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. 069You quote a tight market and get lifted on your offer immediately. Are you happy?Market makingIntermediatetechnicalProp trading firmsQuant trading

   Say this

   No, not immediately. An instant fill is usually bad news: it means my offer was the cheapest thing available, which suggests my fair value was too low. I would shift my market up, not celebrate the spread I just earned.

   Then walk it

   1. The right frame is that a fill is information. If the market wanted my offer that fast, my offer was probably below consensus fair value.
   2. The fill I actually want is slow and two-sided: I buy on the bid, sell on the offer, and end the day roughly flat having collected the spread many times. Getting filled on one side only is a warning.
   3. So the immediate action is to move both quotes in the direction of the flow and reconsider the width. The mid moves up, and I may widen because I am now less sure where fair value is.
   4. How to measure whether it was actually bad: markout. Look at the mid a minute later. If the market is above where I sold, I was adversely selected regardless of the spread I booked. Booking the spread and losing on the markout is the classic way a market maker loses money while showing positive spread capture.
   5. The one case where I am genuinely happy is if I know the flow is uninformed, for instance a retail-sized order or a predictable end-of-day hedger. Then an instant fill is exactly the business. So the honest answer is: it depends who traded with me, and I would want to know that before I formed a view.

   Where candidates lose it

   Saying yes, I made the spread. That is the answer of somebody who thinks the spread is profit rather than gross revenue. Instant one-sided fills are the signature of adverse selection, and the interviewer is checking whether your instinct is to update or to congratulate yourself.

   Expect next

   • How would you check whether you were picked off?
   • What do you do with your quotes now?
   • When would an instant fill be good news?
2. 070Something goes badly wrong on your book during the session. How do you react?Market makingIntermediatetechnicalOld Mission CapitalProp Trading · Chicago · 2025

   Say this

   Reduce risk first, diagnose second, and tell someone immediately. In that order. The instinct to understand the problem before acting on it is the wrong instinct when the position is still live and the loss is still growing.

   Then walk it

   1. Step one, stop the bleeding. Pull quotes, flatten or hedge the exposure I did not intend to have, and cap any automated system that might still be adding to it. Getting smaller is almost never the wrong move under uncertainty.
   2. Step two, escalate. Tell the senior trader on the desk and the risk desk straight away, before I know the cause. Every trading floor's disaster stories are about someone who tried to fix it quietly first.
   3. Step three, establish the facts. What is my actual position, what is the realised and unrealised loss, is the pricing wrong or is the position wrong, and is anything still running that I have not stopped.
   4. Step four, only then diagnose and fix. A bad parameter, a stale feed, a hedge that did not go through, a fat finger, a genuine adverse move.
   5. And afterwards, write it up. A one-page post-mortem with a concrete control change is what stops the same failure twice. What a desk actually wants to hear from a junior candidate is that you act to reduce risk without needing permission, and escalate without needing to look competent first. Composure plus disclosure, in that order.

   Where candidates lose it

   Answering that you would investigate the cause first. On a live book that is exactly backwards, and a prop trading interviewer is listening for the reduce-then-escalate-then-diagnose sequence. Also do not claim you would stay completely calm. Say you would act on a checklist precisely because you would not be calm.

   Expect next

   • Who do you tell, and how quickly?
   • Tell me about a time you made a real mistake and what you did.
   • What would you put in the post-mortem?

   Reported by candidates at Old Mission Capital (Prop Trading, Chicago, 2025). Source: Wall Street Oasis.

3. 072Where does the money come from in market making versus a systematic hedge fund strategy?Market makingIntermediatetechnicalProp trading firmsQuant trading

   Say this

   A market maker gets paid a fee for providing immediacy and aims to be flat at the end of the day. A systematic fund takes a position because it forecasts a return and holds risk overnight. One sells a service, the other takes a view.

   Then walk it

   1. Market making: high turnover, tiny edge per trade, thousands of trades a day, Sharpe ratios that can be very high because the law of large numbers works for you, and capacity limited by volume rather than capital. Risk is inventory and adverse selection, measured in seconds to minutes.
   2. Systematic trading: lower turnover, larger edge per position, Sharpe typically 0.5 to 2, capacity limited by market impact, and risk measured in days to months. You are exposed to being simply wrong about the forecast.
   3. The counterparty differs, which is the deepest version of the answer. A market maker's profit comes from other participants' demand for immediate execution. A systematic fund's profit comes from other participants' mispricing, behavioural bias, or need to shed risk.
   4. Which tells you what kills each one. Market makers die from a fast informed move against a large inventory, or from technology failure. Systematic funds die from crowding, regime change, and leverage in a deleveraging.
   5. And it explains the career difference, which is usually the real reason the question is asked. Market making gives you feedback in minutes and rewards fast reaction under pressure. Research gives you feedback in months and rewards patience and statistical honesty. Saying which one suits you, with a reason, is what they are listening for.

   Where candidates lose it

   Treating them as the same job with different time horizons. The economic source of the profit is different, and saying it plainly, a fee for liquidity versus a return for taking a view, is what demonstrates real understanding. Then connect it to which seat you want, because that is where the question is going.

   Expect next

   • Which of those do you want to do and why?
   • Why can market makers run much higher Sharpe ratios?
   • What kills each business?
4. 075How has electronic market making changed over the last decade, and where do you think the edge is now?Market makingIntermediatetechnicalProp trading firmsQuant trading

   Say this

   Spreads have compressed to a tick or less in liquid products, the pure speed race has largely been won and commoditised by a handful of firms, and the remaining edge has moved to breadth of product, quality of the pricing model, and access to less-contested flow.

   Then walk it

   1. What changed: colocation and microwave or hollow-core fibre links turned latency into a fixed capital cost rather than an edge, exchange data got faster and cheaper, and the number of firms who can compete at the top tier is small.
   2. Where it went. First, breadth: applying the same infrastructure across equities, options, futures, crypto, ETFs and fixed income, since each new product is incremental revenue on a paid-for stack. Second, modelling: in options and ETFs the hard part is pricing thousands of related instruments consistently, which is a research problem, not a wire problem.
   3. Third, flow quality. Internalising or purchasing retail flow is valuable precisely because it is less informed. That is the economics behind payment for order flow, and it is the reason the regulatory debate about it matters commercially.
   4. The structural trend in fixed income and credit is worth naming: electronic market making has moved into products that were voice-traded a decade ago, and ETF creation and redemption is the mechanism that makes bond market making hedgeable at all.
   5. My honest view, offered as a view and not a fact: the marginal edge now sits in products where pricing is genuinely hard rather than where speed is hard, because speed has a ceiling that has been reached and modelling does not. And I would caveat that I am reading this from the outside, which is part of why I want to work somewhere that sees it from the inside.

   Where candidates lose it

   Reciting high-frequency trading is about speed as if it were still 2010. The interviewer works at one of these firms and will know instantly. Have a specific, current view, name the shift from latency to breadth and modelling, and flag that it is your view rather than asserting inside knowledge you do not have.

   Expect next

   • Is payment for order flow good or bad for the end investor?
   • Why is options market making harder than equities?
   • What do you think our firm's edge is?
5. 076You have K sorted arrays on disk, too large to load at once. How do you merge them into one sorted output?ProgrammingIntermediatetechnicalCitadelEquity Capital Markets · New York · 2026

   Say this

   K-way merge with a min heap of size K. Push the first element of each array into the heap, repeatedly pop the minimum and write it out, then push the next element from whichever array the minimum came from. Time is N log K, memory is O(K) plus your buffers.

   Then walk it

   1. The heap holds one candidate per array, each entry tagged with which array it came from and the index within it. Pop the smallest, emit it, and refill from that same array.
   2. Complexity: N total elements, each pushed and popped once, each operation log K. So N log K, which beats concatenate-and-sort at N log N whenever K is much smaller than N.
   3. The disk part is the real content of the question. You do not read element by element, you read blocks. Keep a buffer per array, say a few megabytes each, refill it when it drains, and write the output through a large buffer too. The heap operations are free compared with I/O, so the design goal is sequential reads and few of them.
   4. If K is very large, K times the buffer size exceeds memory, and then you merge in passes: merge groups of, say, 100 files at a time, then merge the results. That is exactly how external merge sort works, and total I/O is N times the number of passes.
   5. Practical notes I would raise: use a tournament tree or a loser tree instead of a binary heap if you want fewer comparisons per element, handle the tie-breaking rule explicitly if stability matters, and if this is a real system, check whether the operating system's readahead is already doing your buffering for you before you build it yourself.

   Where candidates lose it

   Answering merge them pairwise, which is K times N in the worst case, or ignoring the on-disk part entirely. The interviewer put the data on disk deliberately, so talk about block-sized buffered reads and what happens when K is too large to buffer. State the N log K complexity explicitly.

   Expect next

   • What if K is a million?
   • How large would you make the buffers, and why?
   • How would you parallelise it?

   Reported by candidates at Citadel (Equity Capital Markets, New York, 2026). Source: Wall Street Oasis.

6. 077Given an array and a window of size k, return the maximum in each window as it slides.ProgrammingIntermediatetechnicalAkuna CapitalQuant Development · Chicago · 2025

   Say this

   Monotonic deque, O(n) total. Keep a deque of indices whose values are strictly decreasing. Before pushing a new index, pop from the back everything smaller than the new value, and pop from the front anything that has fallen out of the window. The front is always the maximum.

   Then walk it

   1. Why the deque is monotonic: if a new element is larger than something behind it, that older smaller element can never be the maximum of any future window, because the new one is both larger and more recent. So it is safe to discard permanently.
   2. Each index is pushed once and popped once, so the total work is O(n) even though a single step can pop many elements. That amortised argument is the thing to say out loud, because it is what distinguishes this from the naive O(n k).
   3. Store indices, not values, so you can test whether the front has expired by comparing front index against i minus k plus 1.
   4. Alternatives and why they are worse: a max heap gives O(n log k) and needs lazy deletion of expired entries. A balanced BST or a multiset gives O(n log k) too. Both are fine and both are beaten by the deque.
   5. Where this actually matters on a trading system, which is worth mentioning: rolling extremes over a tick window, running high and low for a breakout signal, and rolling maximum drawdown. The same structure with the comparison reversed gives you the rolling minimum, and the O(1) amortised cost per tick is what makes it usable in a hot path.

   Where candidates lose it

   Reaching for a heap and stopping there. The heap answer is acceptable but it is not the answer to this question, and the interviewer is specifically looking for the monotonic deque and the amortised O(n) argument. Also remember to expire the front by index, which is the bug that shows up most often in live coding.

   Expect next

   • Prove the amortised complexity.
   • Now give me the rolling median instead.
   • How would you handle a window defined by time rather than by count?

   Reported by candidates at Akuna Capital (Quant Development, Chicago, 2025). Source: Wall Street Oasis.

7. 079How would you store key-value pairs, and what are the tradeoffs between the implementations?ProgrammingIntermediatetechnicalJump TradingEngineering · Cambridge · 2019

   Say this

   Hash table for O(1) average lookup with no ordering, balanced tree for O(log n) with ordered iteration and range queries, and a flat sorted array if the data is static and you care about cache behaviour. The choice is driven by whether you need ordering and what your access pattern looks like in memory.

   Then walk it

   1. Hash table: O(1) average, O(n) worst case on collisions, no ordering, and rehashing causes an occasional large latency spike. That spike is a real problem on a trading hot path and it is why people pre-size their maps.
   2. Balanced tree, red-black or B-tree: O(log n) guaranteed, ordered traversal, range queries, and predictable latency. Worse constants and worse cache locality because of pointer chasing.
   3. The tradeoff that matters most in practice is memory layout, not big-O. C++ unordered_map uses separate chaining with nodes scattered across the heap, so every lookup is potentially a cache miss. An open-addressing flat hash map keeps everything in one array and is commonly two to three times faster in real workloads at the same asymptotic complexity.
   4. For a mostly-static table, a sorted array with binary search beats both: contiguous memory, no pointers, and for small n a linear scan beats binary search because it is branch-predictable and prefetchable. Under about 16 to 32 entries, linear wins.
   5. And on disk the answer changes completely: B-trees for read-heavy workloads because of the branching factor against block size, LSM trees for write-heavy because they turn random writes into sequential ones. I would want to know the read-write ratio and whether the working set fits in cache before choosing anything.

   Where candidates lose it

   Answering hash map, O(1), done. The question says tradeoffs, so it is a systems question and the interviewer at a trading firm cares about tail latency and cache behaviour more than asymptotic complexity. Mention rehashing spikes and pointer chasing, and ask what the access pattern is.

   Expect next

   • Why is std::unordered_map often slow in practice?
   • How would you avoid latency spikes from rehashing?
   • What changes if the data lives on disk?

   Reported by candidates at Jump Trading (Engineering, Cambridge, 2019). Source: Wall Street Oasis.

8. 083Write an algorithm to find all the primes from one to n, and then optimise it.ProgrammingIntermediatetechnicalACAQR Capital ManagementResearch · Greenwich · 2015

   Say this

   Sieve of Eratosthenes. Mark every multiple of each prime as composite, and the unmarked survivors are the primes. Time is n log log n, which is essentially linear, and memory is n bits.

   Then walk it

   1. The baseline to reject first: trial division on each number up to its square root is about n times root n over log n, far worse. Say why the sieve wins before you write it.
   2. The sieve itself: start at p equal to 2, mark 4, 6, 8 and so on, then advance to the next unmarked number. Two optimisations that come free: start marking at p squared rather than 2p, because smaller multiples are already marked, and stop the outer loop at root n.
   3. Memory optimisations: store only odd numbers, halving memory, use a bit array rather than bytes for an eightfold saving, and if n is large, sieve in cache-sized blocks. That last one matters more than anything else in practice, because a naive sieve over 10 to the 9 is dominated by cache misses, and segmenting it can be several times faster at identical complexity.
   4. Further refinements if pushed: a wheel sieve skipping multiples of 2, 3 and 5 removes about 77 percent of the candidates, and the sieve of Atkin is asymptotically better at n over log log n but is slower in practice and much harder to get right.
   5. And the answer to a different question they may be asking: if you want to test whether one large number is prime rather than enumerate a range, the sieve is the wrong tool entirely and you want Miller-Rabin, which is probabilistic and fast. Recognising that enumerate and test are different problems is worth saying.

   Where candidates lose it

   Giving trial division and calling it done, or giving the sieve with no optimisation when the question explicitly asks for one. The optimisations they want in order are: start at p squared, skip evens, use a bit array, then segment for cache. Naming cache blocking is what marks you out, because it is the one that matters at scale and it is not in the textbook answer.

   Expect next

   • What is the memory cost for n equal to a billion, and how would you reduce it?
   • How would you parallelise the sieve?
   • Now test whether one very large number is prime.

   Reported by candidates at AQR Capital Management (Research, Greenwich, 2015). Source: Wall Street Oasis.

9. 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.

10. 087You think the market is overestimating volatility. What options strategy would you use?Options and derivativesIntermediatetechnicalOld Mission CapitalProp Trading · Chicago · 2025

    Say this

    Sell volatility and hedge the direction out. The cleanest expression is a short straddle or strangle, delta-hedged so the position is a bet on volatility rather than on the underlying. If implied vol is above what I think realised vol will be, I collect the difference through the gamma-hedging P&L.

    Then walk it

    1. The mechanism: a delta-hedged short option position makes money when realised volatility comes in below the implied vol you sold. Your P&L is approximately half of gamma times the difference between implied variance and realised variance, integrated over the life of the trade.
    2. The instrument choice. A short straddle at the money has the most vega and gamma per unit of premium, so it is the purest vol expression. A short strangle has less gamma but a wider profitable range and less immediate pin risk. If I wanted a cleaner exposure with no path dependence I would sell a variance swap, where the payoff is literally implied minus realised variance.
    3. Risk management is the whole trade. Short gamma means every hedge is at a worse price than the last, so a gap move is where the loss lives. I would cap it with a long wing, turning the strangle into an iron condor, which sacrifices some premium to remove the unbounded tail.
    4. Sizing from the tail: I would set the position so the worst plausible gap, say a five percent overnight move, is a loss I can carry, not from the expected daily P&L. Short vol positions have positive expected value most days and lose several months of it in one session.
    5. And the honest caveat: implied vol trading above realised vol is the normal state of the world, not a mispricing. The variance risk premium exists because sellers are being paid to warehouse gap risk. So I need to believe implied is rich relative to that premium, not merely rich relative to realised, otherwise I am just collecting a risk premium and calling it alpha.

    Where candidates lose it

    Answering short straddle and stopping. Two things must follow: that you delta hedge to isolate the vol view, and that short gamma means a fat left tail so you cap or size for it. Also the variance risk premium point, because saying implied is above realised therefore sell it is the reasoning that ends careers.

    Expect next

    • How do you make it a pure volatility trade?
    • What happens if the stock gaps ten percent overnight?
    • Why is implied usually above realised in the first place?

    Reported by candidates at Old Mission Capital (Prop 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.