Guide · Optiver
Optiver interview questions and how to prepare
29 problems · 7 min read · updated 2026-09-07
Optiver’s process is the most explicitly timed of the major market makers. It opens with an arithmetic test — dozens of questions in a handful of minutes — and everything after it keeps that tempo: dice expectations you should know cold, markets you must quote in seconds, options questions where the interviewer wants the sign of a Greek before the formula.
This guide is organised around that tempo. Speed sections first, then the market-making and options rounds where the interview is actually won.
Mental math and speed
The arithmetic screen is pass/fail and most candidates who fail Optiver fail here. Beyond raw arithmetic, the questions below are the ones a trader is expected to answer without paper: quick approximations, small expectations, and one-line probabilities.
Using the Taylor expansion , approximate . (Round to 3 decimals.)
Answer: 0.995 · Worked solution →
Three ants sit on the three corners of a triangle. Each independently picks one of the two edges and starts walking. What is the probability that none collide?
Answer: 1/4 · Worked solution →
Two fair six-sided dice are rolled. What is the probability their sum equals 7?
Answer: 1/6 · Worked solution →
You roll a fair die 4 times. What is the probability of getting at least one 6? (Round to 3 decimals.)
Answer: 0.518 · Worked solution →
What is the expected number of rolls of a fair die to get the first 6?
Answer: 6 · Worked solution →
What is the expected number of flips of a fair coin until the first head appears?
Answer: 2 · Worked solution →
Expected value and dice
Optiver loves dice because they make expected value concrete and fast. Expected max and min of two dice, Galileo’s three dice, the broken stick — know these cold, and know how to re-derive them when the die is loaded.
Two fair six-sided dice are rolled. What is the expected value of the larger of the two (ties count as that value)?
Answer: 4.472 · Worked solution →
Two fair dice are rolled. What is the expected value of the smaller of the two (ties count as that value)?
Answer: 91/36 · Worked solution →
Three fair dice are rolled. Gamblers noticed sums of 10 appear more often than sums of 9, though both can be written as 6 unordered combinations. What is the probability of rolling a sum of exactly 10?
Answer: 0.125 · Worked solution →
A stick of length 1 is broken at a point chosen uniformly at random. What is the expected length of the shorter piece?
Answer: 0.25 · Worked solution →
A standard 52-card deck is shuffled. What is the probability the top two cards are both aces? (Enter as a fraction or decimal.)
Answer: 1/221 · Worked solution →
Market making
Quote a fair value, quote a spread, get traded against, manage the inventory you end up with. Fermi questions appear here too — Optiver uses estimation markets ("make me a market on the number of piano tuners in Chicago") to test the same quoting reflex on a number nobody knows.
An interviewer asks you to make a market on the sum of two fair six-sided dice. Before you quote a bid and an ask, you need the fair value. What is it?
Answer: 7 · Worked solution →
A die is loaded so that it shows 6 with probability 1/2; the other five faces are equally likely. You must quote a fair value for one roll. What is it?
Answer: 4.5 · Worked solution →
A betting market quotes decimal odds of 4.0 on an outcome (total payout per $1 staked). Ignoring any bookmaker margin, what probability of the outcome does this quote imply, in percent?
Answer: 25 · Worked solution →
You are a market maker and have accumulated a long position of 5,000 shares that you want to reduce. Fair value is unchanged. Relative to your previous quotes, in which direction do you move your bid and ask — up or down?
Estimate: how many piano tuners work in Chicago? There is no “right” number — the interviewer is grading the structure of your estimate, the reasonableness of each input, and whether the final answer is the right order of magnitude.
Everyone in a large group simultaneously picks a number from 0 to 100. The winner is whoever is closest to two-thirds of the group average. If every player is perfectly rational and knows everyone else is too, what number does game theory say everyone picks?
Answer: 0 · Worked solution →
Options intuition
Optiver is an options market maker and the interview shows it. Signs and limits of the Greeks, delta of a forward, why gamma explodes near expiry, what a straddle’s delta is — intuition first, Black-Scholes second.
Roughly what is the delta of an at-the-money European call on a non-dividend stock with short time to expiry?
Answer: 0.5 · Worked solution →
What is the delta of a forward contract on a non-dividend-paying stock (with respect to the spot)?
Answer: 1 · Worked solution →
As an at-the-money option approaches expiry, what happens to its gamma — and why?
For a long vanilla option with no carry, is theta (sensitivity to the passage of time) typically positive or negative, and why?
Is the vega of a long vanilla option positive or negative, and at what moneyness is it largest?
You are short 100 call options, each with delta 0.4 (each option on 1 share). How many shares do you buy or sell to be delta-neutral?
Answer: 40 · Worked solution →
You buy an at-the-money straddle (one call and one put, same strike and expiry) on a non-dividend stock. Roughly what is the net delta of the position?
Answer: 0 · Worked solution →
A box spread is built from European options with strikes 90 and 110 expiring in 1 year. With a continuously-compounded risk-free rate of 5%, what is its arbitrage-free value today (in dollars)?
Answer: 19.02 · Worked solution →
How to approach these in the interview
Drill the arithmetic screen separately. Ten minutes a day of timed mental arithmetic for two weeks moves most candidates from failing to passing. Nothing else on this page matters if you do not clear it.
Answer with the sign first. For any Greek or sensitivity, say the direction, then the magnitude, then the formula if asked. Optiver interviewers are traders; they think in signs.
Treat estimation as a market. For Fermi questions, give a range and a midpoint, and update if the interviewer offers a trade. They are testing quoting behaviour, not trivia.
Use the Trader track. It orders the dice, market-making and options problems on this page in the sequence Optiver rounds tend to follow.
Frequently asked
What is on the Optiver math test?
Fast mental arithmetic — addition, subtraction, multiplication, division, fractions and decimals — under a tight clock. Candidates commonly report on the order of 80 questions in 8 minutes with a penalty for wrong answers, though the exact format varies by year and office, so accuracy and knowing when to skip both matter. It is a screen: pass it to reach the interviews.
Does Optiver ask about options in the trader interview?
Yes, and more than most competitors, because it is an options market maker. Expect questions on the sign and behaviour of delta, gamma, theta and vega, delta hedging, and simple spread valuations, with an emphasis on intuition over formulas.
How is Optiver different from Jane Street and SIG?
Optiver is the fastest and most arithmetic-heavy; SIG leans on poker-style decision questions; Jane Street goes deeper on fewer questions with follow-ups. All three share the market-making round.
How much probability does Optiver require?
Undergraduate probability done fast: expected value, conditioning, the standard dice and coin results. Depth of theory matters less than being able to produce a number in seconds and defend it.
Practise these with answer checking and spaced review
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