Follow-up once you have quoted a simple market cleanly.
The informed counterparty
The question
You quote a market on a coin flip paying 100 for heads. Your counterparty may have seen the coin. How should your quote change?
Have a go before you open the solution. If you are stuck after a few minutes, the first paragraph below is usually enough of a nudge.
Show the worked solution
The answer
Widen it. With a possibly informed counterparty the unconditional expectation of 50 is not your trading edge.
Unconditionally the payoff is worth 50, but you only trade when the counterparty chooses to, and they choose when it favours them.
If they are informed with probability p, a buy at your offer is evidence the coin is heads, so the value conditional on being lifted is above 50.
Your offer must therefore sit above 50 by enough to cover that conditional shift, and your bid symmetrically below. The spread is the price of adverse selection, not a profit margin.
This is the core of real market making: quote around the value conditional on being traded with, never the unconditional value.
What it is testing
Whether you price conditional on execution rather than in the abstract.
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Preparing properly
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