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COUPON MATH

How probability becomes a coupon.

A probability tells you how likely success is by the longstop. EventsYield converts it into a fixed coupon rate for the matched position. The coupon then accrues continuously.

22% probability$100 notional365 days
01 · INTUITION BEFORE FORMULAS

At 22%, the expected gross coupon is $22.00. If no event qualifies, the maximum gross coupon is $24.8461.

The maximum is higher because the no-event path accrues through longstop. Under this immediate-stopping convention, success paths stop earlier.

Expected and maximum gross coupon curvesThe solid expected Np line and dashed maximum −Nln(1−p) curve rise with quoted probability. The selected 22 percent value is marked on both curves.0%65%$105$022% selected
Gross coupon by quoted longstop probability · $100 notional · 365 days.
Expected gross NpMaximum gross −Nln(1−p)Selected probability
Selected values
At 22%Gross coupon
Expected Np$22.00
Maximum −Nln(1−p)$24.8461
1%65% explainer range
Quoted probability
22%
Expected gross coupon Np
$22.00
Maximum no-event gross coupon
$24.8461
Gross coupon per day
$0.0680716
λ = −ln(1−p) / Tc = NλCmax = −Nln(1−p)∫₀ᵀ Nλe^(−λt)dt = Np

The Np identity is the pure pricing result under constant hazard, immediate stopping, full collateralization, and identical discounting. Resolution latency is treated separately below.

02 · CASH FLOW

BACK pays while it waits. Confirmed success delivers the $100 event payment.

Move the stopping day to trace an illustrative path where success is confirmed immediately. The dotted lines show the no-event path through day 365.

Day 1Day 364
Paired BACK and FADE contractual cash-flow trajectoriesBACK's gross coupon cash flow slopes negative as it pays the coupon, then jumps by 100 on confirmed success. FADE's net coupon slopes positive, then its 100 collateral transfers away. Dotted lines show the no-event path through day 365.Day 0Day 365Day 100BACK grossFADE net
Contractual cash flow, not total P&L. Coupon cash flow and pre-funded escrow are shown separately.
BACK · solid with circle markerFADE · dashed with square markerNo-event reference · dotted
ESCROW RAILSELECTED DAY 100
BACK funding
$24.9890
Coupon accrued
$6.8072
Unused reserve unlocked
$18.1427
FADE collateral transferred
$100.00

The 1.15% coupon fee is split equally. BACK pays half (0.575%) on its funded coupon; FADE bears the other half (0.575%) from its receipt.

CONFIRMED YES

Success pays the event payment.

In this immediate-confirmation illustration, FADE's collateral transfers to BACK on day 100. BACK receives $100 and its unused reserve unlocks; FADE receives the net coupon accrued through that day: $6.7680.

POST-LONGSTOP NO

Longstop starts resolution.

If no petition is funded earlier, ordinary accrual stops at longstop and post-longstop resolution begins without a new petition bond. NO becomes final only after evidence, a sealed ballot, and appeal finality. FADE then recovers its collateral and keeps $24.7033 net coupon through day 365; returned or unlocked capital is not profit.

03 · TIMING CONVENTION

A convention, not a forecast of when the event happens.

One probability plus one longstop gives one reproducible coupon. Constant hazard is a pricing convention, not an objective timing forecast. Coupon accrues continuously and lazily; per-day is display only.

Coupon accrues until a petition is fully funded—not until the real-world event happens. It is suspended from that point to final confirmation: YES returns the suspended coupon to BACK; NOT YET pays it to FADE and reopens the market. Without an earlier funded petition, accrual stops at longstop and post-longstop resolution begins without a new petition bond. FADE's collateral returns only after the network confirms NO.