Derivatives Foundation interview preparation

Questions

100

Traced to a firm

29

Firms

19

Updated

September 2026

Asked at

All firmsMSMorgan Stanley4Nomura4Akuna Capital2Amundi2HSBC2PIMCO2Bank of America1Barclays1Citadel1DRW1Goldman Sachs1Jane Street1Millennium Management1Mizuho1Old Mission Capital1RCRBC Capital Markets1Scotiabank1UBS1Wells Fargo Securities1

Topic

All topicsForwards and futures10Options basics8Option pricing7The Greeks10Volatility7Option strategies9Swaps and rates7Credit derivatives4Market structure and clearing6Indian derivatives8Trading and markets9Brainteasers6Fit9

Level

AnyCoreIntermediateHard

Type

AnyTechnicalCaseMarket viewBrainteaserFit

1. 017An option buyer has limited loss and unlimited gain. Why does anyone take the other side?Options basicsIntermediatetechnicalProp trading firmsMarket making

   Say this

   Because the seller gets paid, and on average the premium is more than the payout. Buyers are buying insurance and insurers earn a premium for bearing tail risk. The payoff shape is asymmetric but the expected value is not the same as the shape.

   Then walk it

   1. The empirical fact first: implied volatility exceeds subsequent realised volatility most of the time, in most markets. That wedge — the variance risk premium — is the seller's edge, and it is typically a couple of volatility points on index options.
   2. Why it exists: investors are structurally short the market and want protection, and protection pays off precisely when the rest of the portfolio is losing. That correlation makes it worth paying above fair value for, exactly like fire insurance.
   3. So the seller is not stupid, they are an insurer. The trade works the way insurance works: small steady income, occasional large loss, positive expectancy if priced right and sized right.
   4. The real risk is not the expectancy, it is the path. A short option book has negative skew, so it grinds up and then gives back years of premium in a week. February 2018 wiped out short-vol products in a single session on a move that was not even a large one by historical standards.
   5. Which is why sellers hedge. A market maker is not taking a directional view; they sell the option, delta hedge it, and try to earn the spread between implied and realised volatility. The naked seller and the hedged seller are completely different businesses.
   6. The honest framing: buyers pay for convexity and certainty of maximum loss, sellers earn a premium for supplying it. Neither is a free lunch, and the seller's version has a fatter left tail than a Sharpe ratio will show you.

   Where candidates lose it

   Answering 'because most options expire worthless'. That is a statistic about frequency, not about expected value, and an interviewer will immediately ask whether you would sell 1-in-1000 lottery tickets at any price. Name the variance risk premium and the negative skew of the seller's return.

   Expect next

   • So would you rather be systematically long or short volatility?
   • What happened to short-volatility products in February 2018?
   • How does a market maker sell options without taking a directional view?
2. 020Price a one-period call with a binomial tree. Stock at 100, up to 120 or down to 80, strike 100, rate zero.Option pricingIntermediatetechnicalProp trading firmsQuant trading

   Say this

   Ten. The risk-neutral up probability is 0.5 because the up and down moves are symmetric around 100 with a zero rate, so the option is worth 0.5 times 20 plus 0.5 times 0, undiscounted. And I can prove it with a hedge rather than a probability.

   Then walk it

   1. Risk-neutral probability: p equals one plus r minus d over u minus d. With u of 1.2, d of 0.8 and r of zero, p is 0.2 over 0.4, so 0.5. Payoffs are 20 up and 0 down, so the value is 10.
   2. Now the replication, which is the answer they actually want. Delta is the payoff spread over the price spread: 20 minus 0 over 120 minus 80, so 0.5. Hold half a share, which costs 50, and borrow 40. In the up state the half share is worth 60, repay 40, net 20. In the down state 40 minus 40 is zero. Both match, and the portfolio cost 10.
   3. So the hedge ratio and the price come out of the same arithmetic, and the 0.5 that appears twice is a coincidence of the symmetric tree — one is a delta, the other a probability.
   4. Note that p is not a forecast. If I told you the stock has a 90 percent chance of going up, the option is still 10, because I can hedge it. The real probability affects whether you want the trade, not what it costs.
   5. Add a rate and both pieces move: p shifts up because the risk-neutral drift is higher, and you discount the expectation. With r at 5 percent p becomes 0.625 and the value rises to about 11.9.
   6. The limitation worth saying: a one-period tree is a cartoon. It only works because two states and two instruments make the market complete. Add a third state and I can no longer hedge exactly, and the price becomes a range rather than a number — which is the real world with jumps in it.

   Where candidates lose it

   Using the real-world probability, or averaging 120 and 80 to get an expected stock price and working from there. Also, do the replication: the interviewer wants to see you derive delta as the ratio of payoff spread to price spread, not quote a formula.

   Expect next

   • Redo it with the rate at 5 percent.
   • What if I tell you the real probability of the up move is 90 percent?
   • Now make it two periods and tell me what changes about the hedge.
3. 031You have sold a call and you are delta hedging it. Walk me through what you actually do over the option's life.The GreeksIntermediatetechnicalMarket makingEquity derivatives

   Say this

   You buy delta shares against the short call and rebalance as spot moves. Because you are short gamma, every rebalance means buying higher and selling lower, so you lose money on the hedge and you are paid theta to compensate. Over the life, your profit is the premium you collected less what the hedging actually cost you.

   Then walk it

   1. Day one: sell the 100-strike call at, say, 4.00 with a 0.5 delta, so buy 50 shares per contract. You are locally flat.
   2. Stock rises to 105. Delta is now 0.65, so you buy 15 more shares at 105. Stock falls back to 100, delta is 0.5, so you sell 15 shares at 100. You have just bought at 105 and sold at 100. That loss is what being short gamma means, and it is unavoidable.
   3. Do that repeatedly and the total hedging loss is roughly proportional to the realised variance of the stock. You keep money only if the stock realises less volatility than the 20-ish implied you sold at.
   4. So the profit and loss decomposition is clean: premium received, minus the realised variance cost, plus or minus the error from hedging discretely rather than continuously, minus bid-offer and financing on the share position.
   5. How often to rebalance is a real decision, not a technicality. Hedge too often and transaction costs eat you; too rarely and you run naked gamma between hedges. Desks usually hedge on a delta band — rebalance when delta moves more than some threshold — rather than on a clock.
   6. The failure mode to state: a gap. If the stock jumps from 100 to 130 overnight on a takeover, no rebalancing schedule saves you, because you were hedged for the 0.65 delta and you needed 1.0. Delta hedging manages diffusion risk, not jump risk, and that is exactly the assumption Black-Scholes makes and reality does not.

   Where candidates lose it

   Describing the mechanics without ever stating that the hedge loses money. Short gamma means the rebalancing is systematically adverse, and the theta you collect is the payment for it. If your answer does not contain 'buy high, sell low', you have not understood the trade.

   Expect next

   • How often would you rebalance, and what decides it?
   • Decompose your final profit and loss into its pieces.
   • The stock gaps 30 percent overnight. What happens to you?
4. 035You have just taken over a derivatives book from someone who left suddenly. What do you look at, in what order?The GreeksIntermediatesuperdayEquity derivativesRisk management

   Say this

   Directional exposure first, then convexity, then the things that cannot be hedged. Concretely: net delta, then gamma and where it is concentrated by strike and expiry, then vega bucketed by maturity, then the operational calendar — expiries, ex-dividend dates, barriers and any physically settled contract.

   Then walk it

   1. Net delta first, because it is the biggest and the easiest to neutralise. I want to be able to say in one number how much I make or lose on a 1 percent market move, and I would hedge any large residual with futures within the hour.
   2. Then gamma, and not just the total — where it sits. A book that is gamma-flat overall but long gamma at 24,000 and short at 25,000 is a different animal from a genuinely flat one, and the strike concentration tells you where the pain is.
   3. Then vega by expiry bucket. A summed vega number hides term structure risk. I want front month, second month, and beyond separately, because they do not move together.
   4. Then the calendar risks, which is where inherited books actually blow up: what expires this week, what has a barrier near spot, which names go ex-dividend, and whether anything settles physically rather than in cash.
   5. Then the stress grid. Profit and loss under spot down 10 and volatility up 10, spot down 20 and volatility up 25, and a single-name gap. Greeks are local; the grid is what tells me if there is a hole.
   6. And the unglamorous parts, said out loud because they are what catch people: does the position in the risk system reconcile with the clearing house, is there any trade with a manual mark, and what are the margin requirements if the market moves against me. I would rather find an unreconciled position on day one than on the day it matters.

   Where candidates lose it

   Listing all the Greeks in textbook order with no prioritisation. The question is about triage under uncertainty. Lead with 'hedge the delta first because it is the biggest and cheapest to fix', and include the operational checks — reconciliation and the expiry calendar — which is what someone who has actually held a book says.

   Expect next

   • What would you hedge in the first hour, and what would you leave?
   • Why does bucketing vega by expiry matter?
   • What operational risk would worry you most on a book you have not seen before?
5. 044A client holds a large concentrated equity position and wants protection but hates paying premium. What do you show them?Option strategiesIntermediatetechnicalWealth managementEquity derivatives

   Say this

   A zero-cost collar: buy a put, fund it by selling a call, struck so the premiums net to zero. It gives them a floor without a cash outlay, and the price is giving up the upside above the call strike. If they will not accept an upside cap, the honest answer is that protection costs money and there is no way around it.

   Then walk it

   1. Structure it concretely: stock at 100, buy the 90 put, sell the 112 call, and the two premiums roughly offset. They are now locked into a band between 90 and 112 with no premium paid.
   2. The asymmetry in the strikes is the skew at work. Puts are more expensive than equidistant calls, so to fund a 10 percent-out put you have to sell a call closer than 10 percent out. Explaining that asymmetry to the client is part of the job.
   3. Alternatives worth showing: a put spread, which is cheaper than an outright put and still leaves upside open but only protects a band; or a longer-dated put, which costs more in absolute terms but far less per month of protection because vega scales with root time.
   4. For a genuinely concentrated founder position, there are also prepaid variable forwards and exchange funds, which address the concentration rather than just the price risk. Those have tax and lock-up consequences that usually dominate the pricing question.
   5. Constraints to raise before the structure: is the client an insider, does the position have a lock-up or pledge, and what does the collar do to their tax position. In several jurisdictions a tight collar can be treated as a constructive sale, which triggers the tax event they were trying to defer. That is the reason the call strike is often set wider than the pricing alone would suggest.
   6. And the behavioural risk: a collar that caps upside at 112 will feel like a mistake if the stock goes to 160, and the client will remember whose idea it was. So I would document the trade-off in their own words, and size the collar over part of the position rather than all of it.

   Where candidates lose it

   Presenting the zero-cost collar as free. It is not free, it is paid for with the upside, and the skew means the upside you give up is closer than the downside you protect. Also raise the tax and constructive-sale issue — that is the difference between a textbook answer and advice.

   Expect next

   • Why is the call strike closer than the put strike?
   • What are the tax consequences of a tight collar?
   • What would you do instead if the client refuses any upside cap?
6. 046If you think the market is overestimating volatility, what options strategy can you use?Option strategiesIntermediatetechnicalOld Mission CapitalProp Trading · Chicago · 2025

   Say this

   Sell a delta-hedged straddle, or sell a variance swap if one is available. The view is that implied volatility is above what will be realised, so you want to be short implied and long nothing directional — which means selling options and hedging the delta as you go, not just selling a strangle and hoping.

   Then walk it

   1. Cleanest expression: short at-the-money straddle, delta hedged continuously. You collect the premium and pay away the realised variance, so if realised comes in below the implied you sold, the difference is your profit.
   2. Even cleaner if the market exists: short a variance swap. The payoff is exactly the strike variance minus realised, with no re-striking and no path dependence in the exposure.
   3. If the view is specifically that implied volatility itself will fall rather than that realised will be low, sell longer-dated options where vega dominates, or sell VIX futures or calls. Those are different trades — one is a realised-volatility view, the other a mark-to-market view on the surface.
   4. Then the risk management, which is really what the question is testing. Naked short volatility has unbounded loss and negative convexity, so the professional version is an iron condor or a short straddle with wings bought — you cap the tail, give up some premium, and survive the event that proves you wrong.
   5. Sizing rule I would say out loud: size to the loss in a plausible tail, not to the premium collected. If a 5 standard deviation move ends the account, the position is too big whatever the expected value says.
   6. And the honest caveat: implied above realised is the normal state, so being short volatility is a bet that the premium is bigger than usual, not that it exists. You need a reason — a specific event that has passed, a supply imbalance, a spike that has already resolved — rather than a general sense that options are expensive.

   Where candidates lose it

   Answering 'sell a straddle' and stopping. A prop shop is testing whether you delta hedge, whether you cap the tail, and whether you can distinguish a realised-volatility view from a view on implied. Volunteer the sizing rule before they ask what happens in a crash.

   Expect next

   • How do you cap the tail, and what does it cost you?
   • Is your view about realised volatility or about implied volatility falling?
   • How would you size it?

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

7. 056Given a portfolio of three bonds, explain how the portfolio changes if duration increases.Swaps and ratesIntermediatetechnicalPIMCOGeneralist · Los Angeles · 2026

   Say this

   Portfolio duration is the market-value-weighted average of the individual durations, so if it increases you have become more exposed to rates — you gain more when yields fall and lose more when they rise. The question is which lever moved it: the weights, a change in the bonds themselves, or a shift in yields.

   Then walk it

   1. Start with the arithmetic. Say a 2-year at 30 percent weight with duration 1.9, a 10-year at 40 percent with duration 8.2, and a 30-year at 30 percent with duration 19. Portfolio duration is 0.57 plus 3.28 plus 5.7, about 9.6 years.
   2. Shift 10 percent from the 2-year into the 30-year and duration goes to about 11.3. So the sensitivity per 100 basis points has gone from 9.6 percent of value to 11.3 — you have added roughly 1.7 percent of NAV per 100 basis point move.
   3. Duration can also rise without you trading. Yields falling raises duration mechanically, and the long bond's weight in the portfolio grows because it rallied most. So a bull market in bonds lengthens your duration passively, which is a real drift risk in an unmanaged book.
   4. The long bond dominates. It is 30 percent of the money and nearly 60 percent of the risk, and that concentration is the first thing I would point out. Weighting by market value tells you nothing about where the risk sits; dollar duration does.
   5. Convexity rises too, and non-linearly, so the portfolio becomes more asymmetric: better in a large rally than duration predicts, better than a shorter portfolio in a large selloff too, relative to its own duration.
   6. Two limitations to volunteer. First, averaging durations assumes a parallel shift — this portfolio is really a bet on the whole curve, and a flattening would hurt the 30-year and help the 2-year regardless of the average. Second, if any bond has credit risk, the spread duration is a separate exposure, and in a selloff spreads and rates often move together.

   Where candidates lose it

   Answering qualitatively — 'more rate sensitive' — without doing the weighted average. Put numbers on it, then make the two real points: the long bond carries most of the risk despite a modest weight, and duration drifts upward on its own in a rally. That is what a fixed income manager wants to hear.

   Expect next

   • Which bond carries most of the risk, and is that what the weights suggest?
   • How would you bring the duration back down without selling the long bond?
   • What if the curve flattens instead of shifting in parallel?

   Reported by candidates at PIMCO (Generalist, Los Angeles, 2026). Source: Wall Street Oasis.

8. 070Explain the weekly expiry ecosystem in Indian index options and what it does to pricing.Indian derivativesIntermediatetechnicalIndian derivatives desksIndian broking

   Say this

   Weekly expiries created a market where most of the volume is in options with one to four days of life, which means enormous gamma and theta and almost no vega. Pricing on expiry day stops looking like Black-Scholes and starts looking like a supply and demand auction on a few strikes around spot, with implied volatility on the wings that no model would produce.

   Then walk it

   1. The mechanics: exchanges staggered weekly expiries across indices so that at one point there was an expiry nearly every day of the week, which concentrated retail activity into a daily cycle rather than a monthly one. SEBI cut this back to one weekly expiry per exchange in late 2024.
   2. What short dating does to the Greeks: a one-day at-the-money option has enormous gamma and theta and essentially no vega. So the trade is a pure gamma-versus-theta contest, and the volatility surface becomes almost meaningless as a level.
   3. The observable distortion: far out-of-the-money weekly options trade at implied volatilities of 60, 80, sometimes over 100 percent, not because anyone forecasts that volatility but because the option costs 2 rupees and there is a floor on the tick. Lottery demand sets the price of the wings.
   4. On expiry day the flow dominates. Large short-gamma positions must hedge in the direction of the move, so you get sharp intraday trends into the close, and then a pin towards the strike with the biggest open interest. That is dealer hedging mechanics, not information.
   5. The settlement convention interacts with it: because settlement is a VWAP of the last half hour, hedging demand is concentrated in that window, which is where you see the volume spike and the sharpest moves.
   6. The commercial honesty: this ecosystem exists because it generates extraordinary exchange and broker revenue and because retail demand for lottery payoffs is real. SEBI's own analysis found the large majority of individual derivative traders lose money, and the reforms since 2024 — fewer expiries, larger lots, higher margins near expiry — are a direct response. Anyone interviewing on an Indian desk should be able to say both that the ecosystem is a genuine liquidity pool and that its retail side is a wealth transfer.

   Where candidates lose it

   Describing weekly expiries as just a shorter-dated option. The interviewer wants the consequences: gamma and theta dominate, vega vanishes, wing implied volatilities become meaningless, and expiry-day price action is dealer hedging rather than information. And be able to state the retail loss data without editorialising.

   Expect next

   • Why do far out-of-the-money weeklies show implied volatilities over 80 percent?
   • What causes the sharp moves in the last half hour of expiry day?
   • What did SEBI change in 2024 and why?
9. 084What would your allocation be in today's market?Trading and marketsIntermediatetechnicalAmundiRates · London · 2018

   Say this

   Start with the benchmark and state your deviations, because an allocation answer with no anchor is untestable. Then give three or four active positions, each with a reason, a size and a way of being wrong. And for a rates seat, make duration and curve positioning the centre of the answer rather than an afterthought.

   Then walk it

   1. Anchor first: 'against a 60-40 benchmark' or 'against a global aggregate index'. Then your tilts are measurable and the conversation can be about the tilts rather than about taste.
   2. Then the positions with sizes. Something like: duration slightly short of benchmark because the curve has too much easing priced; overweight the front end versus the long end, which is a steepener; underweight credit because spreads are near cycle tights and the compensation for illiquidity is thin; and a small allocation to convexity through options rather than cash.
   3. Each position needs one sentence of reasoning that refers to a price, not a sentiment. 'Spreads at X basis points against a cycle median of Y' is a reason. 'Credit feels expensive' is not.
   4. For a rates desk, be specific about the curve rather than the level. Level views are crowded and hard; curve and cross-market views — this country's five-year against that one's — are where rates managers actually take risk, and saying so shows you know the seat.
   5. Then the risk budget, which is what separates an allocation from a list. Say how much of your tracking error each position consumes, and note that a steepener and a credit underweight are correlated positions in a risk-off event, so you cannot size them independently.
   6. And the falsifier: name the data point that would make you cut. For the duration view it is a run of inflation prints above expectation; for the credit view it is spreads tightening through a level at which the carry no longer compensates. Ending on what would change your mind is the difference between an allocation and an opinion.

   Where candidates lose it

   Listing asset classes with adjectives and no benchmark, no sizes and no correlations. The interviewer is testing portfolio construction, not market views. And on a rates seat, if your answer is entirely about the level of yields and never about the shape of the curve, you have answered the wrong question.

   Expect next

   • Which two of those positions are correlated?
   • How much of your risk budget does each consume?
   • What would make you cut the duration position?

   Reported by candidates at Amundi (Rates, London, 2018). Source: Wall Street Oasis.

10. 085How would you allocate one million dollars versus one billion dollars?Trading and marketsIntermediatetechnicalScotiabankSales and Trading · Toronto · 2025

    Say this

    The million is a pure return problem, the billion is a liquidity and market-impact problem. At a million I can own whatever I like and get in and out in a day. At a billion my own trading moves prices, my universe shrinks to what can absorb size, and the constraint becomes how I build and exit a position rather than what I want to own.

    Then walk it

    1. At a million: concentrated is rational. Five to ten positions, small and mid caps available, options strategies viable in size because a hundred contracts is nothing to the market. Transaction costs are a rounding error.
    2. At a billion, capacity binds. A 5 percent position is 50 million, and in a small cap that is weeks of average daily volume — so the small and mid cap universe largely disappears, and I am pushed towards large caps, index derivatives and government bonds.
    3. Market impact becomes the dominant cost. Building 50 million in a moderately liquid name will move it, and the impact is not recovered. So execution — algorithms, participation rates, blocks, working the order over days — becomes part of the investment decision rather than a back-office task.
    4. The derivative alternative is the interesting answer for this desk: at a billion, index futures and total return swaps let me take beta exposure instantly without moving underlying stocks. Get the market exposure on cheaply in futures, then build the alpha positions slowly underneath.
    5. Number of positions rises for capacity reasons rather than diversification reasons, and that mechanically dilutes any edge. This is the core reason large funds' returns converge towards the index — not worse ideas, just less ability to express them.
    6. And the exit is the part people forget. A position you can build over three weeks may need to be sold in three days in a crisis, when liquidity is a fraction of normal. So at a billion I would size positions against stressed liquidity, not average liquidity, and keep a derivative overlay as the fast lever. The reason to do this is not theoretical: it is exactly the mismatch that forced the 2022 UK LDI funds and several credit funds into distressed selling.

    Where candidates lose it

    Answering it as a risk-tolerance question — 'more diversified with more money'. The real answer is capacity, market impact and exit liquidity, and the derivatives-desk version is that futures and swaps let you separate getting the exposure on from building the position. Size against stressed liquidity, not average.

    Expect next

    • How would you get the beta on quickly at a billion?
    • How does capacity dilute your edge?
    • How would you size against stressed liquidity rather than average?

    Reported by candidates at Scotiabank (Sales and Trading, Toronto, 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.