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. 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?
2. 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?
3. 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?
4. 017An option buyer has limited loss and unlimited gain. Why does anyone take the other side?Options basicsIntermediatetechnicalProp trading firmsMarket making

   Say this

   Because the seller gets paid, and on average the premium is more than the payout. Buyers are buying insurance and insurers earn a premium for bearing tail risk. The payoff shape is asymmetric but the expected value is not the same as the shape.

   Then walk it

   1. The empirical fact first: implied volatility exceeds subsequent realised volatility most of the time, in most markets. That wedge — the variance risk premium — is the seller's edge, and it is typically a couple of volatility points on index options.
   2. Why it exists: investors are structurally short the market and want protection, and protection pays off precisely when the rest of the portfolio is losing. That correlation makes it worth paying above fair value for, exactly like fire insurance.
   3. So the seller is not stupid, they are an insurer. The trade works the way insurance works: small steady income, occasional large loss, positive expectancy if priced right and sized right.
   4. The real risk is not the expectancy, it is the path. A short option book has negative skew, so it grinds up and then gives back years of premium in a week. February 2018 wiped out short-vol products in a single session on a move that was not even a large one by historical standards.
   5. Which is why sellers hedge. A market maker is not taking a directional view; they sell the option, delta hedge it, and try to earn the spread between implied and realised volatility. The naked seller and the hedged seller are completely different businesses.
   6. The honest framing: buyers pay for convexity and certainty of maximum loss, sellers earn a premium for supplying it. Neither is a free lunch, and the seller's version has a fatter left tail than a Sharpe ratio will show you.

   Where candidates lose it

   Answering 'because most options expire worthless'. That is a statistic about frequency, not about expected value, and an interviewer will immediately ask whether you would sell 1-in-1000 lottery tickets at any price. Name the variance risk premium and the negative skew of the seller's return.

   Expect next

   • So would you rather be systematically long or short volatility?
   • What happened to short-volatility products in February 2018?
   • How does a market maker sell options without taking a directional view?

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.