Reading the Term Structure of a Binary Event

Right now on Kalshi, five markets ask the same binary question — will the US and Iran sign a permanent peace deal? — with different deadlines:

The shape of that curve isn't an accident. Each price contains information about when the market thinks resolution is most likely, not just whether. Reading the curve is its own discipline.

The Naive Read

Most traders look at the May 31 market — 14¢ — and stop. "14% chance by end of month." Buy or don't buy.

But the prices across deadlines form a term structure, and the term structure tells you about the marginal probability density — how the market expects probability to accrue over time.

Marginal Probability Density

Subtract adjacent prices, divide by the time gap:

Two humps. The first is the next 13 days at 1.08¢/day. The second is the back half of June at 0.87¢/day. The rest of the curve decays.

In English: the market expects a deal announcement most plausibly in the next two weeks. Failing that, there's a second window late June. After mid-July, the per-day probability flattens out — meaning the market doesn't think the timing is concentrated, just that the eventual probability keeps accumulating.

This is a structured claim about the world. Maybe right, maybe wrong. But it's testable — you can update it as news arrives.

Cross-Entity Comparison

Same Kalshi corpus, same deadlines, different counterparties:

The Israel-Iran deal market for May 31 trades at 3¢ — roughly a quarter of the US-Iran probability for the same date.

Why? Markets are pricing the diplomatic geometry. A US-mediated outcome is more plausible than a direct Israel-Iran handshake. Third-party intermediaries reduce face-loss costs for primary belligerents. This is how Camp David, the Iran nuclear deal, the Abraham Accords all happened — through a third party.

The cross-entity gap also sanity-checks the US-Iran read. If you buy US-Iran May 31 at 14¢ on a "multilateral deal imminent" thesis, you'd expect Israel-Iran to move correlatedly when news breaks. If it doesn't, your thesis is broken.

Trading Lens

Calendar spreads are the natural expression of a term-structure view.

Buy Jun 30, sell May 31 if you think the deal is more likely in the back half of June than the front. Cost: 34¢ - 14¢ = 20¢. Payoff: if the deal happens between June 1 and June 30, you make 100 - 20 = 80¢ on the long leg, lose 0 on the short. Net +80¢. If it happens by May 31, you make 100 on the short (well, short means you sold and the buyer paid you 14¢ but now owe 100), so you lose 86¢ on the short and gain ~0 on the long depending on timing. Net negative. If no deal by June 30, you lose 20¢.

Buy May 31, sell Dec 31 if you think the deal happens this month or not at all (a "concentrated timing" view). Sell the Dec 31 NO leg at 32¢ (which is 1 - 0.68). Net cost: 14¢ - 32¢ = -18¢ credit. The position pays if a deal happens by May 31 (you collect 100¢ on the long, owe 100¢ on the short NO settling at 0). The position loses if a deal happens between June 1 and December 31 (long leg pays 0, short NO pays 100, you owe 100).

Calendar spreads on binary events have a peculiar property: they're directional on timing, not on outcome. You can be right that the deal happens and still lose money because your timing was off.

This is the same shape as a butterfly on a directional option. If your view is "I think this resolves in window X but not window Y," a calendar spread expresses it more cleanly than buying one leg outright.

Why This Matters

Most prediction market analysis treats each contract as standalone. That misses the most useful structural information.

Binary events with term structure are everywhere:

• Election prediction markets with markets for "by Nov 3" vs "by Nov 4" vs "by Nov 10" if there's recount risk
• Fed rate cut markets across each FOMC meeting through year-end
• Hurricane landfall markets at daily granularity through the season
• Sports markets across "team to win this week," "team to win playoffs," "team to win championship"
• Earnings markets across consecutive quarterly reports

Each has a term structure if you look. Reading the shape gives you three things:

1. Implied marginal probability over time windows — what the market thinks about timing, not just outcome
2. Cross-checks for noise — if same event prices weirdly at adjacent deadlines, one is mispriced
3. Calendar spread opportunities — when the curve shape disagrees with your view, you can trade timing directly

How to Find Them

/api/public/scan?q=<event keyword> returns all markets matching a phrase. Group by event, sort by deadline. The shape becomes visible.

Monotonic and smooth: boring. Hump-shaped or with a kink: interesting. The interesting ones usually signal that the market is pricing a specific catalyst at a specific time.

That's the whole game.