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. 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?

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.