Optiver interview questions

A first-round market-microstructure check for candidates new to electronic trading.

A stock is quoted at $49.98 bid and $50.02 offer. You want to buy 1,000 shares now. Explain the difference between sending a market order and a limit order at $50.00.

A first-round electronic-trading screen checks that a candidate can read a two-sided market precisely.

An ETF is quoted at $101.20 bid and $101.28 offer. What are the mid-price and bid-ask spread? If you buy 500 shares at the offer and immediately value them at the mid-price, what is your…

Fermi estimation is a standard prop trading round. You have sixty seconds.

How many tennis balls fit in a Boeing 747? You have one minute.

A prop-trading technical round checks whether you can construct a hedge from payoffs rather than memorise Greeks.

A stock is $100 today. Tomorrow it will be either $120 or $90. A call with a $100 strike pays $20 in the up state and $0 in the down state. How many shares hedge one short call in this one-period…

The interactive trading game used at every prop firm.

I have a bag with 10 balls, each numbered 1 to 10. I draw three and the contract settles on their sum. Make me a market. Then I show you that one of the balls drawn is a 10, what's your new market?

Options market making interviews probe what you do when you cannot hedge continuously.

You're short gamma into the close, with earnings after the bell. What are your options, and what do you do?

Electronic market making interviews test whether you understand the microstructure you'd trade in.

Why does latency matter to a market maker, and what is queue position worth?

Tests whether you reason about why a bet is being offered, not just its expected value.

I offer you a bet: I roll a fair die, and if it comes up 6 I pay you $10; otherwise you pay me $1. Do you take it? How much would you pay for the right to play 100 times?

The core mechanic of market making, tested with a live scenario.

You're making a market at 99 / 101 in a contract. You get hit on the bid three times in a row and are now long 300 lots. What do you do with your quote?

Trading firms use this to test whether you understand compounding and ruin.

You have an edge: a bet that pays 2:1 and wins 40% of the time. What fraction of your capital should you bet, and why not more?

A systematic-trading review after a research backtest appears to generate alpha around splits, special dividends and index changes.

A daily equity signal shows a sharp return improvement after a new corporate-action vendor feed is added. The gain is concentrated around special dividends, rights issues and spin-offs. How would you…

Asked to see whether you can explain a counterintuitive result clearly under pressure.

Three doors: one hides a car, two hide goats. You pick door 1. The host. Who knows what's behind each door. Opens door 3 revealing a goat, then offers you the chance to switch to door 2. Should you…

Tests recursive reasoning. A staple at trading firms.

You roll a fair six-sided die. You may either take the value shown in dollars, or re-roll. You get at most two rolls total. What is the expected value of the game if you play optimally? Then: what if…

Tests whether you can approximate rather than recall.

In a room of 23 people, what is the probability at least two share a birthday? Explain your reasoning and why the answer surprises people.

A classic Bayesian warm-up at quant trading firms.

You have two coins. One is fair; the other lands heads 75% of the time. You pick one at random and flip it 3 times, getting heads every time. What is the probability you picked the biased coin?

The signature exercise at proprietary trading firms.

Make me a market on the sum of the digits of a randomly chosen phone number in the room. Then I'll trade against you. Explain how you'd think through the whole exercise.

A recurring structure in quant interviews. Set up the recursion, don't simulate.

You start at position 0. Each step you move +1 with probability 0.5 and −1 with probability 0.5. What is the expected number of steps to first reach +3? Then: what changes if the walk is bounded below…

Volatility desks use this to test whether candidates understand what an option seller is actually betting on.

A dealer sells a one-month at-the-money straddle at 30% implied volatility and delta-hedges it daily. Realised volatility over the month is 20%, with no jump large enough to disrupt hedging. Did the…

Trading interviews use this to test whether you can construct an arbitrage on the spot.

State put-call parity. A stock trades at $100. The $100 strike call trades at $8, the put at $5, and the risk-free rate is 4% with 1 year to expiry, no dividends. Is there an arbitrage? If so,…

Standard for derivatives desks and quant trading interviews.

Name the inputs to the Black-Scholes model and the direction each moves a call option's price. Which input is not observable, and what does that imply?

Market-making interviews will push hard on gamma.

Define delta and gamma. You are short a straddle and delta-hedged. Explain what happens to your position as the underlying moves, and what you're actually long or short.

Volatility desks ask this after the skew question.

Implied volatility differs across expiries as well as strikes. What does an upward-sloping vol term structure mean, and what does it mean when it inverts?

Volatility desks ask this to see whether you understand the market, not the model.

Equity index options show higher implied volatility for downside strikes than upside. Explain why the skew exists and what it tells you about the market's assumptions.

Central to any market-making interview at a prop firm or bank.

You're making a market in a stock. What determines the width of your bid-ask spread? A large institutional client asks for a two-way price in size. How does that change your quote?