Most of that expected cost is structural, not spike risk: because the ceiling C is a cumulative-lifetime cap and the index compounds at a positive mean, the central path carries cumulative growth past the 30% ceiling by about year five and pays the gap every year thereafter — so even at zero volatility the expected cost is already ~26% of revenue, and volatility's marginal contribution shows up in the tail (the Value-at-Risk runs about 1.5× the mean). The hedge is unavailable; capping the indexation costs the operator's premium (US$573m); so the recommendation is the stabilisation fund — hold it, but book and provision it. A quarter of the concession's real revenue is an unbooked contingent claim on the public, and nothing in the standard accounts says so.

8.2 The Chilean electricity freeze — the ceiling breached hard

Calibrated to the Chile PEC/MPC episode (§9): a regulated tariff with ~US$4.5 billion per year of revenue over six years (present value US$22.1 billion), the affordability ceiling set at ~9% cumulative — Chile's PEC froze a single pending ~9.2% annual increase, which we map onto a cumulative-lifetime ceiling that is therefore breached early and persistently over the freeze horizon, consistent with the deferred debt that in fact began accruing from year one — and the index carrying wrong-way risk: dollar-indexed power contracts against a depreciating peso, modelled as a higher-mean, higher-volatility index (6.5% / 11%):

The expected ceiling cost is US$2.7 billion — near the US$3.15 billion statutory ceiling Chile actually legislated for its stabilisation funds — and the Value-at-Risk is US$6.5 billion, near the ~US$6 billion the deferred debt actually reached once the wrong-way FX risk blew it past the statutory cap (§9). With its inputs calibrated to the PEC/MPC magnitudes, the instrument places the expected cost near the statutory ceiling and the tail near the realised debt — illustrating, not predicting, the gap between what Chile planned to warehouse and what it did — and it names the placement Chile chose under duress, a stabilisation fund, as the right one, with the warning that the realised tail ran to more than twice (~2.4×) the expectation. One detail sharpens the wrong-way point: at a Value-at-Risk of 29.3% of revenue the electricity case sits just under the engine's own 30% wrong-way warning threshold and does not trip it, while the milder concession (37%) and the FX case (58%) do — a reminder that the single-index proxy understates the very FX–inflation co-movement that blew the realised debt past its statutory cap. The threshold is a floor, not a forecast.

8.3 FX as the ceiling-zero case

The same engine, an FX-indexed payment, affordability ceiling zero: real revenue US$100 million per year for twenty years (PV US$1,147 million), an 8% / 12% exchange-rate view.

The expected cost is US$456 million (40% of revenue) — the Silent FX Liability of Paper 6 recovered on the loss side as the zero-ceiling instance of the same instrument (the tail coincides with the FX engine; the expected cost sits ~2% above it because the call floors the appreciation gains the FX position nets, §3.2). Read across §8.1–§8.3, a higher affordability ceiling passes more of the index to users and shrinks the sovereign's call; holding the index view fixed, the shipped ceiling-sweep confirms the cost falls monotonically as C rises — the ceiling is the strike, and where the gate sets it is much of the decision. (The §8.1 and §8.3 cases also differ in their index view, so the 25%-versus-40% spread reflects both the higher ceiling and the milder inflation assumption, not the ceiling alone.)

8.4 Carry-forward — smoothing the same two cases

Now re-run the concession and the electricity tariff under the carry-forward cap of §3.4 — the cap binds on the annual increase and the suppressed indexation is recovered from later slack — against the contrast of a hard per-period cap that loses the gap every year (the per-period analogue of Retain). Same revenue and index views as §8.1–§8.2; the per-period cap replaces the cumulative ceiling.

The concession's per-period cap of 6% — its inflation mean — costs US$236 million (18% of revenue) under a hard cap and US$107 million (8%) under carry-forward: the smoothing recovers about 55% of the expected cost from years where inflation runs below the cap. But the tail tells the real story. The hard cap's Value-at-Risk is US$365 million (29%) and carry-forward's is US$255 million (20%) — the mean fell by 55% while the tail fell only ~30%, so the tail-to-mean ratio climbs from ~1.5× to ~2.4×. The electricity case, at the per-period 9% cap faithful to the PEC's frozen ~9.2% annual hike, says the same at scale: carry-forward cuts the expected cost by nearly half (to US$1.0 billion, ~47% recovered) but still carries a US$3.5 billion wrong-way tail. The carry-forward is the right instinct — recover from slack rather than write a cheque — but it cures the transitory spike, not persistent inflation: the state in which the bank never drains is the state the sovereign most fears, and §9 shows Chile living exactly that distinction.

8.5 Calibrating the cap to a minimum DSCR — the realized shock vs the sustained tail

The cap is not the sovereign's to set alone; the lenders set a floor under it (§3.5). Take the §8.1 concession with a stylised SPV — opex 25% of revenue, UF-indexed senior debt sized to a 1.40× DSCR at full pass-through, a 1.20× lock-up covenant — and read the worst-year DSCR off the capped tariff under three deterministic inflation paths: a normal 3%/yr environment; Chile's realized 2021–23 CPI (annual averages ≈4.5 / 12.8 / 7.6%, after the pension-fund withdrawals); and a sustained stress of three years at ≈12–13%, harsher and more prolonged than the realized episode.

The honest result is the contrast. Against the realized Chilean path, a 6%/yr cap holds — worst-year DSCR 1.26×, and the bankability floor is only ~4.3%/yr, comfortably under a 6% affordability ceiling: the band stays open because the episode was largely one big year, and the catch-up began before coverage broke. The danger is the sustained tail. Stretch the shock to three years at ≈12–13% — well within emerging-market experience, and the kind of episode a repeat of the withdrawal-driven demand shock could produce — and the 6% cap drops the worst-year DSCR to 1.16×, a covenant breach, while the bankability floor climbs to ~6.9%/yr, above the 6% ceiling. The band is then empty: no single cap is both affordable and bankable, and the residual is necessarily the sovereign's. That sovereign backstop is precisely the logic behind Chile's state guarantee on the electricity MPC balances (§9) — the severe, wrong-way case where the band did empty. And the withdrawals sharpen it from both ends: they drove the inflation and drained the local appetite for UF debt, so the SPV could not refinance through the DSCR trough — the capital-market thinning that pushes emerging-market projects toward the hard-currency funding, and the FX mismatch, of Paper 6.

9. The evidence — Chile

Why this matters: the framework predicts that an indexed tariff whose ceiling binds becomes a public liability in the worst macro state. Chile's recent record lets us check it — and demands honesty about which mechanism actually did what.

9.1 A correction, first

The intuition that motivated this paper was that Chile, during the pandemic, suspended the contractual inflation indexation on its road concessions and compensated the operators for the forgone revenue. The record does not support that as stated: the UF/CPI reajuste on road and airport concessions kept being applied through the pandemic⁹. What actually happened on the roads is milder and in-contract — facing 13.3% accumulated inflation, the Ministry of Public Works and the urban-highway operators agreed in 2023 to split the indexed increase into two steps of about 6.65% each, with the forgone revenue reintegrated to the operators through contract-specific formulas (a concession-term extension, a payment at term, or a payment in a year of fiscal surplus)⁹. That is the ceiling logic at low intensity — a smoothing, not a freeze with a lump-sum bill, and the reintegration amount is unpublished. We say so plainly, in the spirit of this series' willingness to follow the record rather than the intuition.

9.2 The electricity freeze — the ceiling breached hard

The clean, fully-documented instance is the electricity tariff freeze. After the October 2019 social unrest, Chile enacted Law 21.185 (the PEC), which froze regulated electricity tariffs at first-half-2019 levels, cancelling a pending ~9.2% increase — the affordability ceiling binding exactly as the framework describes⁸. Distributors kept billing the frozen tariff while owing generators the real, higher price; the gap accrued as deferred debt to the generators, with an initial statutory ceiling of US$1.35 billion. Law 21.472 (2022, the MPC) extended the mechanism, added a state guarantee on the MPC balances, and lifted the statutory ceiling by a further US$1.8 billion — about US$3.15 billion in legislated headroom⁸.

It was not enough, and why it was not enough is the paper's point: the deferred debt carried wrong-way risk — many power contracts were dollar-indexed while the peso fell, so the obligation the freeze was hiding inflated in exactly the state where the freeze could not be lifted. The stabilised debt grew past US$6 billion (close to 2% of GDP), with the regulator projecting total mechanism flows of roughly US$7.2 billion to 2035, including ~US$1.9 billion of interest⁸. When the tariffs were finally unfrozen in 2024 (Law 21.667), the recovery fell on ratepayers, through increases of up to ~60% — a reminder that where the gap lands is jurisdiction-specific: here it ran from the generators' receivable, through a state-backstopped fund, to ratepayers, with the sovereign standing behind the MPC guarantee rather than writing a direct cheque. Chile even securitised part of the deferred liability through an Inter-American Development Bank (IDB) Invest-supported ~US$2.4 billion transaction — the stabilisation-fund placement of §4.2, monetised after the fact⁸.

9.3 What the pair shows

Read together, the two Chilean cases are the placement menu. Electricity is the ceiling breached hard and warehoused as a multi-year, state-backed deferred debt, its tail blown out by wrong-way FX correlation — the stabilisation-fund placement, chosen late and under stress. That deferred debt was, precisely, the carry-forward balancing account of §3.4 and §8.4: tariffs frozen, the suppressed indexation banked to be recovered when prices allowed. It is the textbook illustration of that section's warning — the mechanism works while there is slack, but a persistent wrong-way peso meant the bank never drained, so the state guarantee and the >US$6bn realised debt were the residual the carry-forward could not recover. Roads is the same ceiling logic at low intensity, smoothed inside the contract with no sovereign debt vehicle — the cap/rebalancing placement. The spread between them — statutory headroom versus realised debt, sovereign-backed warehouse versus contractual smoothing — is precisely the axis the instrument prices. The lesson is not that Chile chose badly; under duress it built the fund the framework recommends. The lesson is that the fund, the ceiling, and the wrong-way tail should be priced and booked at the gate, not legislated in an emergency.

10. Limitations

• The ceiling is a political parameter, not an observed one. The instrument prices the cost of breaching a ceiling the gate must itself set; it does not predict where the political limit lies, any more than Paper 6 forecast the exchange rate. Its contribution is to turn an assumed ceiling into a priced, booked liability.
• It prices a view of the index, not a forecast. The expected cost and the tail are only as good as the inflation/FX/demand view supplied; the index model is a deliberately simple mean-and-volatility process and should be stressed with explicit scenarios alongside the distribution.
• The wrong-way risk is represented, not modelled as a correlation. The danger of §3.3 — the call is in-the-money when fiscal space is thinnest — is captured by stressing the index's mean and volatility upward (the spike), not by an explicit statistical correlation between the index and a fiscal-capacity variable. That is a deliberate single-index simplification; the correlation to fiscal space is asserted from the macro narrative (and shown, in the Chilean record, by the FX-inflation co-movement that blew out the tail).
• Where the gap lands is jurisdiction-specific. The framework prices a contingent claim; whether it falls on the sovereign, on ratepayers later, or on the operator depends on the contract and the regime (the United States' regulatory-asset doctrine, for instance, routes deferred costs to ratepayers without touching the sovereign). The paper does not claim the sovereign always pays — only that the exposure is real and, in the cases that matter, sovereign-borne.
• The bankability calibration is stylised, and the squeeze is specific to inflation-indexed debt. §3.5/§8.5 run one SPV structure (flat real revenue, 25% opex, UF-indexed senior debt at a 1.40× design DSCR, a 1.20× covenant) against a few deterministic paths; it illustrates the affordability-versus-bankability band and when a shock empties it, not a financing model of any specific project. The DSCR squeeze depends on the debt being UF/CPI-indexed (the Chilean norm): with nominal fixed-rate debt, inflation lifts the capped nominal revenue against a flat debt service and the squeeze largely disappears (in the engine the sustained-shock DSCR stays ~1.44× and the bankability floor falls to ~1%) — the exposure then migrates to refinancing and real-rate risk rather than coverage. A real structuring would also carry the full amortisation profile, a debt-service reserve, and sculpting, and would test a distribution of shocks rather than a handful of scenarios.
• The carry-forward residual charges the lag to the sovereign and assumes no interest on the deferral. The §3.4/§8.4 figure prices the revenue the operator loses while the capped tariff trails the index, attributed to the sovereign as a make-whole; it does not model a balancing account that pays interest on the banked amount and recovers principal-plus-interest from future ratepayers. A fuller account (Chile's MPC accrued ~US$1.9bn of interest) shifts more of the bill onto later users and leaves the sovereign backstopping the terminal balance and the carry — the split turns on the accrual rate versus the discount rate, the same lever the least-present-value-of-revenue (LPVR) placement sequel develops⁶. The figure here is the conservative, one-rate case.
• The worked examples are illustrative. The three sectors demonstrate the instrument; the Chilean figures are calibrated to the documented PEC/MPC magnitudes, and several roads/airport figures are single-source and carried as such.
• The contribution is synthesis and pricing, not discovery. The affordability ceiling (APMG), contingent-liability doctrine (Polackova, Irwin), compensation events (APMG, Guasch), and the quasi-fiscal-deficit framing are prior art; what is new is unifying the indexation family and pricing the ceiling as an option.

11. The policy lead

Why this matters: the instrument serves one ministry at one gate; the policy point is for the doctrine and the standard tools.

The recurring failure is not that countries chose the wrong placement — under duress Chile built the right one — but that they did not see the ceiling until it bound. The lead is therefore to stop holding indexation-ceiling exposure silently. A ceiling that is priced, booked as a contingent liability, provisioned against (a stabilisation fund built deliberately rather than legislated in a crisis), and aggregated across the portfolio alongside the guarantees and the FX mismatches is a position a Ministry of Finance can manage. The same exposure unpriced is what becomes a multi-billion deferred debt blown out by a wrong-way currency move.

11.1 Roadmap

• The FCCL standard should book the indexation-ceiling leg. The clearest doctrinal step is to bring the affordability-ceiling exposure of indexed tariffs inside the contingent-liability frameworks alongside explicit guarantees — and to give PFRAM an object for a suspended-indexation draw, which it currently lacks.
• Prefer a collar or a pre-funded fund to a silent pass-through. A two-way cap-and-floor on the indexation bounds both sides' tails; a stabilisation fund built at the gate is cheaper than one legislated in an emergency.
• If you carry the gap forward, size the fund to the state where the bank never drains. A carry-forward balancing account (§3.4) is cheaper than a cheque and is what good practice already reaches for — but it recovers only from slack, so it must be provisioned against the persistent-inflation tail it cannot amortise, not against its much smaller expected cost.
• Manage indexation as one family. Inflation, FX, and demand indexation are one object at different strikes (§3.2); a ministry should price and aggregate them together, not in separate silos.

Appendix A — Reproducible API call

POST /workspaces/{workspace_id}/fm/indexation-ceiling/compare
Authorization: Bearer <token>
Content-Type: application/json

{
  "revenue_base": [100, 100, 100, ... ],     // 25 years, real terms
  "index_label": "CPI/UF",
  "currency": "LCY",
  "discount_rate_pct": 6.0,
  "scenario": {
    "annual_growth_mean_pct": 6.0, "annual_growth_vol_pct": 6.0,
    "n_sims": 20000, "seed": 42, "var_pct": 95.0
  },
  "params": {
    "affordability_ceiling_pct": 30.0,
    "hedge_load_pct": 30.0, "hedge_available": false,
    "sponsor_premium_pct": 20.0, "lambda_passthrough": 1.0,
    "provision_fee_pct": 0.0, "provision_cap_pct": 0.0
  }
}

The response carries revenue_base_npv, expected_ceiling_cost_npv, var_ceiling_cost_npv, the four priced placements with their risk-holders and feasibility, and the recommendation (cheapest feasible placement, preferring a tail-free option at equal cost and the explicit fund over silent retention). Set affordability_ceiling_pct to 0 and index_label to "FX" to recover the Silent FX Liability instrument.

Appendix B — Field reference

The four placements: Retain (sovereign, implicit), Stabilisation fund (sovereign, explicit — same cost/tail as Retain in the default), Hedge the index (counterparty, certain, feasibility-gated), Cap / push to operator (operator, via a higher tariff).

Appendix C — Glossary

• Affordability ceiling (C) — the maximum cumulative tariff increase a population will bear; the strike of the indexation option.
• Indexation pass-through — the contractual rise of a tariff with an index (inflation/UF, FX, demand).
• Ceiling payout — the public's real-terms cost when the index breaches the ceiling: revenue × (g − C)⁺/(1 + g), bounded by revenue.
• Wrong-way risk — the exposure is largest exactly in the worst macro state, when the index spikes and fiscal space is thinnest.
• Stabilisation fund — a pre-funded vehicle that absorbs the ceiling gap (Chile's PEC/MPC).
• PEC / MPC — Chile's Precio Estabilizado a Cliente (Law 21.185, 2019) and Mecanismo de Protección al Cliente (Law 21.472, 2022) electricity tariff-stabilisation mechanisms.
• UF — unidad de fomento, Chile's inflation-indexed unit of account.
• FCCL — fiscal commitments and contingent liabilities.

Appendix D — Pseudocode

rev_npv = NPV(revenue_base, real_discount_rate)
# ceiling payout distribution (seeded Monte Carlo)
for sim in 1..n_sims:
    gfac = 1
    for t, rev in revenue_base:
        gfac *= max(0.01, 1 + Normal(index_mean, index_vol))   # cumulative index factor
        g_t   = gfac - 1
        pay[t] = rev * max(0, g_t - C) / (1 + g_t)              # written call, bounded by rev
    payout_sim[sim] = NPV(pay, real_discount_rate)
E = mean(payout_sim);   VaR = percentile(payout_sim, var_pct)   # C=0 -> the FX paper's loss

retain    = (cost=E,                       tail=VaR,  holder=sovereign-implicit, tail=yes)
# fund: defaults fee=cap=0 -> identical to retain; a fee/cap make it weakly cheaper/thinner
fund      = (cost=mean(min(payout,cap))-fee, tail=percentile(...)-fee, holder=sovereign-explicit, tail=yes)
hedge     = (cost=E*(1+hedge_load),        tail=cost, holder=counterparty, feasible=hedge_available)
push      = (cost=lambda*(E + premium*rev_npv), tail=cost, holder=operator)

recommended = argmin(expected_cost over feasible,
                     tie-break: remove the tail, then explicit fund over silent retain)

Carry-forward variant (§3.4 / §8.4) — per-period cap c, bank the rest, recover from slack:

for sim in 1..n_sims:
    owed = paid = hard = 1
    for t, rev in revenue_base:
        owed *= max(0.01, 1 + Normal(mean, vol))      # full pass-through (the index)
        hard *= max(0.01, 1 + min(annual, c))         # hard per-period cap: gap lost each yr
        app   = max(0, min(c, owed/paid - 1))         # capped annual increase, one-sided
        paid *= 1 + app                               # tariff catches up when there is slack
        cf[t]   = rev * max(0, owed - paid) / owed     # shortfall the catch-up never delivers
        hcap[t] = rev * max(0, owed - hard) / owed
    cf_sim[sim]   = NPV(cf,   real_discount_rate)      # drains on transitory spikes;
    hard_sim[sim] = NPV(hcap, real_discount_rate)      # persists when growth outruns c (the tail)
# carry-forward recovers (1 − E[cf]/E[hard]) of the hard-cap expected cost from slack,
# but its VaR/E ratio is larger — the wrong-way tail survives the smoothing.

References & notes