Quant interview preparation

Prop market making and quantitative research, weighted the way the interviews actually are: probability and expected value, statistics and machine learning, market making logic, programming and options. Every question is either traced to a named firm from a public candidate report, or tagged at desk level when we could not trace it, and every probability answer shows the reasoning path rather than just the number.

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100 questions, mapped to the firms that asked them

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100
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September 2026
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All firmsOld Mission Capital12Tower Research Capital10Jump Trading7Akuna Capital5Citadel4D.E. Shaw3Jane Street3AQR Capital Management2DRW2Millennium Management2Schonfeld2Squarepoint Capital2Susquehanna International Group2Belvedere Trading1Optiver1
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  1. 086Explain how you would price an option.Options and derivativesIntermediatetechnicalDRWQuantitative Trading · Chicago · 2025

    Say this

    The core idea is replication. If I can build a portfolio of the underlying and cash that matches the option's payoff in every state of the world, then no-arbitrage says the option must cost what that portfolio costs. Everything else, Black-Scholes included, is a way of computing that cost.

    Then walk it

    1. Start with one period and two states, because it makes the logic visible. Stock at 100 goes to 110 or 90, a call struck at 100 pays 10 or 0. Hold delta shares plus B in cash and solve two equations: delta is (10 minus 0) over (110 minus 90), which is 0.5, and then B falls out. The option price is 0.5 times 100 plus B. No probabilities were used anywhere.
    2. That is the key insight to state explicitly: the price does not depend on the real-world probability of the up move, only on the size of the moves. Rearranging gives the risk-neutral probability, which is the probability that makes the discounted stock a martingale, and pricing becomes a discounted expectation under that measure.
    3. Extend the tree to many steps and you get the binomial model, which handles American exercise naturally because you compare intrinsic against continuation at each node. Take the limit with the step size going to zero and you get Black-Scholes.
    4. Black-Scholes in words: the price is the discounted risk-neutral expectation of the payoff when the stock follows geometric Brownian motion with constant volatility. The formula's two N terms are the risk-neutral probability of finishing in the money and the delta-weighted version of it.
    5. Then the practical truth, which is the answer a trading firm actually wants: nobody uses Black-Scholes to find the price, because the price is on the screen. You use it as a translator from price to implied volatility, then you trade the volatility surface. Constant vol is false, the smile proves it, so the real work is interpolating and extrapolating the surface consistently and hedging the Greeks it implies.

    Where candidates lose it

    Reciting the Black-Scholes formula. Anyone can memorise it. The interviewer wants replication and no-arbitrage, and specifically wants to hear that the real-world probability drops out. Then close by saying the formula is used backwards, to extract implied vol from a market price. That last move is what marks a trader rather than a student.

    Expect next

    • Why does the real-world probability not appear in the price?
    • What are the assumptions, and which one fails hardest?
    • How would you price an American put?

    Reported by candidates at DRW (Quantitative Trading, Chicago, 2025). Source: Wall Street Oasis.

Firm tags come from public, anonymous candidate reports on Wall Street Oasis: strong signal, not sworn testimony. Firms are named as the places a question was reported, not as partners of Fin Maverick. Answers are written for this page to show how to think out loud; they are not scripts to recite.