Pricing and Hedging Event Contracts
An event contract, a claim paying one unit if a described event occurs, is a digital option, payoff-identical to one and instrument-adjacent in settlement, collateral, and counterparty. The Black–Scholes price of a cash-or-nothing digital, e−rTN(d₂), is the discounted risk-neutral probability of the event, and the discount factor the theory installs by construction has now been measured in the field as the settlement discount of event venues. But the identity carries a boundary clause. A Black–Scholes price is enforced rather than estimated: continuous delta-hedging of a tradeable underlying makes any other price an arbitrage. And you cannot delta-hedge an election. Where the underlying trades (crypto- and commodity-price events), replication tethers event prices to options-implied distributions; where the underlying itself does not trade, though a correlated instrument does (elections that move currencies and rates, macro prints that track inflation swaps), partial spanning bounds the price to a band; and where nothing hedges the state (championships, idiosyncratic rulings), no arbitrage binds, risk premia and the favorite–longshot bias persist, and pricing is model-based estimation, not enforced. Where replication ends, estimation begins, and estimation is now automatable. This paper builds the estimation machinery as a three-layer Event Option Architecture: belief dynamics (the latent probability path as a jump–diffusion pinned to {0,1}, a bridge, fit per event class); the adjustment stack (the five measured wedges separating a quoted price from a probability); and the decision layer (CVaR-optimal hedge construction over Monte Carlo scenarios, the efficient hedging frontier as the deliverable, and event-Greeks computed by perturbation where closed forms do not exist). The payoff is the hedging thesis: event markets complete the market for idiosyncratic real-world exposures that no insurer writes and no traditional derivative spans (zero-sum in dollars, positive-sum in utility), provided the buyer survives basis risk, binary payouts, thin books, locked capital, and their own board’s resulting. The claim that estimation is automatable is offered as a conjecture and a design, not a validated result: the paper states the out-of-sample test it would have to pass (§9).
In 1973, Black and Scholes turned the option price from an opinion into a manufacturing cost: a continuously rebalanced position in the stock and the bond reproduces the call’s payoff exactly, so the option must trade at the cost of the reproduction; Merton put the argument on general no-arbitrage foundations. Among the formula’s descendants is the instrument an option desk would call exotic and an event venue would call the product: the binary, or digital, option. It pays a fixed amount if a condition holds at expiry, nothing otherwise. Its Black–Scholes price is e−rTN(d₂): the risk-neutral probability of the condition, discounted for the wait. A price that is a discounted probability, the object event markets are famous for quoting.
The resemblance is not a resemblance. An event contract (one unit if the described event occurs, zero otherwise) is a cash-or-nothing digital option on the event, and when the event is itself a statement about a traded price, it is the same instrument an options desk has priced and hedged for decades, listed on a different venue. The identity pays in both directions: the discount factor e−rT that Black–Scholes installs by construction has now been measured in the field as the settlement discount of event venues, and every empirical regularity of event prices (the discount, the spread structure, the favorite–longshot bias) becomes a statement about which part of option-pricing theory survives the trip from the options venue to the event venue.
The part that does not survive is the enforcement. A Black–Scholes price is a bound rather than a good estimate, policed by replication: deviate, and the delta-hedger manufactures the payoff for less and sells it to you. The apparatus presupposes a tradeable underlying, and most events have none. You cannot delta-hedge an election. No replication, no arbitrage bound; no arbitrage bound, no enforced price. What remains is estimation: a model-based, unenforced regime, actuarial only by analogy, since these events are one-shot and non-diversifiable and lack the loss history classical actuarial pricing rests on. The price is somebody’s model plus somebody’s risk premium, and deviations persist because correcting them requires risky, capital-locked, hold-to-resolution positions. The thesis in one line: where replication ends, estimation begins, and estimation is now automatable. The three layers this paper assembles (a dynamics model, a measurement stack, an optimizer) are model-fitting, data plumbing, and linear programming; all of it can run as software, which makes disciplined event pricing tractable outside the handful of desks that could previously afford it.
Four things are new here:
The paper proceeds from identity (§2) to boundary (§3) to machinery (§§4–6) to use (§§7–8), then open problems and conclusion. One scope line, drawn once and early: this is analysis, not advice; no venue is recommended and no trade is suggested.
Three payoff shapes exhaust the vocabulary a hedger needs (Figure 1). The linear instrument (forward, future) transfers exposure one-for-one, both directions, no premium. The convex instrument (the vanilla option) pays only on one side: insurance with a deductible set by the strike, bought for a premium. The all-or-nothing instrument (the digital, the binary, the event contract) pays a fixed amount on a condition: pure insurance on a yes/no state of the world, the payoff shape closest to Arrow’s (1964) primitive security. The perpetual future is the linear instrument with its expiry removed by a funding-rate tether; the event contract sits on the option branch: terminal, all-or-nothing in payout.
The identity, then. An event contract pays 1 if a described event E occurs by a date T; a cash-or-nothing digital call pays 1 if ST > K. When the event is a price condition on a traded asset, the two are the same contract on different rails, and the desk formula applies literally (Box 1). Two readings of that formula organize everything downstream. The probability reading: N(d₂) is a probability under Q, the pricing measure, not under P, the physical one (Harrison and Kreps 1979); the quote already contains risk preference, which is why even a perfectly arbitraged digital price is not a forecast. The discount reading: e−rT prices the wait. A certain-to-win claim trades below 1 until it settles.
The discount reading has now been measured where it was never installed by construction. On event venues, positions are fully collateralized (the buyer’s cash is locked until resolution), and event prices sit below objective settlement probabilities by a maturity-dependent discount, largest where capital is locked longest (Gebele and Matthes 2026), a structure Antweiler (2012) predicted for long-horizon markets from first principles. This is e−rT re-derived by the market itself, with one sharpening correction: the discount rate is the trader’s opportunity cost of collateral rather than the risk-free r. The closest thing to a causal test is estimated in agent-based simulation with LLM traders (Maresca 2026): paying interest on locked positions removes roughly 83 percent of the horizon effect on accuracy and roughly triples participation, and removing the lockup collapses the discount, which is what a carry term, not a behavioral quirk, would do. The oldest factor in the oldest formula is alive in the newest market, wearing the local cost of capital.
The identity buys the practitioner a disciplined starting point: every event quote decomposes as discounted probability, plus wedges. The discount is the first wedge; the rest are the subject of §5. But first the identity’s limit must be drawn, because the limit (not the formula) is the paper’s thesis.
Ask why the Black–Scholes price is right: binding rather than accurate. The authority is enforcement rather than realism: lognormality is false and everyone has known it for decades, yet the price is enforced. The delta-hedger manufactures the option’s payoff at a known cost by continuous rebalancing, and any quote above manufacturing cost is sold and manufactured, any quote below bought and reverse-manufactured; the deviation is a riskless profit either way. The formula’s authority is the arbitrageur’s capital. Every input to that enforcement is structural: a tradeable underlying, traded continuously, with depth, at low cost. Weaken the inputs and the bound softens into a band, but the discipline survives as long as there is something to hold.
Now remove the underlying entirely. An election has no spot market; a court ruling has no forward curve; a championship has no borrowable inventory. There is nothing to hold Δ units of, so there is no replication recipe and no arbitrage that binds the price to a model. What disciplines the quote is only the willingness of estimators to bet against it, a risky, one-shot, hold-to-resolution position: capital locked to the settlement date, no offsetting hedge, sized against a thin book, truth revealed only once. The Shleifer–Vishny (1997) limits-of-arbitrage argument applies in its purest form: correction requires capital, the capital bears risk, and its principals judge on interim results, so mispricings persist at exactly the size and horizon where correction is most expensive. The favorite–longshot bias is the standing exhibit: a century of parimutuel data documents it (Thaler and Ziemba 1988; misperception the identified mechanism, Snowberg and Wolfers 2010), the bias is public knowledge, and it persists, because harvesting it means shorting lottery tickets one resolution at a time with locked capital. In the replication regime the market cannot stay wrong; in the estimation regime it can stay wrong precisely as long as being right is expensive.
The regime boundary also redraws the measure theory. With replication, the price is an expectation under Q and the P-versus-Q gap is the cleanly defined risk premium. Without replication there is no unique pricing measure: the quote is a market-clearing aggregate of beliefs, premia, and constraints (Manski’s (2006) partial-identification result and the Wolfers–Zitzewitz (2006) preference-dependence result are the formal statements), and “the risk-neutral probability” becomes a phrase without a referent. The practical translation: in the replication regime you read probabilities off prices after discounting; in the estimation regime you must build the probability independently and treat the price as evidence about it. That asymmetry is the entire justification for the architecture of §§4–6; Table 1 summarizes the regimes.
Between the two regimes lies a third, and most of the interesting middle of the event economy sits in it. The underlying itself does not trade, but a correlated instrument does: an election moves currency, rate, and sector baskets; a macro print is shadowed by inflation swaps and rate futures; an antitrust ruling reprices the litigant’s listed equity. Here replication is partial. A position in the correlated tradable removes some of the risk but not all of it, so no-arbitrage stops pinning a single price and instead bounds a band around one. The tools are the incomplete-markets classics: Carr and Madan’s (1998) static spanning of a payoff by traded options where the proxy is close, the Föllmer–Schweizer (1991) minimum-variance (quadratic) hedge and its decomposition for the unspanned residual, and Cochrane and Saá-Requejo’s (2000) good-deal bounds, which tighten the interval by ruling out implausibly high Sharpe ratios; utility-indifference pricing supplies the buyer’s point inside the band. The practical consequence is that the dividing line of Figure 2 is really a band: full replication where the underlying trades, free estimation where nothing correlates, and a graded partial-spanning zone in between where the price is banded rather than free. The rest of the paper works the estimation end of that spectrum, where the band is widest and the actuarial machinery carries the whole load.
| Replication regime | Partial-spanning regime | Estimation regime | |
|---|---|---|---|
| What sets the price | Manufacturing cost of the replicating portfolio | Good-deal / minimum-variance bounds off a correlated tradable | Market-clearing aggregate of beliefs, premia, constraints |
| What enforces it | Static call-spread super/sub-replication; band set by strike spacing and frictions | Quadratic hedging in correlated instruments; the no-good-deal restriction | Risky, capital-locked, hold-to-resolution betting |
| Probability content | Q-probability, read off the price after discounting | A band of Q-measures; price pinned to an interval | No unique measure; price partially identifies beliefs |
| Residual biases | Small, friction-bounded bands | Bounded by hedgeable variance; residual basis unpriced | Favorite–longshot, horizon discount, expressive distortion persist |
| Natural toolkit | Closed forms; surface interpolation; call-spread replication | Föllmer–Schweizer decomposition; good-deal bounds; utility-indifference pricing | Actuarial: dynamics models, calibration, simulation (§§4–6) |
| Event classes | Price events on liquid crypto assets and commodities | Elections moving FX and rates; macro prints on inflation swaps; rulings repricing a litigant’s equity | Championships, idiosyncratic rulings, approvals: most of the event economy |
Two binary questions sort every event contract into its regime and its dynamics model (Figure 2). Is the underlying tradeable? fixes the pricing regime. Is the expiry scheduled? fixes the time structure: a scheduled resolution makes the contract a bridge pinned to a known date (§4); an unscheduled one (“X happens before date D”) makes it a first-passage or hazard-rate problem, where the resolution time itself is random.
The right-hand column is the corner where the two venue worlds are already coupled: a price event on a liquid crypto asset trades simultaneously as an event contract and as a call spread, the replication of Box 1 makes the two quotes one price up to frictions, and disciplined flow does move between markets. Whoever quotes a price event without checking the options surface is volunteering to be the counterparty of whoever does. The corner’s lesson generalizes: wherever a tradeable proxy exists, import its implied distribution as the prior and let estimation start from there. The rest of the paper works in the left-hand column, where no surface exists to import and the actuarial machinery must carry the whole load.
The estimation regime needs an object to estimate, and the right object is not the price. Define pt = P(E | Ft): the probability of the event given the information at time t, under the physical measure. This latent probability path is the underlying the event contract never had (modelable though not tradeable), and its dynamics are constrained more tightly than an asset price’s, because a probability knows where it is going. Three structural facts pin the model class down: the path is a martingale (honest beliefs have no predictable direction); the path is bounded and absorbed (it lives in [0,1] and lands on {0,1} at resolution); and consequently uncertainty has a budget: the expected accumulated squared movement over the contract’s whole life is exactly p₀(1−p₀) (Box 2), so a model that spends too much motion early must go quiet later, or vice versa. This is the bridge constraint, and it is what makes event dynamics a distinct discipline rather than a reskin of asset-price dynamics: an equity diffuses forever; an event contract’s path is a bridge from p₀ to a coin flip’s two shores (Figure 3).
The decomposition into diffusion plus scheduled jumps is where event classes acquire personalities. An election diffuses on polls for months, jumps at debates and rulings, and resolves in a final cascade. A scheduled court ruling is the opposite creature: nearly flat for weeks, then a single jump to a shore on decision day, its entire uncertainty budget spent in one instant, which is why quoting it continuously is mostly quoting the settlement discount. An in-play sports contract is a bridge on fast-forward, its whole life compressed into hours. A macro print is quiet diffusion plus one scheduled jump at release. These are parameter regions of Box 2’s model rather than metaphors (σ(p,t) profiles, jump calendars, jump-size distributions), and they are fittable. The open Polymarket-v1 archive (1.2 billion trades across 1.3 million markets, with ground-truth trade direction; Qin and Yang 2026) is the natural fitting corpus, large enough to estimate class-conditional dynamics rather than one blended average. No public library of per-class belief-dynamics parameters yet exists; §9 lists it as the field’s most buildable gap.
Two disciplines keep Layer 1 honest. Measure hygiene: the path is fit under the physical measure (realized frequencies, calibration curves), never under the venue’s quotes, which embed the wedges of §5; fitting dynamics to quotes and then “discovering” those dynamics in the quotes is the circularity the layer separation exists to prevent. And an exogeneity caveat: the latent-path model treats the event as external to the market pricing it, and at sufficient scale that assumption degrades: reflexivity runs from price to outcome, weakest for a box score, strongest for politics. Layer 1’s outputs (a distribution over paths, not a point estimate) feed the decision layer’s simulations directly; the same paths that price the contract will stress the hedge.
Layer 1 models what the probability is; Layer 2 models why the quote isn’t it. The licensing theory is Manski (the price only partially identifies the belief distribution) and Wolfers–Zitzewitz (price equals mean belief only under specific preference and wealth assumptions, with systematic deviations otherwise): these deviations are structure to be measured and inverted rather than noise to be averaged away. Five wedges separate a venue’s quote from an estimate of pt (Table 2), and the stack’s output is deliberately a probability estimate with wedge-sized error bars rather than a corrected point, because each correction is itself estimated.
Wedge one: the settlement discount. Already developed in §2: the market’s own e−r̂τ, with r̂ the opportunity cost of the locked collateral and τ the expected time to settlement. It is the one wedge with a theory-fixed sign and a nearly mechanical correction: multiply out the carry. But the correction is two-sided, and the naive one-sided form misleads. A single multiplicative factor e−r̂τp would pull a favorite toward the middle and push a longshot further from it; the compression seen at both ends comes instead from collateral being posted on both sides. The short in a longshot quoted at 0.03 locks 0.97 to earn 0.03, so its carry cost per unit of return is largest exactly in the tails, and the price it will quote is bid up toward the center. Netting the two sides, the collateral-cost adjustment compresses both tails toward the middle, and a contract two years out carries enough of it to dominate genuine probability information in the tails. It stays separate from the P-versus-Q risk-premium miscalibration (the favorite–longshot bias of Layer 1), a different mechanism with a different sign.
Wedge two: the longshot spread premium. In the lowest-probability decile, measured spreads run 1,300–1,800 basis points (Dubach 2026). On a contract quoted at 3 cents, the spread can exceed the price. A quote in the tail is an inventory-risk schedule rather than a probability: compensation for warehousing a position that pays off rarely, resolves suddenly, and cannot be hedged (§3). The rules follow: treat tail quotes as intervals, not points; and where the favorite–longshot map says the tail is also biased, compound the two corrections rather than netting them: different mechanisms, different signs.
Wedge three: expressive-flow distortion. The price is a mixture of populations (expressive small-ticket flow, exposure-sized hedging flow, conviction-sized informed flow, market-making flow), and the bet-size distribution is the observable that decomposes it. Stake-weighted and count-weighted implied beliefs diverge exactly where expressive flow distorts the price, and size-conditional calibration tells you which stratum of the book to believe: a price moved by ten thousand small expressive tickets and one moved by three institutional fills print the same number and deserve opposite treatment. Where the venue exposes fill-level sizes, this wedge is computable market by market; elsewhere it enters as a class-level prior fit from the open archive.
Wedge four: resolution-wording risk. The contract pays on the description of the event as read by an adjudicator rather than on the event itself. Semantically near-identical contracts sustain persistent 2–4 percent cross-platform price gaps traceable to wording and oracle differences (Gebele and Matthes 2026b), so at least that much of any quote is attributable to the words rather than the world. For the estimator this is a spread between P(E) and P(contract pays); for the hedger it is the seed of basis risk (§7). The correction is contractual rather than numerical: price the wording as a separate event, and prefer numeric, machine-readable resolution criteria wherever the class allows them.
Wedge five: venue risk. The quote assumes the venue pays winners, the oracle reads honestly, and the displayed liquidity exists. Each assumption has measured failure modes: headline volume inflated roughly 2.5× by mint-and-burn accounting on the largest crypto-native venue (displayed depth is not fill-able depth; Tsang and Yang 2026), plus documented oracle and adjudication attack surfaces. The regulated class concentrates counterparty risk into clearing and adds regulatory-perimeter risk; the crypto-native class trades those for custody, smart-contract, and oracle risk. Venue risk enters the stack as a haircut on the payout, not on the probability: it caps how much any quote, however well corrected, can be worth to a hedger who needs the payment to arrive.
| Wedge | Direction on quote | Measured magnitude | Evidence | Correction |
|---|---|---|---|---|
| Settlement discount | Below probability; grows with horizon | Maturity-dependent; dominant at multi-month horizons | Measured field discount (Gebele–Matthes 2026); interest-payment counterfactual removes ~83% of horizon effect in simulation (Maresca 2026) | Multiply out carry at r̂ = collateral opportunity cost |
| Longshot spread premium | Tail quotes widened both sides; mid unreliable | 1,300–1,800 bps spread, lowest-probability decile | Exchange fill data (Dubach 2026) | Treat tails as intervals; compound with favorite–longshot map |
| Expressive-flow distortion | Either; largest where small-ticket flow dominates | Market-specific; trade-size calibration component measured at archive scale | Bet-size mixture decomposition | Stake-weighted vs. count-weighted divergence; size-conditional calibration |
| Resolution wording | Either; quote prices words + adjudicator, not the event | 2–4% cross-platform law-of-one-price violations | Cross-venue contract pairs (Gebele–Matthes 2026b) | Price wording as separate event; prefer numeric criteria |
| Venue risk | Haircut on payout, not probability | Depth overstated ~2.5× by wash accounting (one venue class) | Volume forensics (Tsang–Yang 2026); oracle-attack analysis | Payout haircut per venue class; cap hedge reliance |
Order and humility. The wedges are not independent (the discount and the longshot bias both live in the tails, expressive flow feeds the longshot bias), so the stack is applied as a joint model where the data allow and as sequential corrections with widened error bars where they do not. The honest output of Layer 2 is a posterior over pt given the quote: sometimes tight, sometimes so wide that the quote is barely informative. Both outputs are useful; only one is tradeable-against, and the decision layer treats them accordingly.
The three layers now assemble (Figure 4). Layer 1 turns an event class into a distribution over probability paths; Layer 2 turns a venue quote into a probability estimate with error bars and a payout haircut; Layer 3 consumes both and answers the only questions a decision-maker actually asks: how exposed am I, what does removing the exposure cost, and how does the position behave while I hold it? The separation is the architecture’s point: the dynamics model never sees the quote it might imitate, the quote translation estimates the market’s risk preference (the collateral carry r̂ of §5 is exactly that) but imports none of the hedger’s, and every parameter of the hedger’s own risk preference lives in exactly one place: here.
The risk measure comes first, because the choice is load-bearing for binary instruments. Variance is the wrong lens: an event exposure is a tail, a lump of probability mass sitting on one bad branch. Value-at-risk names the branch but not its depth, and famously fails subadditivity, which disqualifies it for exactly the portfolio decisions this layer exists to make. Conditional value-at-risk (the expected loss in the worst (1−α) tail) is coherent in the Artzner (1999) sense, and, decisively for this setting, Rockafellar and Uryasev (2000) showed its minimization convexifies: with the expectation replaced by Monte Carlo scenarios the whole problem is a linear program (Box 3). That property is what welds Layer 3 to Layer 1: the scenario set the LP needs is precisely what the belief-dynamics simulation produces. One caution travels with the convenience: scenario CVaR at α = 0.95 optimizes over the sampled tail and is coherent but fragile (Lim, Shanthikumar, and Vahn 2011), so the frontier below is reported with scenario-count guidance and confidence bands, and where Layer 2’s error bars are wide the LP is replaced by its distributionally-robust form: worst-case CVaR over an ambiguity set sized to those bars (Zhu and Fukushima 2009). The Rockafellar–Uryasev formulation itself is untouched; only the scenario measure is hardened.
Hedge construction: exposure measured by simulation. Exposure should be simulated rather than guessed. Model the exposed firm or portfolio as a Markov decision process, with the event E entering as an exogenous branch in the transition structure, and simulate forward on both branches. The branch gap G = E[V | ¬E] − E[V | E] (more precisely, the whole distribution of the gap) is the measured exposure: what the event is actually worth to this balance sheet, including second-order effects (the contract that dies, the covenant that trips, the refinancing that reprices) that a back-of-envelope “we’d lose about X” misses. First-order, the hedge notional approximates the gap: a contract paying 1 on E, bought in size n ≈ G, transfers the branch difference. Exactly, n comes out of the LP: minimize CVaRα of terminal value over n (and over ladders of related contracts, §7), subject to the premium budget, Layer 2’s payout haircut, and the depth cap, with fill prices walked up the book rather than taken from the touch, Kyle’s (1985) price impact now the hedger’s own tax.
The efficient hedging frontier is the deliverable. Sweep the premium budget from zero upward and re-solve; the locus of (premium spent, residual CVaR) is the efficient hedging frontier (Figure 5), a decreasing, convex curve (diminishing risk reduction per dollar, the residual CVaR being the optimal value of a convex program in the budget), because the first contracts remove the cheapest tail and each further dollar buys less. The cost axis carries more than premium: collateral lockup and settlement latency belong on it too, since a payout that clears weeks after the covenant it protects has already tripped is a weaker hedge at the same price. The frontier is the artifact a treasurer should be shown instead of a trade ticket, for three reasons. It makes the decision a policy choice: pick a point, knowing what the next basis point of premium buys. It makes alternatives commensurable: an insurance quote, where one exists, is just another point in the same plane. And it makes the decision auditable after the fact (§8): the point chosen, the curve it was chosen from, and the price paid are recorded at purchase, which is what allows the hedge to be judged as insurance rather than as a bet that lost.
Event-Greeks, by perturbation. While the position is held it must be managed, and management needs sensitivities. On the quasi-Black–Scholes corner they exist in closed form; off the corner they do not (there is no underlying to differentiate against), but the architecture computes working equivalents by perturbation (Box 4): re-run the Layer 1 simulation with a driving metric nudged, the uncertainty scale nudged, the clock advanced, and difference the repriced outputs under common random numbers. Delta becomes sensitivity to whatever observable drives the class; vega becomes sensitivity to how unsettled the question is; theta decomposes into the two deterministic drifts already developed: settlement-discount accretion and bridge convergence. And the digital’s pin risk returns in event costume: near resolution with p ≈ 0.5 (election night, a final-possession game), simulated deltas grow without useful bound, and the honest instruction is the desk’s old one: size for the whipsaw in advance, because there is no continuous hedge to run when the bridge tightens.
One boundary stone closes the layer. Everything above is the hedger’s mathematics: size from exposure. The alpha seat (size from edge, Kelly (1956) and its portfolio forms) consumes the same two lower layers with a different objective on top: same instruments, same estimation machinery, opposite reasons for the position. A book that cannot say which seat a position belongs to is not running either discipline.
Arrow’s theorem is usually taught as an abstraction: optimal risk-bearing requires a market for every state of the world, and real economies fall short. The shortfall is not evenly distributed. Continuous financial states are spanned many times over by listed derivatives; insurable states by actuarial contracts with centuries of book behind them. What remains unspanned is a broad middle: idiosyncratic public events, the election that moves a tax regime, the regulatory decision that opens or closes a market, the protocol approval a crypto treasury lives on, the court ruling that reprices a sector. Insurers ration these rather than writing them freely: the demand is too correlated, the loss book is empty, and the perimeter of insurable interest is legally fenced. Partial covers do exist for parts of the middle (political-risk insurance through Lloyd’s and MIGA, deal-contingent hedges, litigation insurance), but each is bespoke, capacity-limited, and priced for exactly the correlation that makes it scarce. No listed derivative spans the rest: the nearest proxy carries a hedge-defeating load of unrelated risk. The event contract is the missing Arrow security for exactly this middle (a claim that pays on the state itself, not on a correlated shadow of it), and the hedging thesis is that pricing machinery of the kind §§4–6 describe turns that observation from a slogan into a transaction: simulation is the actuarial engine that turns event contracts from bets into priced, sized, auditable hedges.
The hedger is one persona at two scales. At one end, a household or small business with a lumpy, undiversifiable exposure to a public outcome: the café by the stadium and the host-city vote, the small importer and the tariff schedule. At the other, a corporate treasurer with the same shape of problem and more zeros. One asymmetry across the scales is decisive and cuts against the grander reading of the thesis: the books are deep enough to complete the retail and small-business end, but a corporate gap routinely exceeds available depth, so at institutional scale the honest claim is a partial hedge plus a research program, not a completed market. Between the scales, nothing in the mathematics changes: the branch gap is simulated, the frontier is traced, a point is chosen. What changes is who takes the other side and what it costs. Hedging flow is exposure-sized, not belief-sized. The hedger is structurally a noise trader, and Kyle’s tuition equation reads differently from this seat: the expected dollar loss to better-informed flow is the premium rather than a leak, the insurance loading paid for the transfer of a risk nobody else would write. The counterparty will usually be professional (concentrated skilled winners and market-making programs absorb most flow), which is precisely what a functioning insurance market looks like from the buyer’s side: you pay a professional to warehouse your tail. What no one warehouses cheaply is the correlated part: because every hedger of a given event needs the same side at the same moment, one-sided flow blows spreads out exactly when demand peaks, which is why event-hedging capacity is structurally small and the venue prices what the insurer rations. The venue completes the market by making the tail tradeable at a public price, not by conjuring bottomless capacity to absorb it. Zero-sum in dollars, positive-sum in utility: both parties are better off, the standard welfare account of derivatives hedging, and the respectable half of options markets and event markets alike. Hedging is today the nascent motive in event flow while expressive trading is the norm; this machinery is, among other things, an argument that the nascent half can be industrialized.
The caveats are half the thesis rather than a footnote, and each one binds. Basis risk. The contract pays on the description, not the loss: the ruling arrives but grandfathers your case; the election resolves but the policy dies in committee. The 2–4 percent semantic gaps of §5 are the measured floor of this risk. The honest treatment is inside the simulation: paid-but-still-lost and lost-but-not-paid scenarios belong in the LP’s scenario set, and they are why the frontier flattens rather than reaching zero. Binary-versus-continuous mismatch. Exposures are mostly continuous in severity; the contract pays a step. A ladder of strikes approximates the continuous payoff as a staircase of digitals; each rung adds its own spread cost, and the approximation error is itself simulatable. Depth caps. Thin books cap the notional: walking a book moves the price against the hedger and (worse, without traditional analogue) broadcasts the exposure on venues where flow is public. Large corporate gaps will often exhaust the frontier before the exposure is covered; a partial hedge honestly labeled is the correct output, not a failure of the method. Capital lockup. The cost is the collateral rather than the premium. Event positions are fully funded and locked to resolution, so the hedger pays the same carry the settlement discount prices. That lockup is a deterministic carry to a known resolution date, already inside the settlement-discount wedge, and not a separate stochastic marketability discount. For a treasurer, lockup converts to a working-capital line item on the frontier’s cost axis alongside the premium. Venue risk. Last and least modelable: the hedge is only as good as the venue’s solvency, the oracle’s honesty, and the contract class’s continued permission to exist. Two of these do not behave like a smooth haircut and belong in the LP as their own branch: an oracle or dispute failure (a contested UMA resolution, say) tends to fail in the exact contested state the hedge was bought for, a correlated wipeout rather than a fractional loss, and settlement latency can leave a payout arriving after the covenant it protects has already tripped. Layer 2’s payout haircut carries the smoothly-modelable remainder, the wipeout branch and the latency term enter the scenario set directly, and concentration limits per venue are the blunt but correct instrument. A hedge wearing all five caveats is still a hedge, one whose residual risks have names, magnitudes, and lines in the ledger, which is more than can be said for the unhedged branch gap it replaces.
The last risk to the hedge is not on the venue; it is in the boardroom. A well-constructed event hedge loses money in most years by design (the tail it covers is improbable by construction), so its natural history is: premium paid, event fails to occur, position expires worthless, repeat. Each repetition is presented, at budget time, as evidence. The judgment error has a name in the decision literature (resulting, grading a decision by its outcome rather than by the quality of the choice given what was knowable; Duke 2018), and its institutional expression is stable: the buyer is blamed for the “wasted” premium, the program is trimmed, and the cancellation lands some quarters before the branch it existed for finally arrives. Nothing in the mathematics of §6 defends against this; frontiers do not attend budget meetings.
The defense is institutional: the decision ledger, the organization’s timestamped record of judgments, made with reasons, evaluated against what was knowable. The ledger entry is the one §6 already specified: at purchase, record the simulated branch gap and its scenario set, the frontier the point was chosen from, the point chosen, and the CVaR removed at the price paid. The hedge is then judged (every year, including the years it “loses”) by the insurance standard: variance removed at the price paid, against the frontier available at the time. Premium P&L is not the score; it was never the score for the fire policy either. An organization that cannot make this move should not run an event-hedging program, because it will cancel it at precisely the wrong moment; an organization that can has acquired, in the ledger, the one asset that lets a hedging program compound: institutional memory of why the insurance was worth buying.
Three gaps stand open, each buildable, none built. (i) Event-Greeks off the corner. There is no published closed-form or even standardized numerical definition of delta, vega, or theta for event contracts without a tradeable underlying: Box 4’s perturbation definitions are offered as a starting convention, and their sampling-error properties deserve real treatment. (ii) Per-class belief-dynamics libraries. The bridge-plus-jumps family of Box 2 is fittable at archive scale, but no public library of fitted per-event-class dynamics (jump calendars, jump-size distributions, diffusion profiles, favorite–longshot maps by class) exists; it is the field’s most direct path from measurement to engineering. (iii) Hedge-effectiveness accounting. No accounting standard addresses hedge-effectiveness treatment for event contracts, so a corporate buyer today books the hedge as a speculative position, a gap that quietly prices many treasurers out of the instrument, and one the branch-gap measurement of §6 seems purpose-built to inform. A fourth gap is measurement: the hedger share of event flow is currently inferred, not measured; its trajectory is the empirical test of the thesis that the nascent motive can be industrialized. And the central conjecture, that estimation is now automatable, has a concrete validation the paper does not itself run: fit one event class end-to-end on the Polymarket-v1 archive, then show, out of sample, that the Layer 1–2 probability is better calibrated than the carry-corrected quote it is meant to improve on, the efficient-market null. Until that test is passed the architecture is a design, not a result.
The paper has argued one identity, one boundary, and one architecture. The identity: an event contract is a digital option, and the oldest formula in derivatives already prices it as a discounted probability, a discount the newest markets have re-derived empirically as the settlement discount. The boundary: the formula’s authority comes from replication, replication needs a tradeable underlying, and most events have none, so event pricing splits into a replication regime, where arbitrage tethers quotes to options-implied distributions, and an estimation regime, where the price is actuarial and its biases persist under the ordinary economics of limited arbitrage. The architecture: in the estimation regime, price and hedge by simulation: a bridge-constrained belief model fit per event class, an adjustment stack that inverts the five measured wedges between quote and probability, and a CVaR decision layer that measures exposure as a simulated branch gap and delivers the efficient hedging frontier rather than a trade. Where replication ends, estimation begins, and estimation is now automatable.
What the paper does not claim: that the machinery beats the market; that the hedges are clean (five named caveats bind); or that the architecture is validated at industrial scale (its parts are individually sound: the wedges are measured, the LP is standard, the archive is public, but the assembly is a working design, not a track record). What it does claim is narrower and durable: the event economy’s pricing problem is the actuary’s, not the arbitrageur’s; the actuary’s tools are now software; and a hedge bought on a recorded frontier, judged by the variance it removed at the price paid, is the form in which event markets earn the respectable half of their comparison to options, completing the retail and small-business end of the market for the risks ordinary balance sheets actually carry, one honestly-priced tail at a time.