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. 001What is the difference between a forward and a future?Forwards and futuresCorephone / first roundSell-side sales and trading

   Say this

   Economically they are the same trade: an agreement today to transact at a fixed price on a future date. The differences are all plumbing, and the plumbing changes the risk. A future is exchange-traded, standardised and margined daily through a clearing house; a forward is a bilateral OTC contract with no daily cash movement and live counterparty risk.

   Then walk it

   1. Standardisation: a future has a fixed contract size, fixed delivery dates and a fixed deliverable grade. A forward is whatever the two parties write down, which is why corporates use forwards to hedge an exact exposure.
   2. Credit: the future faces a central counterparty, so your credit exposure is to the clearing house and it is collateralised every day. A forward leaves you exposed to the other side for the whole life of the trade.
   3. Cash flow: a future is marked to market daily and variation margin moves in cash, so your profit and loss is realised as you go. A forward settles once, at maturity.
   4. Liquidity: you close a future by trading out of it on the exchange. You close a forward by negotiating an unwind with the same counterparty, or by writing an offsetting trade and carrying both.
   5. The one real pricing difference falls out of the daily cash flows. Because margin is paid and received at whatever the short rate is, a future and a forward on the same asset only have identical fair prices if rates are deterministic.
   6. In practice the daily margin is the point. A hedge that is economically perfect can still kill you if the variation margin calls arrive before the offsetting gain does, which is what happened to Metallgesellschaft.

   Where candidates lose it

   Listing exchange-traded versus OTC and stopping there. The interviewer wants you to connect the plumbing to a risk: daily margin turns a paper loss into a cash call, and that liquidity risk is the reason the distinction matters on a desk.

   Expect next

   • So is the fair forward price ever different from the fair futures price?
   • Which would a corporate treasurer prefer for hedging a dollar payable, and why?
   • What happens to your hedge if you get margin-called and cannot fund it?
2. 002Price a one-year forward on a non-dividend-paying stock trading at 100, with rates at 5 percent. Show me why it has to be that number.Forwards and futuresCoretechnicalProp trading firms

   Say this

   105, or 105.13 if you compound continuously. The forward price is the spot price grown at the risk-free rate, and the reason is not a model — it is that any other number lets me build a portfolio that makes money with no risk and no capital.

   Then walk it

   1. The replication: borrow 100 at 5 percent, buy the stock today, hold it for a year. At maturity I own the stock and owe 105. So locking in delivery at 105 costs me nothing today.
   2. If the forward traded at 110, I do exactly that trade and simultaneously sell the forward at 110. In a year I deliver the stock, collect 110, repay 105, and keep 5 with zero risk and zero net investment. Everyone would do it until the price fell back.
   3. If the forward traded at 100, I reverse it: short the stock, invest the 100 at 5 percent, buy the forward. A year later I have 105, pay 100 for the stock, return the borrow, keep 5.
   4. So F equals S times e to the rt, or S times one plus r for annual compounding. Nothing about expected returns, volatility or the stock's beta enters it.
   5. Add dividends and they subtract, because holding the stock pays you something the forward does not: F equals S times e to the r minus q times t. On a commodity, storage cost adds and convenience yield subtracts.
   6. The honest caveat: the arbitrage assumes I can borrow at the risk-free rate, short freely and hold to maturity with no margin. In practice the borrow cost on a hard-to-short name, or a wide repo spread, opens a band around the theoretical price inside which no arbitrage is available.

   Where candidates lose it

   Reaching for expected stock returns. Candidates feel that a forward on a high-beta stock should be priced higher. It is not, because the forward is replicated by holding the stock itself, so the risk premium is already inside the spot price. Say the replication out loud before you say the formula.

   Expect next

   • Now add a 2 percent dividend yield.
   • What if you cannot borrow the stock to short it?
   • Does the answer change if I tell you the stock has a beta of 2?
3. 003What is cost of carry, and what do contango and backwardation tell you?Forwards and futuresCoretechnicalCommodities trading

   Say this

   Cost of carry is everything it costs or pays you to hold the physical asset instead of the forward: financing, plus storage and insurance, minus any yield you earn by owning it. Contango is when futures trade above spot, which is the normal state when carry is positive. Backwardation is futures below spot, and it tells you the market is short of the physical right now.

   Then walk it

   1. The identity: futures equals spot, plus financing, plus storage, minus convenience yield. Contango means financing and storage dominate. Backwardation means convenience yield dominates.
   2. Convenience yield is the value of having the barrel or the bushel in your hand. A refinery that runs out of crude stops; a refinery holding inventory does not. That option has value and it shows up as a negative carry term.
   3. So backwardation is a scarcity signal. It is the physical market saying it will pay a premium for delivery now rather than in three months, which is exactly what you see during a supply shock.
   4. Financial assets are almost always in contango, because there is no convenience yield in owning an index and storage is free. Equity index futures trade above spot by financing less dividends.
   5. The trading consequence is roll yield. A long position in a contango market sells the cheap near contract and buys the expensive far one every month, so you bleed. In backwardation, rolling pays you. This is why long commodity index products underperformed spot through most of the 2010s.
   6. The limit of the framework: you can arbitrage contango wider than full carry by buying spot and storing, but you cannot arbitrage backwardation, because you cannot borrow a barrel of oil that does not exist. That asymmetry is why backwardation can go to extremes and contango cannot.

   Where candidates lose it

   Defining contango and backwardation as shapes on a chart without naming convenience yield or roll yield. The two follow-ups are always 'why can't you arbitrage backwardation' and 'what does that do to a long ETF holder'. Have both ready.

   Expect next

   • Why can you arbitrage a contango that is too steep but not a backwardation?
   • What does the curve shape do to a long commodity ETF's return versus spot?
   • Crude went to a negative price in April 2020. How does that fit your framework?
4. 004Explain initial margin, variation margin and mark-to-market on a futures position.Forwards and futuresCoretechnicalClearing and risk

   Say this

   Initial margin is the good-faith deposit you post before you trade, sized to cover a bad one- or two-day move. Variation margin is the daily cash settlement of your profit and loss. Mark-to-market is the process that computes it: every evening the clearing house revalues your position at the settlement price and moves cash between accounts.

   Then walk it

   1. Initial margin is a risk number, not a price. Exchanges set it from a volatility model — SPAN or a value-at-risk approach — so it rises when the market gets wild, usually at the worst moment for the people holding losing positions.
   2. Variation margin is real cash, paid daily, and it is a settlement rather than collateral. Your loss leaves your account permanently; you do not get it back when the position recovers, you get it back through the next day's gain.
   3. Maintenance margin is the floor. Fall below it and you get a margin call to top back up to initial, and if you do not meet it the broker closes you out. The close-out is not discretionary and it does not wait for your view to be right.
   4. Worked example: one Nifty futures lot at 25,000 with a lot size of 25 is about 6.25 lakh of notional. At roughly 12 percent margin you post about 75,000. A 1 percent adverse move is 6,250 of variation margin, so 8 percent of your posted margin gone in a day on a 1 percent move.
   5. That leverage is the whole point of the question. Futures let you carry ten times your cash, which means a move that is trivial to a cash investor is existential to a futures position.
   6. The risk to name: this is a liquidity mechanism as much as a credit one. A hedger who is economically flat can still be forced out because the margin on the futures leg is cash today while the gain on the physical leg is months away.

   Where candidates lose it

   Calling variation margin collateral. It is a daily settlement of profit and loss, which is why futures have no accumulated credit exposure and forwards do. Also, give a number. An answer with no arithmetic reads as read rather than done.

   Expect next

   • What is the difference between variation margin and collateral posted under a CSA?
   • Why does initial margin rise exactly when you can least afford it?
   • How did the margin mechanism cause the nickel squeeze on the LME in 2022?
5. 011Draw me the payoff of a long call and a short put. They both make money when the stock goes up, so what is the difference?Options basicsCorephone / first roundProp trading firms

   Say this

   Both are long delta, but the shapes are opposite. The long call has limited loss and unlimited upside, a hockey stick that bends upward. The short put has limited upside capped at the premium and unlimited loss below the strike, a hockey stick that bends downward. One is long convexity, the other is short it.

   Then walk it

   1. Long call: pay premium, nothing happens below the strike, then you participate one for one above it. Maximum loss is the premium, maximum gain is unbounded.
   2. Short put: receive premium, keep it above the strike, then you lose one for one below it down to zero. Maximum gain is the premium, maximum loss is strike minus premium.
   3. Deltas agree at the money — both are roughly plus 0.5 — so if you only look at the first derivative they are the same trade. Everything that separates them is in the second derivative.
   4. Gamma is where they split. The call is long gamma, so your delta grows as you are proved right and shrinks as you are proved wrong. The short put is short gamma, so your delta grows as you are proved wrong. That is the same as saying the position gets worse the more it moves against you.
   5. Theta and vega split with it. The call pays theta and is long vega, so time hurts and a volatility spike helps. The short put collects theta and is short vega, so time pays and a volatility spike hurts, usually at the same moment as the price move.
   6. The trade expression is the honest version: buy the call when you want the move and are willing to pay for it, sell the put when you are happy to own the stock 10 percent lower and want to be paid to wait. They are the same direction and completely different risks.

   Where candidates lose it

   Saying they are equivalent because both are bullish. The interviewer is testing whether you think in gamma and not just delta. Say the words 'long convexity versus short convexity' and describe what happens in a gap move: the call owner's worst case is already paid, the put seller's is not.

   Expect next

   • Which one loses more in a 20 percent overnight gap down?
   • Combine a long call and a short put at the same strike. What do you own?
   • Which would you rather hold into an earnings print, and why?
6. 012Break an option price into intrinsic and time value. Can time value ever be negative?Options basicsCoretechnicalDerivatives operations

   Say this

   Intrinsic value is what you would get by exercising right now — max of zero and spot minus strike for a call. Time value is everything else, and it is the market paying for the chance that the option ends up further in the money. For a European option time value cannot be negative, but the quoted price of a deep in-the-money European option can sit below intrinsic against spot, and that confuses people.

   Then walk it

   1. A 100-strike call with the stock at 110 trading at 14 has 10 of intrinsic and 4 of time value. The 4 is the value of optionality: unlimited participation above, protected below.
   2. Time value is largest at the money and decays towards zero in both directions. Deep out of the money there is almost no chance of finishing in the money; deep in the money the option behaves like the stock and the insurance is nearly worthless.
   3. Time value cannot be negative for an American option, because you could exercise for intrinsic immediately, so intrinsic is a hard floor. That arbitrage is the whole reason for the floor.
   4. For a European option the floor is different, and this is the subtlety: the true lower bound is spot minus the discounted strike, not spot minus strike. A deep in-the-money European put on a high-rate currency can trade below its naive intrinsic value all day and no arbitrage exists, because you cannot exercise early to capture it.
   5. The other case that looks like negative time value is a large dividend before expiry. A deep in-the-money American call becomes worth exercising early to capture the dividend, which is why its time value collapses to nothing.
   6. The practical use of the split: it tells you what you are actually buying. If you pay 14 for 10 of intrinsic, you are paying 4 for the volatility view, and it is that 4 that theta eats, not the 10.

   Where candidates lose it

   Stating the naive intrinsic formula and asserting time value is always positive. The interviewer's follow-up is a deep in-the-money European put. Get the discounting into your lower bound — spot minus the present value of the strike — and you have answered the real question.

   Expect next

   • Show me the lower bound for a European put and why it involves discounting.
   • Where is time value largest, and why?
   • How does a big dividend change the picture for an American call?
7. 016List the inputs to an option price and tell me which way each one moves a call and a put.Options basicsCorephone / first roundDerivatives operations

   Say this

   Six inputs: spot, strike, time, volatility, the risk-free rate and dividends. Spot up helps calls and hurts puts, higher strike does the reverse. More time and more volatility help both. Higher rates help calls and hurt puts. Dividends hurt calls and help puts.

   Then walk it

   1. Volatility is the only input that raises both, and that is the single most important line in the answer. Options are convex payoffs, so a wider distribution increases expected payoff without increasing the downside, which is already capped at the premium.
   2. Time works the same way for both, with one exception: a deep in-the-money European put can be worth less with more time, because the discounting of the strike dominates the extra optionality.
   3. Rates: a higher rate lowers the present value of the strike you will pay, which helps the call. For a put you are receiving the strike, so discounting it harder hurts. Another way to say it is that a call is a leveraged long, so financing cost is baked into it.
   4. Dividends reduce the forward. Lower forward means lower calls and higher puts. This is why you cannot price an equity option off spot without a dividend forecast, and why dividend risk is a real trading exposure on a long-dated book.
   5. Magnitudes matter more than signs. On a one-month ATM option, one volatility point typically moves the price far more than a 25 basis point rate change. Rates and dividends only dominate on long-dated structures.
   6. The check I would do out loud: only volatility and time raise both a call and a put, and everything else is a tug of war. If you can state that, you have not memorised a table, you have understood the shape.

   Where candidates lose it

   Reciting the table without being able to explain why volatility raises both. If you cannot say 'the payoff is convex and the downside is capped at the premium', the interviewer will assume you learned a grid rather than a mechanism.

   Expect next

   • Why does volatility raise both a call and a put?
   • When is more time worth less for a put?
   • Which input would you least trust in a real pricing run?
8. 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?
9. 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?
10. 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?

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.