HardMarket Making & Games
Quoting Against Informed Flow
Citadel SecuritiesSIG / Susquehanna
A binary asset settles at 100 or 0, each with probability 1/2. Of the traders who arrive, 20% are informed (they know the outcome and trade in its direction) and 80% are noise traders who buy or sell with probability 1/2 each. A single trader arrives and buys from you at your ask. To break even in expectation against this flow, what is the lowest ask you can quote?
Approach
The fact that the trader chose to buy tells you something about V.
Compute P(V = 100 | buy) with Bayes’ rule.
Answer
Show the final answer
The answer is 60. Sign in free for the full worked solution and to check your own answer.
Related problems
Make a Market on Two DiceEasyRoll, Keep or Re-rollMediumThe Red–Black Card GameHardTwo Bookmakers, One ArbitrageMediumThe Bookmaker’s EdgeMediumKelly with 2-to-1 OddsMedium
More in Market Making & Games.