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?

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.