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. 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?
2. 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?
3. 013What does at the money mean exactly — is it the spot or the forward?Options basicsIntermediatetechnicalEquity derivativesFX derivatives

   Say this

   It depends on who is speaking, and the difference matters. Retail and screens mean at the money spot, strike equals the current price. A derivatives desk usually means at the money forward, strike equals the forward price, because that is the strike where a call and a put have the same value and the same absolute delta.

   Then walk it

   1. Moneyness in general: in the money means exercising now has value, out of the money means it does not, at the money means the strike sits at the reference price.
   2. The forward is the honest reference, because an option's fair value is driven by the forward, not the spot. Put-call parity is written against the discounted forward, so at the money forward is the strike where call and put prices coincide.
   3. At the money forward is also the delta-neutral strike in the sense that matters for a straddle: an ATM-forward straddle starts with roughly zero delta, while an ATM-spot straddle does not when rates or dividends are non-trivial.
   4. How big is the gap? On a one-month index option with rates at 5 percent and a 1.5 percent dividend yield, the forward is about 0.3 percent above spot. Trivial. On a two-year option, or a high-carry currency like the rupee where the forward points are 4 to 5 percent a year, it is a different strike entirely.
   5. FX desks quote off delta rather than strike for exactly this reason: 25-delta risk reversal, 10-delta butterfly. Delta is unambiguous across carry regimes in a way that 'at the money' is not.
   6. The practical answer on a desk: if someone says ATM I ask which one, especially on a long-dated or high-carry underlying. The confusion is a real source of trade breaks and mispriced quotes, and it is cheap to eliminate by asking.

   Where candidates lose it

   Answering just 'strike equals spot'. That answer is fine for a one-week Nifty option and wrong for a two-year USD/INR option where the forward is 10 percent away. Volunteer the forward definition and say when the two diverge enough to matter.

   Expect next

   • At which strike do a call and a put have the same price?
   • Why do FX desks quote by delta instead of by strike?
   • For a two-year USD/INR option, how far is ATM forward from ATM spot?
4. 014State put-call parity and tell me exactly what arbitrage enforces it.Options basicsIntermediatetechnicalProp trading firmsMarket making

   Say this

   Call minus put equals spot minus the present value of the strike, for European options on the same underlying, strike and expiry. What enforces it is the conversion and reversal trade: long call, short put, short stock is a riskless package that must be worth the discounted strike, so any deviation is free money.

   Then walk it

   1. Write it as C minus P equals S minus K times e to the minus rt, and subtract dividends from S if the stock pays them.
   2. The intuition in one line: a long call plus a short put at the same strike is a synthetic long forward. It has a delta of one and pays off spot minus strike at expiry regardless of direction, so it must cost the same as a forward.
   3. The enforcing trade is a conversion. Buy the stock, buy the put, sell the call. Whatever happens, you deliver at K, so you have bought a zero-coupon bond. If you can assemble that package for less than the discounted strike, you have picked up risk-free basis points.
   4. The reversal is the mirror: short stock, short put, long call. This is where the constraint usually breaks in practice, because it needs a stock borrow.
   5. So the deviations you see on a screen are almost never mispricings. Hard-to-borrow names show a persistent parity gap that is exactly the borrow cost, which is why the options market is where you read a stock's true short fee. Discrete dividends, early exercise on American options and financing spreads open the rest of the band.
   6. The reason to know this cold: parity is the only completely model-free relationship in options. It holds without any assumption about volatility or distribution, which makes it the one thing you can check a screen against.

   Where candidates lose it

   Reciting the formula without the replication. The question is 'what enforces it', so the answer is a trade: conversion and reversal. And do not claim a parity gap on a hard-to-borrow name is arbitrage — it is the borrow fee, and saying so is what separates someone who has traded from someone who has read.

   Expect next

   • You see a 40 cent parity violation on a small cap. Is that free money?
   • Does parity hold for American options?
   • How would you back out the implied borrow cost from option prices?
5. 015When would you exercise an American option early?Options basicsIntermediatetechnicalEquity derivativesMarket making

   Say this

   Almost never for a call on a non-dividend-paying stock, and reasonably often for a deep in-the-money put. The general rule is that you exercise early when the interest or dividend you pick up is worth more than the optionality you throw away.

   Then walk it

   1. Never for a call on a stock that pays no dividend. Exercising means paying the strike early, so you lose the interest on it, and you give up the downside protection the option gave you for free. It is always better to sell the option than exercise it.
   2. The exception is a dividend. If the stock pays 3 dollars tomorrow and your deep in-the-money call has less than 3 of remaining time value, exercise the day before the ex-date to capture the dividend. That is why open interest in deep ITM calls collapses into an ex-date.
   3. Puts are different, because exercising a put brings cash in early. A deep in-the-money put on a stock near zero is essentially a claim on the strike, and holding it means forgoing interest on that cash. With rates at 5 percent that is a real cost, so early exercise becomes optimal.
   4. There is a critical price for the put below which immediate exercise beats holding, and it rises with the interest rate and falls with volatility. Zero rates make early exercise on puts nearly irrelevant, which is why the whole topic went quiet from 2010 to 2021 and came back with rate hikes.
   5. So American calls on non-dividend stocks are worth exactly the European price; American puts are worth strictly more, and the difference is the early exercise premium.
   6. The desk-level version: assignment risk. If you are short a deep ITM call into an ex-date you can be assigned, which turns you short stock and short the dividend overnight. Managing that calendar is a daily job on an equity derivatives book.

   Where candidates lose it

   Answering 'never, because optionality has value' and stopping. That is right for the textbook call and wrong for a dividend-paying stock and wrong for puts. Split the answer into calls-with-dividends and puts-with-interest, and name assignment risk.

   Expect next

   • Where does the critical price for a put sit and what moves it?
   • If you are short a deep in-the-money call into an ex-date, what is your risk?
   • Why did early exercise stop mattering between 2010 and 2021?
6. 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?
7. 018Give me the bounds on a European call price without using any model.Options basicsHardtechnicalProp trading firmsMarket making

   Say this

   The price sits between max of zero and spot minus the discounted strike, and spot itself. Below that lower bound or above spot, there is a static arbitrage that does not depend on any model, any distribution or any volatility assumption.

   Then walk it

   1. Upper bound: a call can never be worth more than the stock, because the most it ever delivers is the stock, and only after you pay the strike. If a call traded above spot I would sell the call, buy the stock, and be guaranteed a profit.
   2. Lower bound: the call must be worth at least spot minus the present value of the strike. If it were cheaper, I buy the call, short the stock, invest the proceeds. At expiry I exercise or buy in the market, and I have locked in the gap risk-free.
   3. Note the discounting in the lower bound. Naive intrinsic, spot minus strike, is the wrong floor for a European option, and getting that right is the point of the question.
   4. Beyond bounds there are model-free shape constraints. Call prices must be decreasing in strike, and convex in strike — the butterfly constraint. A violation means a butterfly spread with a negative cost and a non-negative payoff.
   5. And calendar monotonicity: a longer-dated call cannot be cheaper than a shorter-dated one at the same strike, for European options on a non-dividend payer.
   6. These constraints are what production systems police. An arbitrage-free volatility surface is defined by exactly these inequalities, and a fitted surface that violates butterfly convexity will let a trader book a position the risk system prices as free money. That is why the checks run before the model does.

   Where candidates lose it

   Giving spot minus strike as the lower bound. The discounting is the whole test. And the strong follow-up is the convexity-in-strike condition — if you can name the butterfly argument, you have said something most candidates cannot.

   Expect next

   • Why must call prices be convex in strike?
   • Show me the arbitrage if they are not.
   • How do those constraints get used when fitting a volatility surface?

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.