Methodology

Design philosophy

Prometheus is built around a single conviction: an emissions trading system is best understood as the interaction of two markets — a market for abatement and a market for allowances — mediated by a policy design. Every modelling decision follows from wanting those interactions to emerge endogenously rather than being asserted. We deliberately avoid reducing the system to a closed-form equilibrium; the clearing price is produced by order flow, not solved for, because the pedagogical payoff lives in watching price discovery happen under friction.

The abatement side: marginal abatement cost curves

Each firm is endowed with a discrete marginal abatement cost (MAC) curve— an ordered set of abatement options, each with a cost per tonne and an abatement potential. Representing abatement as a step function of lumpy, discrete projects rather than a smooth continuous curve is a deliberate choice: real decarbonisation comes in indivisible investments (a kiln retrofit, a fuel switch, a capture unit), and the lumpiness is what makes the abate-versus-trade decision interesting. A firm compares the marginal cost of its cheapest remaining option against the prevailing allowance price and acts accordingly — the textbook equimarginal principle, but discovered rather than imposed.

Abatement investment is modelled with realistic friction. Adopting an option carries an implementation lag — projects take time to come online — and its cost is split between an upfront capital outlay and an operating cost spread across subsequent compliance periods. Adoption is treated as effectively irreversible from the firm’s side, which forces players to reckon with commitment under price uncertainty rather than costlessly toggling decisions.

The allowance side: continuous double auction

Allowances trade on a continuous double-auction limit order book with strict price-time-priority matching. Orders rest in the book and execute against incoming counter-orders in the canonical sequence: best price first, and within a price level, earliest order first. The engine supports limit and market orders together with immediate-or-cancel and fill-or-kill conditions, applies maker-price execution with price-improvement returned to the aggressor where the resting order is more favourable, and enforces self-trade prevention so a participant cannot cross with its own resting orders.

A configurable price band / circuit breakerconstrains how far a single trade may move from the prevailing reference price, mirroring the volatility controls real venues run and giving instructors a lever to demonstrate the effect of such controls. Locked and free balances are tracked separately, so an order’s collateral is reserved at placement and released or settled on fill or cancel — the same pre-trade risk discipline a real exchange imposes.

Two regulatory architectures

Prometheus models both dominant ETS families, because the contrast is itself a lesson.

Absolute cap-and-trade

In the absolute architecture (the EU ETS lineage), a fixed quantity of allowances is issued ex ante through free allocation, and the cap tightens over time via a linear reduction factor. Compliance is settled at period end by surrendering allowances against verified emissions. Scarcity is a quantity decision the regulator makes directly, and the price is whatever the market pays to clear that quantity.

Intensity-based rate benchmarking

In the intensity architecture (the India CCTS lineage), obligations are defined relative to output through an emissions-intensity benchmark rather than an absolute cap. Settlement is ex post: a firm’s position is computed against its realised output once the period closes, generating credits when it beats the benchmark and a shortfall when it misses. The benchmark follows a tightening trajectorythat ratchets the rate downward over successive compliance years. Because obligations scale with production, this design decouples the carbon constraint from output growth — a property that matters in fast-growing economies and one that students feel immediately when their output expands.

Modelling the two side by side surfaces the deep distinction between an ex-ante quantity instrument and an ex-post rate instrument— how each handles growth, banking, and price formation differently — which is hard to convey any other way.

Free allocation methodologies

The way allowances are handed out shapes firm behaviour as much as the cap itself, so the allocation method is first-class. Prometheus supports benchmarking(allocation tied to an output-based performance standard) and grandparenting(allocation anchored to historical emissions), as well as hybrid approaches between them. The intensity architecture also models the bootstrapping problem every real rate-based system faces — how to seed initial market liquidity before the first settlement cycle has produced any credits — through a configurable opening endowment with a clear narrative rationale.

Compliance, banking, and penalties

Compliance runs at the close of each period: settlement is computed, available allowances or credits are applied against the obligation, and any residual shortfall is penalised. The penalty is a multipleof a reference allowance price — deliberately punitive so that non-compliance is never a cheap option, consistent with how real make-good provisions are designed to sit above the market price. Penalty payments leave the system as regulatory deadweight loss rather than recirculating, which is the realistic treatment of a fine. Banking— carrying surplus allowances forward into later periods — is supported and configurable, letting instructors explore how intertemporal flexibility changes both price paths and abatement timing.

Heterogeneous firms and behavioural archetypes

Realistic market dynamics require realistic dispersion, so firms are deliberately heterogeneous. They differ in abatement-cost structure, in starting capital(scaled to reflect the capital intensity of their sector), and in emissions endowment. This heterogeneity is what produces natural market segmentation — capital-rich, high-cost abaters tend to buy, while firms with cheap options tend to abate and sell — rather than a degenerate market where everyone faces identical incentives.

Automated participants are driven by a rational decision procedure: they form an expected net position over the remaining horizon, compare the marginal cost of abatement against the expected market price, and choose to abate, buy, or sell accordingly, subject to liquidity and coverage guards. Layered on top are distinct behavioural archetypesthat vary order aggressiveness, spread-crossing behaviour, and order sizing — some cross the spread to take liquidity, others rest patiently in the queue. The result is a book that feels alive, with the mix of impatience and discipline that characterises a real trading population.

Real-world calibration

The default scenario is grounded in India CCTS sector baselines— production levels, baseline emissions intensities, and sector-specific growth rates for the scheme’s real obligated sectors — together with abatement options drawn from the corresponding cost data. Firm-level parameters are derived from these sector aggregates with randomised dispersion, so that each firm is plausible individually while the population aggregates back to a realistic sector. The framework is structured so that other jurisdictions can be added as comparable data is assembled.

What this page is not

This note describes approach and intent. It deliberately does not publish the exact functional forms, coefficients, calibration constants, or tuning parameters that define a specific scenario — those are part of the simulator’s design, not a public specification. Educators who want to understand a particular configuration in depth are welcome to get in touch.