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. 019Explain how you would price an option.Option pricingIntermediatetechnicalDRWQuantitative Trading · Chicago · 2025

   Say this

   By replication, not by forecasting. I build a portfolio of the underlying and cash that reproduces the option's payoff in every state, and the option has to cost what that portfolio costs, or there is an arbitrage. Everything else — binomial trees, Black-Scholes, Monte Carlo — is just machinery for doing that in different settings.

   Then walk it

   1. Start with the simplest case, one period, two states. If the stock goes to 110 or 90 and I hold a 100-strike call, I can find a number of shares and a cash amount that pays exactly 10 in the up state and 0 in the down state. That portfolio's cost today is the option price.
   2. The striking thing is that the real probabilities never appear. They cancel, because I am hedging rather than betting. That is why the answer is the same whether you think the stock is going up or down, and it is the single most important idea in the subject.
   3. Equivalently, discount the expected payoff under the risk-neutral measure, where the underlying is assumed to drift at the risk-free rate. Same number, and easier to compute.
   4. Take that to many small steps and it becomes the binomial tree; take the limit and you get Black-Scholes, a closed form for a European option on a lognormal underlying. For a path-dependent payoff you simulate instead, and for an American feature you need a tree or a backward induction so you can test early exercise at every node.
   5. Then the practical part, which is where the real work is. The only unobservable input is volatility, so in practice the model is run backwards: I take the market price and solve for implied volatility, then trade the volatility rather than the price.
   6. And the limitation up front: replication assumes continuous hedging with no transaction costs and no gaps. In the real world I hedge discretely and pay spread, so my realised profit and loss is implied minus realised volatility, less the cost of hedging — which is why a theoretically fair option can still lose money.

   Where candidates lose it

   Leading with the Black-Scholes formula. DRW and every prop shop are asking whether you understand replication and risk-neutral valuation, not whether you can recall a closed form. If you cannot explain why the real-world probability drops out, you have not answered the question.

   Expect next

   • Why do the real-world probabilities disappear?
   • Now price it in a two-step tree and tell me what changes.
   • What is the one input you cannot observe, and what do you do about it?

   Reported by candidates at DRW (Quantitative Trading, Chicago, 2025). Source: Wall Street Oasis.

2. 021Explain Black-Scholes.Option pricingIntermediatetechnicalGoldman SachsWealth Management · Zurich · 2025

   Say this

   It is a closed-form price for a European option, derived from the insight that an option can be perfectly hedged with the underlying. If you can hedge it, its price cannot depend on your view or on risk appetite — only on volatility, time, rates and the distance to the strike. The formula is the answer to that hedging argument, not a forecasting model.

   Then walk it

   1. The derivation in one line: build a portfolio that is long the option and short delta of the stock, and the random term cancels. What is left grows at the risk-free rate, and imposing that gives a differential equation whose solution is the formula.
   2. In words, the call price is the discounted expected payoff under a lognormal distribution: spot times N of d1, less the discounted strike times N of d2. N of d2 is roughly the risk-neutral probability of finishing in the money; spot times N of d1 is the expected value of the stock you receive if you do.
   3. So the inputs are spot, strike, time, rate, dividend and volatility. Five are observable. Volatility is not, which means in practice the formula is used inverted — you put the market price in and read the implied volatility out.
   4. That is its real job on a desk. Nobody believes the assumptions. It is a translation device that turns option prices in dollars into a single comparable number in volatility terms, so you can compare a one-month Nifty option with a two-year S&P option on the same axis.
   5. For a private client I would put it plainly: the formula prices the insurance. The further out of the money, the shorter the time and the calmer the market, the cheaper the insurance — and the fair price of that insurance is what the model gives you.
   6. The limitation, said before being asked: it assumes constant volatility and continuous, costless hedging, and it assumes prices do not jump. All three are false, which is why the market charges a different implied volatility for every strike. That pattern is the volatility smile, and it is the market's way of correcting the model.

   Where candidates lose it

   Writing out the formula and naming the terms without ever saying why the hedging argument removes the drift. And on a wealth management desk specifically: if you cannot restate it in one plain sentence about the price of insurance, you have failed the actual test, which was whether you can explain it to a client.

   Expect next

   • Which assumption fails worst in practice?
   • What does N of d2 actually represent?
   • If nobody believes the assumptions, why is it still on every screen?

   Reported by candidates at Goldman Sachs (Wealth Management, Zurich, 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.