Optiver Interview Questions
The real Optiver quant-interview problems candidates report — expected value, options pricing and probability — each with a full worked solution.
Inside the Optiver interview
Optiver is a global options market maker that lives on fast, accurate pricing under time pressure. Its interviews are built around mental math and expected value, options-pricing intuition, and quick probability and combinatorics puzzles.
What they test
The dominant block is expectation and EV reasoning (24 problems) — betting games, fair-value of a payoff, and pricing a wager you'd actually make a market in. Right behind it sit a real options-pricing strand (12: payoff diagrams, put-call parity, when to exercise) and a probability / combinatorics core (11 + 10: dice, draws, counting arrangements), with game-theory (8) and a lighter coding tail (7).
The recurring shapes
Most questions reduce to computing an expected value and comparing it to a price — you're quoting a number you'd be willing to trade on, so an answer that's merely 'fair' isn't enough. On the options side they probe whether you can read a payoff from first principles; put-call parity ties a call, a put, the spot, and the strike together and shows up again and again.
How to approach
Lead with linearity of expectation and symmetry to get a clean number fast, then state the price you'd make and the edge you're protecting. For options, draw the payoff and reason from parity rather than memorized formulas; for the game-theory and combinatorics puzzles, condition on the first move or count carefully, and narrate your arithmetic so a fast-but-wrong answer doesn't slip through.
The mix skews hard — 41 hard and 40 medium against just 12 easy — so train for speed under pressure across all three pillars rather than leaning on warm-ups.
Optiver expected value questions (24)
- Optimal Stopping: Three-Roll Dice Game
- Bus Waiting Paradox
- Expected Draws to Complete a Tile Hand
- Expected Steps for a Reflecting Random Walk
- Choosing Among Mutually Exclusive Coin-Flip Bets
- Monte Carlo Backtest of Kelly and Fractional Kelly Strategies
- Last Roll of a Cumulative Sum Game
- Expected Maximum of Standard Normal Random Variables
- Extinction Probability of a Branching Process
- Kelly Versus Target-Based Betting Over Three Rounds
- Expected Minimum vs. Expected Difference of Two Dice
- Expected Flips for Three Consecutive Heads
- Volatility Regime Markov Chain
- Expected Waiting Time With Random Bus Delays
- Expected Position of the Ace of Spades in a Shuffled Deck
- Expected Rolls to Reach Position 10 in a Symmetric Random Walk
- Expected Sum of Two Dice with Cancellation on Doubles
- Card Product Betting and Kelly Growth
- Dice Bets: Expected Profit and Kelly Criterion
- Estimating Your Opponent's Card Sum
- Expected Draws Until Three of the Same Rank
- Expected Total Reward in a Random Walk with Absorbing Barriers
- Standard Normal MGF and Even Moments
- Sum-of-Three-Cards Market Making
Optiver options pricing questions (12)
- FX Put-Call Parity and Arbitrage
- Theta-Gamma Relationship and Delta-Hedged P&L
- Delta-Gamma-Vega Hedging With Two Options
- Pricing a Call on the Dice-Cancellation Sum
- Bayesian Coin Selection with Adverse Market Making
- Bayesian Market Making on a Biased Coin
- Down-and-Out Call: Pricing and Monte Carlo
- Delta of a Digital Call Option
- Dynamic Replication of Tournament Champion Contracts
- Vertical Call Spread Greeks Analysis
- Black-Scholes Monte Carlo Pricer
- Butterfly Spread Greeks and Smile Recentering
Optiver probability questions (11)
- Unknown Die with Uniform Sum
- Simpson's Paradox with Poisson Scoring
- Casino Edge Over 10,000 Plays
- Probability That 1 Was Selected Given Increasing Order
- Probability of Rolling a Sum of 4 Before a Sum of 2
- Probability the Last Die Roll Is Two When Summing Past 100
- No Common Numbers Between Two Independent Draws
- Probability All Dice Show the Same Value
- Sum of 8 Given At Least One Die Shows 3
- Bookmaker Mispricing and Static Arbitrage
- Card Color Pattern and Distinct Ranks
Optiver combinatorics questions (10)
- Twelve-Digit Numbers with Prime Digits and Product One Million
- Minimum Clues for a Unique Sudoku
- Counting Wins in Rock-Paper-Scissors
- Minimum Number of Drainers at a Concert
- Counting Zeros in 1 to 1000
- Guest List with Exclusion Constraint
- Largest Five-Digit Number With Distinct Pairwise Digit Sums
- Scheduling Appointments with a Constraint
- Smallest Integer with Digit Product 96
- Smallest Multiple of 66 At Least 600,000
Optiver game theory questions (8)
- Two-Pile Nim: Winning and Losing Positions
- Array Increment Game: Who Wins?
- Optimal Bet Sizing: Expected Value vs. Kelly Criterion
- Addition Game to N: First or Second Player Wins?
- Nim-Style Counting Game: Optimal Strategy and Losing Positions
- Alternating Addition Game to a Target
- Scoring Game on a Magic Square Grid
- Stone Pile Redistribution Game
Optiver coding questions (7)
- Solving the Sliding Puzzle with A* Search
- Stone Pile Doubling Game
- Streaming Maximum Drawdown With Rolling Window
- Currency Arbitrage Detection in Exchange Rate Graphs
- Longest Subarray With Sum in a Given Range
- Longest Subarray with Sum in a Given Range
- VWAP Aggregation and Interval Queries on Trade Data
Optiver stochastic processes questions (5)
Optiver statistics questions (5)
Optiver market microstructure questions (3)
Optiver brain teasers questions (2)
Optiver optimization questions (2)
Optiver time series questions (2)
Optiver regression questions (1)
Optiver machine learning questions (1)
Optiver interview FAQ
What kind of questions does Optiver ask in quant interviews?
Candidates most often report expected value, options pricing and probability questions. This page collects 93 of them, 16 stamped with the month they were last reported — each with a full worked solution.
How hard are Optiver interview questions?
The set spans 12 easy, 40 medium and 41 hard problems. Most sit at medium difficulty — solvable in a few minutes with clean reasoning — with a harder tail that rewards knowing the canonical tricks.
How do I prepare for the Optiver quant interview?
Work through this set by topic (use the sidebar), starting from your weakest area. 21 problems are free to open with their full solution, so you can judge the quality before anything else. Then walk the full Optiver interview guide for the round-by-round funnel and the online assessment.
Are these the actual Optiver interview questions?
They are built from candidate-reported Optiver questions. We rewrite each prompt for clarity and author the worked solutions ourselves — we don't claim the wording is verbatim, and we never invent questions or recycle generic lists. 16 of 93 carry the month they were last reported.