Quant interview preparation

Questions

100

Traced to a firm

53

Firms

15

Updated

September 2026

Asked at

All firmsOld Mission Capital12Tower Research Capital10Jump Trading7Akuna Capital5Citadel4DED.E. Shaw3Jane Street3ACAQR Capital Management2DRW2Millennium Management2Schonfeld2SCSquarepoint Capital2Susquehanna International Group2Belvedere Trading1Optiver1

Topic

All topicsProbability10Coins, cards and games6Expected value8Statistics11Market making15Estimation and mental maths4Stochastic processes4Regression5Machine learning6Time series6Programming10Options and derivatives8Fit and motivation7

Level

AnyCoreIntermediateHard

Type

AnyBrainteaserTechnicalCaseMarket viewFit

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.

2. 089What is put-call parity, and what would you do if you saw it violated?Options and derivativesIntermediatetechnicalProp trading firmsDerivatives

   Say this

   For European options on a non-dividend-paying stock, call minus put equals spot minus the discounted strike. It is pure arbitrage, no model, because a long call plus a short put plus the discounted strike in cash replicates the stock exactly. If it breaks, you trade both sides and lock a riskless profit.

   Then walk it

   1. The proof is a payoff table. At expiry, long call plus short put pays S minus K in every state, whether S is above or below K. Adding K in cash held to expiry gives you S. So the cost today of call minus put plus K discounted must equal S.
   2. With dividends, subtract the present value of dividends from the spot. With a cost of carry or borrow cost on the short, use the forward: C minus P equals the discounted difference between the forward and the strike.
   3. If I saw a violation, say the call is too expensive: sell the call, buy the put, buy the stock, and borrow the discounted strike. That is a conversion, and the reverse is a reversal. Lock the difference and hold to expiry.
   4. Then the reasons an apparent violation is usually not one, and this is what the question is really testing. Stale quotes on one leg. You are looking at mid prices but must trade at the bid and offer, and the parity gap is usually smaller than the combined spreads. Hard-to-borrow stock making the short leg expensive. American exercise, where early exercise of the put breaks the equality. Discrete dividends you have modelled wrong.
   5. So my actual answer: I would first check whether the apparent edge survives crossing four spreads and paying the borrow. Ninety-nine times out of a hundred it does not, and that is the point of the question. The hundredth time, borrow cost is usually the explanation, and the implied borrow rate you back out of the parity relationship is itself the useful information.

   Where candidates lose it

   Giving the formula and saying you would arbitrage it, with no mention of transaction costs, borrow or American exercise. A trading interviewer asks this specifically to see whether you treat a screen-level inefficiency as free money. Also know that parity holds for European options only, and be able to say why American puts break it.

   Expect next

   • Why does it not hold exactly for American options?
   • How would you back out the implied borrow rate from the option prices?
   • What does a persistent parity gap tell you about the stock?
3. 090What is the difference between implied and realised volatility, and what does the gap between them tell you?Options and derivativesIntermediatetechnicalDerivativesProp trading firms

   Say this

   Implied vol is the market's forward-looking price of volatility, backed out of option prices. Realised vol is a backward-looking statistic computed from returns. Implied sits above realised on average by a few points, and that gap is the variance risk premium, not a free lunch.

   Then walk it

   1. Implied comes from inverting a pricing model on a traded price, so it is a price expressed in volatility units. Realised is the annualised standard deviation of returns over a window, and how you compute it matters: close-to-close, high-low estimators like Parkinson or Garman-Klass, or sums of intraday squared returns.
   2. On the S&P, VIX has historically averaged around 19 to 20 against realised vol nearer 15 to 16. That three to four point gap is persistent and it is compensation to option sellers for taking gap risk and for providing crash insurance.
   3. So the gap does not mean options are overpriced. It means there is a premium for bearing the risk that variance spikes, and that risk is exactly the risk that hurts most when it materialises, since vol spikes coincide with equities falling.
   4. Where the gap becomes information: the term structure, which is normally upward sloping and inverts in a crisis, and the spread between implied and a good realised forecast. If implied is unusually high relative to a GARCH or HAR forecast, that is a candidate signal, but it has to clear the premium first.
   5. And the practical trap to name: implied vol from a monthly option is a forecast of realised vol over the next month, so comparing today's VIX to the last month's realised vol is comparing a forecast to the wrong period. Aligning the horizons correctly makes a lot of apparent signal disappear.

   Where candidates lose it

   Concluding that because implied exceeds realised you should always sell vol. That trade works for years and then loses everything in a week, and interviewers ask it to see whether you know the premium exists for a reason. Also mismatching horizons, which is the technical error that generates fake signals.

   Expect next

   • Why does the variance risk premium exist?
   • How would you actually forecast next month's realised vol?
   • What does an inverted vol term structure tell you?

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.