CONCEPTS/THEORY·14 min read

Prediction Market Valuation Theory: A Capstone

The funnel, the indicator stack, the three-source axis, and null-as-signal — synthesized into one theory of how to value a binary contract. The market is valuable because it is the only forum where these three sources collide in a single price.

By Patrick LiuApril 9, 2026

Prerequisites

Everything else on this site is a piece of one bigger argument. The valuation funnel is the workflow. The pm-indicator-stack is the screening tool. The three-source data axis is the epistemology. The null-as-signal principle is the inversion that turns missing data into entry conditions. Each piece is useful on its own. The real power comes from putting them together, and that synthesis is what this essay is about.

I am going to make a specific claim and then defend it: a binary prediction-market contract is the only financial instrument in the world where reality data, endogenous data, and opinion data collide in real time inside a single observable price. That collision is what makes the price informative. A theory of prediction-market valuation has to take the collision seriously — has to model what it means for three independent data sources to be averaged into one number — or it is just a re-skin of stock valuation that does not fit the asset.

Most of the existing literature does the re-skin. This essay is the alternative.

What a Binary Contract Actually Is

Strip away the framing and a binary prediction-market contract is a very simple instrument. It is an asset that pays 1ifsomeeventhappensand1 if some event happens and 0 if it does not, where the event is observable, the resolution date is known, and the contract trades continuously between now and resolution.

That definition makes it sound like a digital option, and people who come from derivatives trading naturally reach for option-pricing intuitions. But the analogy breaks at the most important point: an option's payoff depends on a price, and that price is itself an asset traded in another market with its own continuous discovery process. A binary prediction-market contract's payoff depends on an event, and the event has no underlying market — the only market for the event is the contract itself. There is nothing else to mark against.

The closer financial analog is a credit-risky zero-coupon bond. You pay some fraction of par now, you hold for a fixed duration, and at maturity you either get par (issuer survives) or you get something less (issuer defaults). A binary contract is a credit-risky zero where the "credit event" is the prediction-market event and the "recovery rate" is exactly zero on the losing side. The bond-trader vocabulary that works for credit-risky zeros — yield, spread, duration — translates directly. That is why implied yield is the right unit and the pm-indicator-stack borrows its design from the bond desk.

But the analogy is incomplete in one direction: a credit-risky zero has an issuer with continuously updating credit information, and the bond price reflects both the risk-free rate and the issuer-specific spread. A binary prediction-market contract has no issuer — only an event. There is no balance sheet to study. There is no rating agency. There is no recovery model. The valuation has to come from somewhere else.

That somewhere else is the three-source axis.

Why Three Sources Is the Right Number

A binary contract's "fair value" is $1 times the true probability of the event. Nothing else. The whole question of valuation reduces to: what is your best estimate of that probability, and how does it compare to the price.

The hard part is that the true probability is unobservable. You can never look it up. You have to infer it from data — and the data you can use breaks cleanly into three categories that correspond to three production processes:

  1. Reality data is the data generated by the world itself, independent of any observer. The physical sensor reading. The official BLS print. The court ruling. This data is causally connected to the eventual outcome — by definition, the contract resolves against this data — but it is slow, expensive, and only available at a few points in time before resolution.

  2. Endogenous data is the data generated by the market itself — the price, the depth, the trade tape, the indicator stack. This data is fast, free, and continuous, but it is recursive: the market reacts to its own price, so endogenous data measures partly the underlying truth and partly the market's self-image. Reading endogenous data without correcting for the recursion is how you confuse momentum for belief.

  3. Opinion data is the data generated by other humans observing the same event you are observing — analysts, journalists, experts, the social media discourse. This data is messy and biased but it has the unique property of containing forecasts and interpretations, not just facts. Opinion data is where future probability estimates live before they become reflected in price.

The three sources are independent in production but they all eventually converge on the same underlying reality, which is the event itself. At resolution, all three collapse into the same fact — the event either happened or did not. Before resolution, they are separate witnesses to the same truth, and the gap between them is the measurement uncertainty in the market price.

This is why three is the right number and not two or four. With two sources you can only check whether they agree; you cannot identify which one is wrong if they disagree. With four sources you start double-counting (most "fourth sources" turn out to be derivatives of the first three). Three is the minimum that lets you triangulate and the maximum that does not duplicate.

The Collision and Why It Matters

Here is the claim that I think is the foundation of this whole framework: in any other market, only one of the three data sources is directly visible in price.

Equity markets price endogenous data. The bid and ask are real, the trade tape is real, the order flow is real — but the equity is not paid out against any single observable event, and the relationship between price and "the truth" is mediated by an entire industry of analysts whose opinion data sits in research reports and earnings models. Equity prices reflect endogenous reality (what people are actually trading) and lagged opinion (what the analysts wrote last week). They do not reflect reality data in any direct sense.

Bond markets are similar. Treasury prices reflect the endogenous reality of trading and the opinion reality of the macro forecast community. Reality data — the actual fiscal trajectory, the actual inflation print — is incorporated only through the opinion layer, which consumes the data and produces a model output that then moves the price.

Sports betting markets are more interesting. They have a clear reality layer (the game outcome), but the time horizon is so short that opinion data and endogenous data dominate the entire pricing process, and reality data only arrives at resolution. There is no "during the bet" reality data layer.

Prediction markets are different. A Kalshi contract on the next jobs report has reality data arriving in chunks throughout the τ window — labor market indicators, ADP, JOLTS, the previous month's revision, weekly claims. Each piece of reality data is publicly available and causally relevant to the eventual print. Opinion data is also flowing throughout — every economist's forecast, every Fed Whisperer piece, every think-piece on monetary policy. And endogenous data is updating continuously as the market price moves.

All three sources are visible to the trader, in real time, against the same single observable contract. That is the collision. The price is the running average of three independent witnesses making predictions about the same event, and the quality of the average depends on how well the trader can read the disagreements between the witnesses.

This is what makes prediction markets uniquely valuable. Not the fact that they exist (they have existed for decades). Not the fact that they are well-calibrated on aggregate (they often are). The unique thing is that they are the only forum where you can simultaneously see what is happening in the world, what is being said about what is happening, and what the trading population is doing about both — all averaged into one number you can buy or sell.

The Funnel as a Procedure for Reading the Collision

The three-stage valuation funnel is the practical procedure for reading the collision in a way that does not get overwhelmed. Each stage corresponds to a specific way of using the data sources:

Stage 1 uses endogenous data only. The indicator stack scans the full universe in milliseconds, pulling out markets where the math suggests there might be a mispricing. This is endogenous-only on purpose: the only data source that scales to 47,000 markets is the data the venue publishes for free. You do not have time to read 47,000 BLS reports or 47,000 expert forecasts. You have time to compute IY and CRI on 47,000 prices.

Stage 2 uses endogenous data more carefully. The orderbook check is still endogenous data, but it is endogenous data at higher resolution — you are looking at depth and spread to verify that the indicator-suggested edge is executable. Stage 2 is where the warm-regime cron coverage matters, where LAS lights up, and where the null-as-signal patterns kick in.

Stage 3 uses all three sources. This is where reality data and opinion data finally enter the conversation. You take the dozen-or-so candidates that survived stages 1 and 2 and you triangulate each one against the other two sources. Does the BLS forecast support this contract? What are the credible commenters saying? Is the endogenous signal consistent with the macro reality, or is it the market reacting to itself? Stage 3 is where the collision is actually read, candidate by candidate.

The funnel is the right shape because the three data sources have very different costs. Endogenous data is cheap and parallelizable. Reality data is slow and expensive. Opinion data requires human judgment to filter. You spend the cheap data first to narrow the universe, then you spend the expensive data on the survivors. Inverting this — starting with reality or opinion data and using endogenous as a check — guarantees you will only ever look at markets that are already in the news, which are the markets with the least edge.

The Indicator Stack as the Endogenous Compressor

Stage 1 of the funnel works only because the pm-indicator-stack compresses raw price data into five numbers that capture most of what matters. The compression is lossy on purpose — you are throwing away the full price history and keeping only the indicators — but the loss is bounded because each indicator is designed to surface a specific kind of mispricing.

Implied yield compresses "is this paying enough." Cliff risk index compresses "is anything happening." Event overround compresses "is the event self-consistent." LAS compresses "can I trade." CVR compresses "has the thesis arrived yet." Five compressions, five different lossy summaries of the raw endogenous tape.

The reason five is enough — and why I keep insisting on five and not eight or twelve — is that the goal of the indicator stack is triage, not valuation. You do not need to know the exact answer for any contract; you need to know which contracts deserve the expensive stage-3 attention. Five well-chosen compressions get you 90% of the triage signal at 5% of the computational cost. Adding more compressions past five hits diminishing returns hard, because the additional compressions are correlated with the first five.

This is the same principle as factor investing in equities: a small number of orthogonal compressions capture most of the cross-sectional variance, and adding more factors mostly adds noise. The indicator stack is the binary-contract version of the factor stack.

Null States as Conditional Strategies

The null-as-signal principle is what closes the loop. Without it, the indicator stack returns null on roughly half the universe (everywhere the warm-regime cron has not run), and naive users treat the null as missing data and exclude those markets from the scan. That exclusion throws away the half of the universe where most of the maker alpha lives.

Treating null as signal means turning the indicator stack into a conditional lookup: not "what is the IY of this market" but "what state is this market in." A market with high IY and high LAS is a taker setup. A market with high IY and null LAS is a virgin-Polymarket maker setup. A market with low CRI and PIV ≈ 0 is a range-MM setup. Each combination of (value, null) states across the five indicators corresponds to a different strategy in the playbook.

The capstone insight is that the indicator stack is not a five-dimensional continuous space; it is a discrete state machine where the presence and absence of each indicator value defines the state. The valuation procedure is a decision tree that walks the state machine and routes you to the appropriate strategy. Null is one of the values in the state machine, not a missing value to be imputed.

This is why the framework is more powerful than a generic quant stack. A generic quant stack treats data quality as a binary (present vs missing) and tries to maximize the present cases. The prediction-market framework treats data presence as a multi-valued classifier and maps each presence pattern to a strategy. You are not trying to maximize coverage; you are trying to read the coverage as itself a feature of the market.

Putting It All Together

A complete valuation procedure for a single binary prediction-market contract, end to end, looks like this:

You scan the universe with the indicator stack and pull the candidates that survive your indicator filters (stage 1, endogenous-only, ~100 candidates from 47,000). You check the orderbook on each candidate to verify executable edge, paying attention to where LAS is null because that null is not noise but a strategy gate (stage 2, endogenous-only at higher resolution, ~30 candidates from ~100). You then take each surviving candidate through the three-source triangulation: pull the relevant reality data for the τ window, scan opinion data for the credible commenters, compare both against the endogenous signal, and identify which candidates have all three sources in alignment (stage 3, full three-source axis, ~3 candidates from ~30).

For each finalist, you build the causal tree of the event — the explicit decomposition of what would have to happen for the contract to resolve in your favor — and you check that the causal tree is consistent with the data you found in stage 3. The candidates that pass the causal check are the trades. The candidates that fail the causal check are interesting failures to remember and add to your follow-list, because they are markets where the indicators flagged something real but the underlying event does not actually support the indicator signal — which is information about the gap between what the market is doing and what the world is doing.

You size each trade according to your risk budget and the strength of the three-source agreement. Three sources strongly agreeing → larger position. Two sources agreeing with the third hedging → smaller position. Anything ambiguous or contradictory → no position. The sizing is how you turn the qualitative triangulation into a quantitative bet.

Then you watch. The position is monitored by re-running the indicator stack on the trade as time passes — looking for CRI to drop (your edge is being captured) or rise (the thesis is being challenged), looking for LAS to thicken (other traders have arrived), looking for the null states to collapse into values (the market has been "discovered"). The same indicator stack that screened the entry is the one that defines the exit conditions.

That is the procedure. Top to bottom, it is one workflow that integrates all four pieces of the framework into a single repeatable process. The CLI shorthand is roughly sf scan --by-iy desc | sf depth --check | sf thesis --triangulate, though the third command is mostly aspirational at the moment because triangulation is still partly human work.

Where the Theory Breaks (Honest Caveats)

A complete theory needs to name the cases where it does not apply.

Markets that resolve too fast. If τ is small enough that you cannot complete stage 3 before resolution, the valuation procedure is impossible. You are stuck reading the indicator stack alone and hoping the endogenous signal is right. This is structurally why I avoid markets with τ < 14 days for non-trivial position sizing.

Markets where opinion data is dominated by other prediction-market traders. If the only people writing about the contract are people who are themselves looking at the price, opinion data has collapsed into endogenous data and you have effectively two sources, not three. Watch for this on the meta markets and on niche financial markets where the discourse is downstream of the tape.

Events with no reality layer until resolution. First-time events, novel rare events, events where the only "data" is a yes/no outcome at maturity. The three-source axis cannot triangulate because there is nothing in the reality slot. The procedure degrades to "endogenous + opinion only" and you should size accordingly.

Cases where the indicator stack disagrees with itself. Two indicators flagging opposite directions on the same contract — high IY suggesting a buy, high CRI in the wrong direction suggesting a fade — is real. The right move is usually to skip the contract, not to break the tie. The indicators are designed to be correlated when there is a real signal; when they are not, you are reading noise.

The framework is not protective against tail risk. Three sources can all agree and the event can still go the other way, because three sources agreeing about a 70% probability still leaves a 30% probability of being wrong. The triangulation procedure improves your expected edge but does not eliminate variance. Always size as if you can be wrong even when you are confident.

The Final Claim

The market is valuable because it is the only forum where these three sources collide in a single price. Reading that price as if it were a single number is reading half the data. Reading it as a collision — as the running average of three independent witnesses, with the gaps between them as informative as the average itself — is what the framework on this site is designed to teach.

The funnel gives you the workflow. The indicator stack gives you the screen. The three-source axis gives you the epistemology. The null-as-signal principle inverts the triage to find the markets nobody else is looking at. Together they are not five separate tools; they are one tool with five interlocking parts, each of which is required for the whole thing to work.

If you have read this far you have read every concept in the framework. The next step is to actually try it on real markets, ideally with small position sizes for the first month so the learning is cheap. The CLI is sf scan, the technicals are linked above, and the rest is practice.

For deeper dives into specific pieces: see the upcoming implied-yield, cliff-risk-index, event-overround, tau-days, and expected-edge concept pages for the long-form derivations of each indicator. See the implied-yield-vs-raw-probability-bond-markets opinion for the philosophical case for the bond-trader framing. See the thesis-driven-prediction-market-strategy for the version of this argument that lives inside stage 3 specifically. See the computing-implied-yield-from-kalshi-tickers technical for the working code.

The framework is the spine. The articles linked from it are the meat. The whole thing is one argument and you have just read its conclusion.

Related Work

capstonetheoryvaluationframeworksynthesis