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. 026What is delta, and give me three different ways to think about it.The GreeksCorephone / first roundMarket making

   Say this

   Delta is the change in the option's value for a one-unit change in the underlying. Three readings: it is the sensitivity, it is the hedge ratio — the number of shares you hold to be flat — and it is approximately the risk-neutral probability of finishing in the money, though only approximately.

   Then walk it

   1. As a sensitivity: a 0.4 delta call gains 40 paise for a 1 rupee move in the stock. Calls run from 0 to 1, puts from 0 to minus 1, and at the money sits near 0.5 in absolute terms.
   2. As a hedge ratio: short one 0.4 delta call and buy 40 shares and you are locally flat. This is the reading that matters on a desk, because it is the trade you actually put on.
   3. As a probability proxy: it is close to N of d2 but not equal to it, so treating a 25-delta option as a 25 percent chance of exercise is a real error that widens with volatility and time.
   4. As exposure: delta times the number of contracts times the contract multiplier gives you delta-equivalent notional, which is how the whole book gets aggregated. A book of 400 different options collapses to one number you can hedge with futures.
   5. The thing that makes delta interesting is that it is not constant. It moves with spot, which is gamma, and it moves with time and volatility, which are charm and vanna. A delta hedge is a snapshot that starts going stale the moment you put it on.
   6. The limitation to state: delta is a first-order local approximation. In a gap move it is nearly useless — a 0.4 delta call in a 15 percent overnight drop does not lose 0.4 times the move, it loses far less, because gamma works in the buyer's favour. Anyone who managed risk through March 2020 with delta alone learned this.

   Where candidates lose it

   Giving one definition and stopping. Junior interviews ask this to see whether you connect the maths sensitivity to the actual hedging trade. If you cannot say 'so I buy 40 shares', you have described a partial derivative rather than a job.

   Expect next

   • What is the delta of an at-the-money option, exactly?
   • How does delta change as expiry approaches?
   • Is delta the probability of expiring in the money?
2. 027What is gamma and why do traders care about it more than delta?The GreeksCoretechnicalMarket makingProp trading firms

   Say this

   Gamma is the rate of change of delta — the curvature of the option's value. Traders care more because delta can be hedged away in one trade, while gamma is what determines whether that hedge keeps working. Gamma is the risk you actually carry between rebalances.

   Then walk it

   1. Long gamma means your delta moves in your favour: you get longer as the market rises and shorter as it falls, so mechanical rebalancing sells high and buys low. Every rebalance banks a small profit.
   2. Short gamma is the reverse and it is vicious. You get shorter into a rally and longer into a selloff, so hedging forces you to buy high and sell low. The losses compound with the size of the move because the payoff is concave.
   3. Gamma is largest at the money and increases sharply as expiry approaches. A one-day ATM option has enormous gamma and almost no vega, which is why expiry-day books are managed completely differently from long-dated ones.
   4. You pay for gamma with theta. A long gamma position bleeds every day it does not move, and the break-even is roughly whether realised volatility exceeds the implied volatility you paid. That trade-off is the core of a market maker's daily profit and loss.
   5. Concrete version: long a 100-strike straddle at 20 implied on a stock that then realises 30 percent volatility. You lose theta every quiet day and make it back on the days that move, and the sum over the life is positive because realised beat implied.
   6. Market-wide, gamma positioning explains a lot of intraday behaviour. When dealers are short gamma they must hedge in the direction of the move, which amplifies it; when they are long they dampen it. That is the mechanism behind the gamma-squeeze stories, and it is real, though usually overstated in the press.

   Where candidates lose it

   Defining gamma as the second derivative and stopping. The interviewer wants the trading consequence: long gamma means your hedges make money, short gamma means they lose money, and you are paying or receiving theta for the privilege. Say what you do on the rebalance.

   Expect next

   • So how do you make money from being long gamma?
   • Where is gamma largest, and what does that do to your hedging on expiry day?
   • What does it mean for the market when dealers are collectively short gamma?
3. 028What is theta, and is collecting theta a strategy?The GreeksCoretechnicalIndian broking

   Say this

   Theta is the change in option value from one day passing, all else equal. For a long option it is negative — you lose a little every day. Collecting theta is not a strategy on its own; it is the premium you receive for being short gamma and short vega, and you only keep it if realised volatility comes in below implied.

   Then walk it

   1. Theta is largest in absolute terms for at-the-money options close to expiry, and it accelerates in the final week. A one-week ATM option can lose a fifth of its value a day near the end.
   2. The relationship to remember: theta and gamma are two sides of one trade. In Black-Scholes, theta is approximately minus half gamma times spot squared times variance. That identity says you are paid theta in exact proportion to the gamma you are short.
   3. So the break-even is not the passage of time, it is a volatility comparison. If you sell an option at 20 implied and the stock realises 15, you keep money. Realise 25 and you lose, no matter how much theta accrued on the way.
   4. This is why 'theta decay strategies' marketed to retail are misleading. Selling weekly index options collects theta reliably and looks like a bond until the week it does not, and one bad week removes many months of accrual. SEBI's own studies on Indian index option traders point at exactly this pattern of losses.
   5. The honest version of a short-theta business is the market maker's: sell options, delta hedge continuously, and earn the implied-minus-realised spread while keeping gamma small and diversified across names and expiries.
   6. Also note theta is not uniform through the day or week. Weekend decay is priced in on Friday, and on a low-realised-volatility day the effective bleed is higher than the model number suggests, because you also fail to earn the gamma.

   Where candidates lose it

   Presenting theta as free income. The interviewer's follow-up is always 'so you would just sell options every week?' Name the theta-gamma identity and say plainly that theta is compensation for short convexity, not a yield.

   Expect next

   • Write down the relationship between theta and gamma.
   • Why do weekly-expiry sellers in India lose money on average?
   • When is theta actually your friend?
4. 029What is vega, and where on the surface is it biggest?The GreeksIntermediatetechnicalEquity derivativesVolatility trading

   Say this

   Vega is the change in option value for a one-point move in implied volatility. It is biggest for long-dated at-the-money options, and it scales roughly with the square root of time. That is the key structural fact: gamma lives at the front of the curve, vega lives at the back.

   Then walk it

   1. Both calls and puts have positive vega, because higher volatility widens the distribution and both are convex payoffs. Being long options is being long volatility, full stop.
   2. Magnitude: vega is proportional to spot times root time times the standard normal density at d1. Root time means a two-year option has about five times the vega of a one-month option on the same notional.
   3. So the division of labour on a desk: if you want to trade the level of volatility you use long-dated options or variance swaps. If you want to trade the movement of the underlying you use short-dated options, where gamma dominates and vega is almost irrelevant.
   4. Vega is not one risk, it is a surface of risks. A book can be vega-flat in total and still be badly exposed if it is long front-month and short back-month volatility — that is vega term structure risk, and desks bucket vega by expiry rather than summing it.
   5. Numbers: an at-the-money one-year index option with 10 million of notional might carry 40,000 of vega, so a three-point volatility spike is 120,000. In March 2020 index implied volatility went from 15 to 80 in three weeks. That is the scale of the risk.
   6. The limitation: vega assumes a parallel shift in implied volatility, and real surfaces do not shift in parallel. Front-month volatility moves far more than back-month, and the skew steepens as the level rises. So you need vanna and volga — the cross-sensitivities to spot and to volatility itself — before your vega number means anything on a skewed book.

   Where candidates lose it

   Saying vega is biggest at the money and stopping, without the root-time scaling. The distinction that matters is that gamma is a short-dated risk and vega a long-dated one; if you cannot say which instrument to use for which view, you have not answered a trading question.

   Expect next

   • So which option would you buy to express a pure view on the level of volatility?
   • Why is a vega-neutral book still exposed to volatility?
   • What are vanna and volga, and when do they matter?
5. 030Rho gets ignored. When does it actually matter?The GreeksIntermediatetechnicalRates derivativesEquity derivatives

   Say this

   Rho is the sensitivity of an option's value to the interest rate. It is negligible on short-dated equity options, which is why nobody talks about it, and it is first-order on long-dated options, on FX, and on anything with a large strike relative to spot. It came back into focus when rates went from zero to five percent.

   Then walk it

   1. Sign: calls have positive rho, puts negative. A higher rate lowers the present value of the strike you will pay, which helps the call and hurts the put.
   2. Size: rho scales with time and with the discounted strike. On a one-month at-the-money option a 25 basis point rate move is a rounding error. On a five-year option it can be worth more than a volatility point.
   3. So where it bites: long-dated structured products, LEAPS, and the embedded options in insurance and pension liabilities. Anyone running a long-dated book in 2022 saw their option values move on rates as much as on volatility.
   4. In FX, rho is not one number but two, because you have the rate on each currency. The forward points are the rate differential, so an FX option's exposure to rates is really an exposure to the carry, and on a high-differential pair like USD/INR that dominates.
   5. Rates also change behaviour, not just value. Early exercise on American puts becomes optimal at higher rates, and the cost of carrying a delta hedge is a financing cost that grows with the rate. At five percent, financing a one-million-share hedge is a real line item in the profit and loss.
   6. The honest caveat: for the typical short-dated index option trade, rho is genuinely ignorable and pretending otherwise is false precision. The judgement being tested is whether you know which Greeks to care about for which instrument, rather than whether you can list five of them.

   Where candidates lose it

   Dismissing rho entirely, or over-claiming its importance. The right answer is a judgement about maturity and instrument: irrelevant for weekly index options, first-order for a five-year structured note and for FX carry. And name the financing cost of the hedge, which most candidates miss.

   Expect next

   • How does rho work differently in FX?
   • What did the 2022 rate cycle do to long-dated option books?
   • How does a higher rate change your delta hedging cost?
6. 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?
7. 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?
8. 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?
9. 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?
10. 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?

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.