Binary YES/NO Contracts

A binary contract is a small contingent claim: it pays 1 unit if a precisely worded event occurs and 0 otherwise. The price is what one share costs now, not the promised profit.

Payoff contract #

Let $Y=1$ when the event resolves YES and $Y=0$ when it resolves NO. A YES share pays

$$Payoff_{YES}=Y,$$

while a true complementary NO share pays

$$Payoff_{NO}=1-Y.$$

Therefore $Payoff_{YES}+Payoff_{NO}=1$. The corresponding probabilities satisfy

$$P(YES)+P(NO)=1$$

only when YES and NO are mutually exclusive and exhaustive under identical resolution rules.

Numeric example #

Buy YES at $p=0.65$. You pay 0.65 immediately. If YES occurs, you receive 1 and profit 0.35. If NO occurs, you receive 0 and lose 0.65. The displayed 0.35 is only the winning-branch profit, not a guaranteed return.

Life analogy #

Think of a refundable ticket that returns 1 unit only if a flight is cancelled. Paying 0.20 is the participation cost; it does not mean the ticket “earns 0.80” unless cancellation actually triggers the payment.

Application to no-hedge #

The formula $fair_{maker}=1-referenceVWAP$ is valid only when the reference contract pays the exact complement of the maker contract. If contract semantics differ, the subtraction has no guaranteed payoff meaning and the strategy must reject the mapping rather than invent a substitute.