Quant interview preparation

Questions

100

Traced to a firm

53

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15

Updated

September 2026

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

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

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1. 092What are the assumptions behind Black-Scholes, and which one fails hardest?Options and derivativesHardtechnicalDerivativesProp trading firms

   Say this

   Constant known volatility, geometric Brownian motion with no jumps, continuous frictionless hedging, constant rates, no dividends and European exercise. The one that fails hardest is constant volatility, and the proof that it fails is the volatility smile.

   Then walk it

   1. If the model were right, every strike and expiry on the same underlying would have the same implied vol. They do not. Equity index options show a pronounced skew, with out-of-the-money puts trading at much higher implied vol than calls, and the smile steepens for shorter expiries.
   2. Two economic reasons for the skew: returns are negatively skewed with crash risk, which a lognormal cannot represent, and there is genuine demand for downside protection that pushes puts rich. Both are real and they reinforce each other.
   3. No jumps is the second failure, and it is the same failure in a different form. Under continuous paths a delta hedge is riskless in the limit; with jumps it is not, and that unhedgeable jump risk is precisely what the skew prices.
   4. Continuous costless hedging fails too, which matters practically. You hedge discretely and pay the spread, so your realised hedging error has a variance proportional to the hedge interval, and a short-gamma book pays that cost repeatedly.
   5. But here is the thing worth saying: the model is still used everywhere despite being false, because it is a lossless translator between price and implied vol. Traders quote in vol, not in price, and Black-Scholes is the shared language. The correct summary is that it is a wrong model used as a coordinate system, with local vol, stochastic vol models like Heston, and jump models layered on top for anything path-dependent.

   Where candidates lose it

   Listing the assumptions without naming the smile as the empirical refutation. That link is the whole point. And do not conclude the model is useless, because that misses why every desk still quotes in Black-Scholes implied vol. Wrong but indispensable as a change of variables is the answer.

   Expect next

   • If you know the model is wrong, why still use it?
   • What is local volatility, and what does it fix?
   • How would you price a barrier option given a smile?
2. 093You are long a delta-hedged call. Where does your profit and loss actually come from?Options and derivativesHardsuperdayProp trading firmsDerivatives

   Say this

   From the difference between realised and implied volatility. You earn gamma by rehedging, buying the underlying when it falls and selling when it rises, and you pay theta for the privilege. If realised vol beats the implied vol you paid, the gamma earnings exceed the theta bill.

   Then walk it

   1. The mechanics of gamma scalping: long a call means delta rises as spot rises. To stay hedged you sell into rallies and buy into dips, which is systematically buying low and selling high. Each round trip banks money proportional to the square of the move.
   2. The algebra: daily P&L is approximately half gamma times (change in S) squared minus theta times the time step. Substituting the Black-Scholes relationship between gamma and theta gives P&L proportional to half gamma S squared times (realised variance minus implied variance) times dt.
   3. So the position is a bet on variance, not on direction, and it settles continuously rather than at expiry. Put a number on it: a one percent daily move against a 20 percent annual implied vol, which implies about 1.26 percent daily, means you lose on that day because the move was smaller than what you paid for.
   4. Real-world frictions that eat the theory: you hedge discretely, so you capture only part of the gamma and the hedging error has variance proportional to the hedge interval. You pay the spread on every rehedge, so hedging too often costs more than the gamma it captures. There is an optimal hedge frequency that trades hedging error against transaction cost, and it scales with gamma and the spread.
   5. And the residual you cannot get rid of: vega. If implied vol falls while realised vol is fine, you lose on the mark even if your gamma P&L is positive. A long-dated option is mostly a vega position where the gamma story barely matters, which is why the expiry you choose determines which of these two effects dominates.

   Where candidates lose it

   Saying you profit if the stock goes up. You are delta hedged, so direction is neutralised by construction. The answer must be realised versus implied volatility, with gamma earned against theta paid. Then volunteer the discrete hedging cost, because in practice it is what determines whether a theoretically profitable long gamma position makes money.

   Expect next

   • How often would you rehedge, and what determines the optimal frequency?
   • What if implied vol collapses but realised vol is high?
   • How does this change for a one-week option versus a one-year option?

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.