Fair prices and margins

Price a toy contingent payoff and distinguish an unconditional valuation from value given a trade.

12 minutes · advanced · Original Poker4Quant lesson

What you will learn

Compute a risk-neutral expected payout and explain the effect of fees and informative selection.

Prerequisites: Expected value as a weighted average · Uncertain opponent frequencies

A model price starts with the contract

Consider an educational contract paying 100 units if an event occurs and zero otherwise. If its modeled probability is p, its expected payout is 100p. Ignoring risk preferences, financing, fees and constraints, a buyer paying price a has expected net payoff 100p−a.

A risk-neutral fair price is therefore 100p in this simplified model. This is not a statement of a real market price or a recommendation to trade. Different information, utility, transaction costs or contractual details can change an actual valuation.

A quoted margin is not automatically earned value

A toy dealer might quote a bid below and ask above an unconditional expected payout. If incoming trades convey no new information, the difference from expected value describes the model’s per-trade margin before costs.

But the event probability conditional on someone choosing to trade may differ from the prior. An informed seller may sell when the claim is worth less, while an informed buyer may buy when it is worth more. Update value for that selection mechanism before claiming that a visible spread is guaranteed profit.

Worked example

An event has modeled probability 35%. A contract pays 100 on success. A buyer pays 32 and a fixed fee of 1. What is expected net payoff?

Expected payout is 0.35×100=35.
Total upfront cost is 32+1=33.
Expected net value is 35−33=2.
If observing the sale changes the modeled probability, recompute the payout expectation conditionally.

The model gives +2 units at the stated probability and costs. It does not guarantee profit or validate the probability estimate.

Hands-on: Filter orders, quote a contract and settle both states

Construct conditional trade populations, adjust a fee-aware dealer ask and reconcile conserved counterfactual wallets. Compare an unconditional spread with value given a trade.

Reading contract…

Common mistakes

Confusing payout with profit after purchase.
Ignoring fees because the spread looks positive.
Assuming trades cannot convey information about value.

Keep these ideas

State the payout contract and costs.
A fair expected payout depends on the model.
Selection by counterparties can change conditional value.