Derivatives Foundation interview preparation

The full derivatives syllabus from no-arbitrage pricing through the Greeks, the volatility surface, swaps, CDS and clearing, plus the Indian index-options market. Every question is either traced to a named firm from a public candidate report, or tagged at desk level when we could not trace it - we do not invent attributions.

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100 questions, mapped to the firms that asked them

Questions
100
Traced to a firm
29
Firms
19
Updated
September 2026
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All firmsMorgan Stanley4Nomura4Akuna Capital2Amundi2HSBC2PIMCO2Bank of America1Barclays1Citadel1DRW1Goldman Sachs1Jane Street1Millennium Management1Mizuho1Old Mission Capital1RBC Capital Markets1Scotiabank1UBS1Wells Fargo Securities1
Topic
All topicsForwards and futures10Options basics8Option pricing7The Greeks10Volatility7Option strategies9Swaps and rates7Credit derivatives4Market structure and clearing6Indian derivatives8Trading and markets9Brainteasers6Fit9
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  1. 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.