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. 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?
2. 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?
3. 037Why is implied volatility usually higher than subsequent realised volatility?VolatilityIntermediatetechnicalVolatility tradingHedge funds

   Say this

   Because options are insurance and insurance is sold above expected loss. Investors are structurally long equities and want protection, protection pays off when everything else is losing, and that correlation makes buyers willing to overpay. The gap is the variance risk premium.

   Then walk it

   1. The demand side: pension funds, insurers and long-only managers are natural buyers of downside protection and natural sellers of upside. That flow is one-directional and persistent, which pushes put implied volatility above fair value.
   2. The risk-premium argument: a payoff that is positive exactly when markets crash has a negative beta to the market, so in any asset pricing framework it should earn a negative expected return. Someone has to be paid to supply it.
   3. Supply is constrained by capital and by the shape of the risk. Selling volatility has a fat left tail and requires margin that rises exactly when you are losing, so the pool of people willing to do it in size is limited. Limited supply against persistent demand means a price above fair value.
   4. Empirically the gap averages two to four volatility points on major indices and is much wider in the puts than in the calls, which is the skew. It is one of the most robust findings in empirical finance.
   5. But the premium is not free money. The return distribution of harvesting it is negatively skewed: many small gains, rare enormous losses. A Sharpe ratio computed on a short-volatility strategy over a calm sample is one of the most misleading numbers in the industry.
   6. And the premium varies. In calm markets it compresses to almost nothing, and that is precisely when short-volatility positioning is largest — because the recent track record looks best. That reflexivity is why the unwinds are violent, and it is what happened on 5 February 2018.

   Where candidates lose it

   Saying 'because option sellers need a profit'. The real answer is a risk premium argument: the payoff has negative beta, so it earns a negative expected return, so buyers pay above expectation. And you must volunteer the negative skew of harvesting it, or you sound like someone about to sell naked options.

   Expect next

   • So why doesn't everyone sell volatility?
   • When is the premium largest, and when is it smallest?
   • How would you harvest it without blowing up?
4. 039The FX smile looks symmetric, the equity smile is a downward smirk and commodities often smirk upward. Why the different shapes?VolatilityIntermediatesuperdayFX derivativesCommodities trading

   Say this

   Because the shape encodes which direction is the scary one for that asset, and that differs by market. Equities crash down, so the put wing is bid. Commodities spike up on supply shocks, so the call wing is bid. A currency pair is somebody's up and somebody else's down, so the tails are more balanced and you get a smile rather than a smirk.

   Then walk it

   1. Equities: gaps are downward and correlated. Leverage amplifies falls, and the entire institutional base is long and buys puts. Result is a steep left wing — a 25-delta put can trade five or more volatility points above the at-the-money.
   2. Commodities: the supply shock is the tail. A hurricane, a refinery fire, a war, an export ban — all push price up violently, and the downside is floored by the cost of production. So calls are bid, and you get inverse skew. Natural gas in winter is the purest example.
   3. FX on a G10 pair: both sides are a major economy, so a fall in one currency is a rise in the other and there is no structural short. You get a roughly symmetric smile driven by kurtosis, and the market quotes it as a butterfly — the average wing over the body.
   4. But an emerging market currency is skewed, and USD/INR is the clean case. The rupee depreciates in jumps and appreciates slowly, partly because the central bank manages it, so USD calls and rupee puts carry a premium. The risk reversal is persistently one-sided.
   5. Rates are their own case. With yields near zero the smile shape changed entirely, and desks moved to normal rather than lognormal volatility to allow negative rates at all. Shape follows what the market believes the tail looks like.
   6. The general principle worth naming: the smile is a picture of where the market thinks the gap risk is, plus who needs the hedge. If you know the structural position of the participants and the physics of the underlying, you can predict the shape before you look at a screen.

   Where candidates lose it

   Describing three shapes without a unifying mechanism. The answer is 'the bid wing is the tail direction plus the hedging demand'. Get USD/INR in there — an India-facing interviewer will expect you to know that the rupee's skew is one-sided and why.

   Expect next

   • What shape would you expect in USD/INR and why?
   • Why does natural gas skew change with the season?
   • How do you quote a smile in FX conventions?
5. 040What does the volatility term structure normally look like, and what does it mean when it inverts?VolatilityIntermediatetechnicalVolatility tradingHedge funds

   Say this

   Normally upward sloping — front-month implied volatility below the longer dates — because volatility mean-reverts and the near term is usually calmer than the long-run average. An inversion means the market is pricing near-term stress: an event, a crisis, or a known catalyst inside the front expiry.

   Then walk it

   1. The mean-reversion logic: if spot volatility is 12 and the long-run mean is 18, then the average over the next two years should be closer to 18 than to 12. So the curve slopes up from a low starting point and slopes down from a high one.
   2. Inversions are therefore a stress signal. In March 2020 the front month went to 80 while one-year implied was in the 30s — the market said the next month is chaos and then it normalises.
   3. There is a milder, non-crisis inversion too: a known event inside the front expiry. An earnings date, an election, a central bank meeting, a court ruling. That produces a local bump in the specific expiry that contains it, not a whole-curve inversion.
   4. Trading it: a calendar spread expresses a view on the slope. Long the back month and short the front is long the term structure and short near-term gamma — that is a bet on mean reversion, and it is the standard trade after a spike.
   5. The carry side of the same fact: an upward-sloping VIX curve means long-volatility ETPs bleed on the roll, which is why products like the short-term futures trackers lose value over time even when spot volatility is unchanged. Roll cost has historically dominated their returns.
   6. The limitation: an inverted curve is information, not a signal. It usually resolves by front-month volatility collapsing, which is why selling the spike works most of the time — and the times it does not, it goes much higher first, which is enough to end a career. Knowing the base rate is not the same as being able to hold the position.

   Where candidates lose it

   Saying inverted means fear and stopping. Add the two distinct causes — systemic stress versus a datable event inside one expiry — and add the roll-cost consequence for volatility ETPs. And be honest that selling an inverted curve is a high-base-rate, high-tail-risk trade.

   Expect next

   • How would you trade an inversion, and how would you size it?
   • Why do long-volatility ETPs lose money in a normal market?
   • What does a bump in one single expiry tell you?
6. 041What is the VIX, and how is it actually computed?VolatilityIntermediatetechnicalVolatility tradingIndian derivatives desks

   Say this

   It is the market's 30-day expected volatility on the S&P 500, expressed annualised in percentage points. It is not an average of implied volatilities — it is built from a strip of out-of-the-money option prices across all strikes, which makes it a model-free estimate of the square root of expected variance.

   Then walk it

   1. The construction: take all reasonably liquid out-of-the-money puts and calls in the two expiries that straddle 30 days, weight each by one over its strike squared, sum, interpolate to exactly 30 days, take the square root and annualise.
   2. The one-over-strike-squared weighting is the part worth knowing. It comes from the mathematics of replicating a variance swap: a portfolio of options weighted that way has a payoff equal to realised variance. So the VIX is the fair strike of a 30-day variance swap, quoted as a volatility.
   3. That is why it is called model-free. It does not use Black-Scholes at all — it reads variance straight off prices. The older VIX methodology up to 2003 did use at-the-money Black-Scholes implieds, and the change matters when you compare long histories.
   4. Because it uses every strike, it is sensitive to the wings. A bid in deep out-of-the-money puts lifts the VIX even if at-the-money implied volatility has not moved, which is why the VIX can rise on a flat day.
   5. You cannot trade the index. You trade VIX futures and options, and the futures are priced off forward variance rather than spot VIX, so they do not track it one for one. In a spike, the front future will lag spot VIX substantially.
   6. India's equivalent is the India VIX, built on Nifty options with the same methodology adapted by the NSE. It matters for the same reason: it is the reference for weekly-expiry positioning and it inverts in exactly the same way in a stress event.

   Where candidates lose it

   Calling it 'an average of option implied volatilities'. It is a variance-swap strike, and the one-over-K-squared weighting is the specific thing the interviewer is checking. Also expect the follow-up on why VIX futures do not track spot VIX — have the forward-variance answer ready.

   Expect next

   • Why doesn't a VIX future track spot VIX?
   • Why can VIX rise on a day when at-the-money implied is unchanged?
   • What is India VIX built on?
7. 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?
8. 045Straddle or strangle — how do you choose?Option strategiesIntermediatetechnicalProp trading firmsVolatility trading

   Say this

   Both are pure volatility positions with no directional view. A straddle buys the at-the-money call and put, so you pay more and get maximum gamma right where spot is. A strangle buys out-of-the-money strikes, so it costs less and needs a bigger move, but it gives you more exposure to the tails per rupee spent.

   Then walk it

   1. Straddle: highest gamma and vega concentrated at the strike, highest premium, highest theta bleed. You want it when you expect a move and you expect it soon, and when you will delta hedge to harvest the path.
   2. Strangle: cheaper, wider break-evens, lower theta per day. You want it when you expect a large move but are unsure of timing, or when you specifically believe the wings are underpriced relative to the body.
   3. The wings-versus-body choice is a skew and kurtosis view, not just a cost decision. Long strangle, short straddle is a butterfly — that is a pure bet that the distribution is fatter-tailed than the smile implies.
   4. Break-even arithmetic: a 4.5 percent straddle needs a 4.5 percent move by expiry. A strangle costing 2 percent with strikes 5 percent out needs a 7 percent move. So the strangle wins only in the big-move scenarios and loses in the moderate ones.
   5. In practice the choice is often dictated by liquidity and margin. In Indian index options the out-of-the-money weekly strikes are extremely liquid and cheap in absolute rupee terms, which is why retail gravitates to strangles — and why the margin framework treats short strangles more punitively after the 2020 peak-margin reforms.
   6. The limitation for both: if you are not delta hedging, you are betting on the terminal price, not on volatility, and a stock that swings wildly and closes flat pays you nothing. State which trade you are actually putting on.

   Where candidates lose it

   Framing it purely as 'strangle is cheaper'. The real distinction is where you want your gamma and whether your view is about the body or the tails of the distribution. And name the unhedged-versus-hedged difference, because otherwise you are describing a direction bet.

   Expect next

   • Long strangle against short straddle — what have you built and what is the view?
   • Which would you rather own into an earnings print?
   • What does margin treatment do to the choice in India?
9. 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.

10. 048Explain a butterfly and an iron condor, and tell me what view each expresses.Option strategiesIntermediatetechnicalProp trading firmsVolatility trading

    Say this

    Both are short-volatility, range-bound structures with capped losses. A butterfly is short the body and long the wings — sell two at-the-money options, buy one either side. An iron condor is the same idea with a gap in the middle: sell an out-of-the-money put and call, buy further-out ones as protection. The view is that the underlying stays in a range and that implied volatility is too high.

    Then walk it

    1. Butterfly payoff: maximum profit if the underlying pins the middle strike at expiry, losses limited to the width less the credit. It has the highest payoff concentration of any standard structure, which is why it is the expiry-day trade of choice.
    2. Iron condor: a wider profit plateau between the two short strikes, smaller maximum profit, higher probability of ending inside the range. It is the same trade with less precision required about where the underlying lands.
    3. Read a long butterfly as short kurtosis. You are selling the body and buying the wings, which is a statement that the distribution is thinner-tailed than the smile implies. That is why butterfly prices are how FX desks quote the curvature of the smile.
    4. Both are short gamma and short vega in the middle, so they make money from time passing and from implied volatility falling. Both have their worst outcome on a large move in either direction, which is bounded by the long wings.
    5. Where they actually get used in India: Nifty and Bank Nifty weekly expiries, because the short-dated theta is large and the structures are margin-efficient once the wings are in place. That is also where they are most frequently oversized by retail traders.
    6. The real risk is the one the payoff diagram hides: the position is fine at expiry and can be badly underwater before it. A move to the edge of the range mid-life produces a mark-to-market loss and a margin call, and traders get closed out of positions that would have been profitable if held. Capped loss is not the same as capped margin.

    Where candidates lose it

    Drawing the payoff diagram and stopping. Two things earn the answer: naming the butterfly as a curvature or kurtosis trade, and pointing out that a capped-loss structure can still force you out early through margin. That second point is where retail traders in weekly options actually lose.

    Expect next

    • Why do FX desks quote the smile using butterflies?
    • Which is safer for a retail trader, and does the margin agree with you?
    • What happens to your iron condor two weeks in with spot at the short put strike?

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.