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.
100 questions, mapped to the firms that asked them
- Questions
- 100
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- Updated
- September 2026
088Compute the probability and then bet on whether you draw another black stone.CitadelQuantitative Trading · New York · 2025
Say this
Two parts, and the second is the real test. Compute the conditional probability by Bayes, updating on what has already been drawn, then price a bet at odds that give you an edge and size it so a wrong answer does not end you. Most candidates get the arithmetic and then bet like the arithmetic is certain.
Then walk it
- Set up the inference properly. If the composition of the bag is unknown, drawing a black stone is evidence about the composition, so you update over the possible bags rather than treating the draw as independent.
- The classic version: two urns, or a bag with an unknown mix, and a black draw raises the posterior weight on black-heavy compositions. With no replacement, conditioning on the draws already made is essential — a common error is to compute the unconditional probability and hand it over.
- Worked case to show the mechanism: three stones, one known black, one known white, one unknown with equal odds. You draw black. Posterior probability the unknown is black rises to two thirds, so the next draw being black is now more likely than the prior suggested. That is the Bayes step they are checking.
- Then the betting step, which is where the interview is decided. If my computed probability is 0.6, I want odds better than 3 to 2 to have an edge. I would quote a market rather than accept theirs — say I am a buyer at 55 and a seller at 65 — because that is the trading answer rather than the maths answer.
- Then sizing. Kelly says stake a fraction equal to the edge over the odds, and in an interview I would bet a small multiple less than Kelly, because my probability estimate is itself uncertain and Kelly assumes it is not.
- And I would say the honest caveat: my probability depends on my prior over the bag's composition, and if I have the prior wrong my edge is imaginary. So I would take the bet at odds that leave room for my model being wrong, which means demanding better than fair odds rather than exactly fair ones.
Where candidates lose it
Computing the probability and then accepting whatever odds are offered. Citadel is watching whether you distinguish your estimate from your confidence in it, quote a two-way market, and size below Kelly because the input is uncertain. The maths is the easy half.
Expect next
- What is your prior over the bag's composition, and how much does the answer depend on it?
- What odds do you need to take the bet?
- How much would you stake, and why not more?
Reported by candidates at Citadel (Quantitative Trading, New York, 2025). Source: Wall Street Oasis.
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.