Quant case studies, worked step by step

Cases
100
Traced to a firm
43
Topics
11
Hard
30
Topic
All topicsSignal research and data tasks10Options and volatility trading10Market-making games14Portfolio construction10Strategy evaluation and backtests9Execution and market microstructure8Fixed income and credit8Regression and model review8Risk measurement and limits9Statistical arbitrage and event trades8Position sizing and bankroll6
Level
AnyWarm upCoreHard
Source
AnyReported at a firmStandard
Showing 1–10 of 13 · filtered from 100Clear filters
  1. 003You make a market in a coin-flip contract paying Rs 100 on heads. One trade in four is the interviewer, who knows the outcome and trades only when it helps; the rest is balanced. What is the narrowest breakeven spread, and what does quoting 45 at 55 cost over 40 trades?Market-making gamesHardCitadel SecuritiesLondon · 2026
  2. 014A contract settles at a die roll, doubled if a coin lands heads, plus 5 if a drawn card is red. Quote it, then decide whether to trade with a bot showing 9.5 bid, 10.5 offer, and whether to make or take.Market-making gamesHardOptiverAustin · 2025
  3. 024You are long 10 contracts on the number of sixes in 30 dice, bought at an average of 5.2 at Rs 100 a point, when the interviewer reveals that none of the first 12 dice shows a six. Reprice, mark your P&L and decide whether to cut.Market-making gamesCoreOptiverAmsterdam · 2023
  4. 026You and three computer quoters make markets on the sum of five cards drawn from one suit numbered 1 to 13. Each bot has seen one card and its mid is 37, 33 or 39. What did each bot see, and where do you quote?Market-making gamesCoreOptiverChicago · 2025
  5. 037In a market on the sum of two dice you sell 3 to interviewer A at 7.5, buy 2 from B at 6.5, sell 4 to A at 7.2 and buy 4 from B at 7.0, at Rs 100 a point. Where is your position, and what is your P and L if it settles at 8?Market-making gamesWarm upOptiverAmsterdam · 2023
  6. 048Make a market on the product of two dice. The fair value is 12.25 with a standard deviation near 8.9 and a long right tail. How wide are you for one lot and for ten, and which way do you lean?Market-making gamesCoreCitadelNew York · 2025
  7. 050Three players are each dealt one card from 1 to 10 without repeats, and the contract settles at the highest card. You hold a 7. Price it, then reprice after another player immediately bids 8.5.Market-making gamesHardBelvedere TradingChicago · 2022
  8. 051Five players trade a contract that settles at the sum of ten dice rolled one at a time in public. After four rolls totalling 17, one player bids 38 and another offers 36. What is fair value, and what can you lock in by trading between them?Market-making gamesWarm upDRWNew York · 2026
  9. 062A bag holds four stones, each black or white, with every count of black stones from 0 to 4 equally likely. Two stones drawn without replacement are both black. Make a market on a contract paying Rs 100 if the third stone is black, then respond when the interviewer lifts your offer at 80.Market-making gamesHardCitadelNew York · 2025
  10. 075A contract settles at the sum of three cards drawn without replacement from ten cards numbered 1 to 10, at Rs 100 a point. Quote a two-way market before any card, after the first card shows 9, and after the second shows 2, keeping pace with the dealer.Market-making gamesHardOptiverChicago · 2026

Company names and figures are illustrative.