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. 032You are long a one-month at-the-money straddle at 20 volatility. Under what conditions do you make money?The GreeksHardtechnicalVolatility tradingProp trading firms

   Say this

   If you delta hedge it, you make money when realised volatility over the month exceeds 20. If you do not hedge it, you make money only if the stock finishes far enough from the strike to cover the combined premium, which is a much harder bar. Those are two completely different trades and the distinction is the answer.

   Then walk it

   1. Unhedged: you paid, say, 4.6 percent of spot for the straddle, so the stock must move more than 4.6 percent in either direction by expiry. Direction does not matter, distance does — and crucially, the path does not help you at all.
   2. Hedged: you rebalance delta daily and harvest the moves. Now the path is everything. A stock that oscillates 2 percent a day and finishes flat pays you handsomely while the unhedged straddle expires worthless.
   3. The break-even in the hedged case is the realised-versus-implied comparison. Twenty percent annualised is about 1.25 percent a day. If the stock is genuinely moving more than that, gamma harvesting beats the theta you bleed.
   4. Arithmetic to make it concrete: 20 volatility on a 30-day option costs roughly 20 times root of 30 over 365, about 5.7 percent of spot for the straddle at a 0.8 scaling — call it 4.5 to 5 percent. So you need about a 5 percent move unhedged, or sustained daily moves above 1.25 percent hedged.
   5. Two things can still beat you even if you are right about realised volatility. Implied volatility can fall, which hits your vega mark immediately, and the realised moves can arrive as one gap rather than as daily oscillation — a gap gives you the payoff once rather than repeatedly.
   6. The honest limitation: long gamma is not a free option on chaos. You pay theta every day, and in a market that grinds quietly for three weeks and then explodes on day 25, you may have been stopped out of the position before the payoff arrives. Sizing and horizon matter as much as the volatility view.

   Where candidates lose it

   Answering only the unhedged version — 'the stock has to move more than the premium'. Any interviewer on a volatility desk is testing whether you know the hedged straddle is a bet on realised variance and the unhedged one is a bet on the terminal price. Say both, and say which one you meant.

   Expect next

   • What if the stock moves 5 percent but in one overnight gap?
   • You were right about realised volatility and still lost money. How?
   • Would you rather own the straddle or a variance swap for this view?
3. 033What is pin risk, and how do you manage a large position into expiry?The GreeksHardsuperdayMarket makingEquity derivatives

   Say this

   Pin risk is the risk that the underlying closes almost exactly at your strike, so you do not know whether you will be assigned. You go into the weekend not knowing whether you are flat or hugely long or short stock, and by the time you find out, the market has moved. It is a settlement risk, not a pricing risk.

   Then walk it

   1. The mechanism: you are short 1,000 at-the-money calls and the stock settles at the strike. If they are exercised you are short 100,000 shares; if not you are flat. You cannot hedge a position you do not know you have.
   2. Gamma explodes into expiry for at-the-money options, so your delta swings between near zero and near one on tiny price moves. The hedge you put on at 3:29 can be completely wrong at 3:30.
   3. How desks manage it: reduce the at-the-money position before the last hour, close out rather than let it go to assignment, and avoid being short large size at a strike where open interest is concentrated.
   4. Cash settlement solves it. Indian index options — Nifty and Bank Nifty — are cash-settled on a weighted average of the last half hour, so there is no assignment ambiguity. But cash settlement creates a different problem: settlement-price manipulation risk, which is exactly why SEBI moved to a VWAP of the closing period rather than a closing print.
   5. That closing-period mechanic is why you see the volume spike into the last thirty minutes on expiry day in India. Large positions need to hedge against the same average that determines their settlement.
   6. The broader lesson to volunteer: pin risk is one of a family of expiry-day operational risks — assignment, settlement price, and the exercise cut-off being after the market closes so you can be assigned on news that broke post-close. These are the risks that lose money on well-hedged books, and they are the reason expiry-day process discipline exists.

   Where candidates lose it

   Explaining pin risk as a pricing phenomenon. It is an operational and settlement risk, and the answer should include what you do about it — reduce size, close rather than assign, and know whether your contract is cash or physically settled. Naming the Indian cash-settlement mechanic shows local knowledge.

   Expect next

   • How does cash settlement change the problem, and what new problem does it create?
   • Why does volume spike in the last half hour of an Indian expiry day?
   • You are assigned on news that broke after the close. What is your exposure?
4. 034Beyond the five standard Greeks, which second-order sensitivities actually get managed?The GreeksHardsuperdayExotics tradingVolatility trading

   Say this

   Vanna and volga, mainly. Vanna is how delta changes when volatility moves, and it is the same thing as how vega changes when spot moves. Volga is the convexity of vega in volatility. On any book with skew — which is every real book — those two determine whether your vega hedge holds up.

   Then walk it

   1. Vanna matters because implied volatility and spot are correlated. In equities the correlation is strongly negative: spot falls, volatility rises. So a position with vanna gets a second hit at exactly the moment the first one arrives, and the two are not independent risks.
   2. Volga is the reason a vega-neutral book is not volatility-neutral for large moves. Wing options have positive volga, so a long-wings, short-body position is vega-flat and still profits from a volatility spike. Every risk reversal and butterfly carries it.
   3. Charm is the decay of delta with time, and it matters near expiry and on barrier books, where your delta changes overnight without the market moving at all.
   4. The FX market prices in these terms directly. The vanna-volga approach prices an exotic by taking the Black-Scholes value and adding the cost of hedging its vanna and volga with the market-quoted risk reversal and butterfly. It is not elegant, but it reproduces market prices better than a naive smile interpolation.
   5. How desks actually manage it: a risk report showing profit and loss under a grid of spot and volatility shocks, rather than a list of Greeks. The grid captures vanna and volga implicitly and does not require you to trust a Taylor expansion.
   6. And the limitation: these are still local derivatives. A scenario grid with a minus 20 percent spot and plus 30 volatility shock tells you more than any second-order Greek, because in a real dislocation the correlations you assumed break and the higher-order terms are no longer small.

   Where candidates lose it

   Rattling off exotic Greek names without connecting them to spot-volatility correlation. Vanna matters in equities specifically because the skew is one-sided and spot and volatility are negatively correlated. If you cannot say that, the names are decoration.

   Expect next

   • Why is vanna so important in equities specifically?
   • How can a vega-neutral book still profit from a volatility spike?
   • Would you rather have a Greek report or a scenario grid, and why?
5. 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?
6. 036What is the difference between implied and realised volatility, and which one are you actually trading?VolatilityCoretechnicalVolatility tradingProp trading firms

   Say this

   Realised volatility is what the underlying actually did — measured from historical returns. Implied volatility is what the option market is charging, backed out of the price. When you buy an option and delta hedge it, you are long realised and short implied: you make money if the world turns out more volatile than the price you paid.

   Then walk it

   1. Realised is backward-looking and measurable: annualise the standard deviation of log returns, typically by multiplying the daily figure by root 252. The answer depends on your window, which is why people argue about it.
   2. Implied is forward-looking and is a price, not a forecast. It contains the market's expectation plus a risk premium plus supply and demand for that specific strike and expiry.
   3. The trade: buying a delta-hedged option is long realised volatility, short implied. The profit over the life is roughly the gamma-weighted difference between the two, which is why a variance swap — whose payoff is exactly realised variance minus a strike — is the clean expression of the view.
   4. A number to anchor it: Nifty realised volatility runs in the low teens in calm periods while India VIX often sits a few points above. That gap is the premium, and it is persistent enough that systematic short-volatility strategies exist to harvest it.
   5. The two are not even measuring the same object. Implied is a risk-neutral expectation over the option's remaining life. Realised is a sample statistic over a past window. Comparing them requires matching horizons, and most casual comparisons do not.
   6. The limitation to volunteer: implied above realised does not mean options are expensive. It means you are being paid for taking crash risk, and the payment looks generous right up to the point where you find out why it existed. February 2018 and March 2020 are the two reference points.

   Where candidates lose it

   Treating implied volatility as the market's forecast of realised volatility. It is a price with a risk premium in it, and a persistent gap is compensation rather than mispricing. Saying so is what separates an answer from a definition.

   Expect next

   • So is a persistent gap between them an inefficiency?
   • How would you measure realised volatility, and over what window?
   • What is the cleanest instrument for trading realised against implied?
7. 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?
8. 038Why does the volatility smile exist?VolatilityHardtechnicalVolatility tradingEquity derivatives

   Say this

   Because the real distribution of returns is not lognormal, and Black-Scholes assumes it is. The market corrects the model by charging a different implied volatility per strike. Fat tails make both wings expensive relative to the body, and in equities negative skewness makes the downside wing much more expensive than the upside — that asymmetry is why the smile is really a smirk.

   Then walk it

   1. Mechanically, implied volatility is just the number you plug into a wrong formula to get the right price. If the true distribution has more mass in the tails than a lognormal, you need a higher volatility input to reproduce the market price of a wing option.
   2. Two distinct effects. Kurtosis — fat tails on both sides — lifts both wings and gives you a symmetric smile, which is roughly what you see in FX on a major pair. Negative skew lifts the left wing only, which is what you see in equity indices.
   3. Why equities are skewed: leverage means falling equity raises the debt-to-equity ratio and therefore the volatility of the remaining equity. Crashes are correlated across names while rallies are not, so index skew is steeper than single-stock skew. And there is a real demand effect — everyone wants to buy puts and sell calls.
   4. So the skew is not purely a distributional statement. Part of it is the price of insurance, which means part of the steepness is a risk premium rather than a forecast of the crash probability.
   5. The models that generate it endogenously are stochastic volatility, where negative spot-volatility correlation produces skew, and jump-diffusion, where a downward jump component produces exactly the left-wing fat tail. Local volatility fits the observed surface exactly but has unrealistic dynamics.
   6. One thing to be careful about: the skew steepened permanently after the 1987 crash. Before it, index implied volatility was roughly flat across strikes. So a large part of the smile is a learned behaviour about crash risk, not a timeless property of returns — which means it can reprice when beliefs change.

   Where candidates lose it

   Explaining the smile as fat tails only. In equities the dominant feature is skew, not kurtosis, and it has three causes — leverage, correlated crashes, and put demand. Also worth saying that the shape post-dates 1987, because it makes clear you understand it is a market convention as much as a statistical fact.

   Expect next

   • Why is index skew steeper than single-stock skew?
   • What did the 1987 crash change about the surface?
   • Which model would you use if you had to price a barrier off this surface?
9. 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?
10. 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?

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.