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. 024When would you use Monte Carlo rather than a closed form or a tree, and what goes wrong with it?Option pricingHardtechnicalQuant tradingStructured products

   Say this

   Monte Carlo when the payoff is path-dependent or there are several underlyings, because both break closed forms and blow up a tree. Its weaknesses are slow convergence, difficulty with early exercise, and the fact that it will happily give you a confident answer to a badly specified model.

   Then walk it

   1. Use it for Asian options where the payoff depends on an average, barriers where it depends on whether a level was touched, and baskets or worst-of structures where the dimensionality kills a tree.
   2. A tree is fine up to two or three factors and is the right tool when you need early exercise, because you can compare continuation against exercise at every node. Monte Carlo runs forward, so American features need something like Longstaff-Schwartz regression, which is doable but adds its own error.
   3. Convergence is the headline cost. The standard error falls as one over root N, so cutting your error in half needs four times the paths. Getting a Greek to three decimal places on a complex payoff is genuinely expensive in compute.
   4. The fixes: antithetic variates, control variates where you simulate a similar payoff with a known closed form and correct by the difference, and quasi-random low-discrepancy sequences. A good control variate is often worth more than a hundred times the paths.
   5. Discretisation bias is the subtle one. Barriers are systematically mispriced by daily time steps, because the simulated path can cross and return between observations. You either use a fine grid, a Brownian bridge correction, or you accept a bias you can measure.
   6. And the real danger, which is not numerical at all: the simulation is only as good as the process you assumed. A Monte Carlo on a geometric Brownian motion gives you a precise answer to a model that has no jumps in it. Precision is not accuracy, and a tight confidence interval around a wrong model is how structured products get mispriced.

   Where candidates lose it

   Treating this as a pure numerical-methods question. The answer that lands names the American-exercise difficulty, gives a variance reduction technique by name, and finishes on model risk — a narrow confidence interval around the wrong dynamics.

   Expect next

   • How would you handle an American feature in a simulation?
   • Name a variance reduction technique and say what it buys you.
   • How would you compute a Greek in a Monte Carlo without four times the runtime?
2. 025How would you price and risk-manage a down-and-in barrier put?Option pricingHardsuperdayStructured productsEquity derivatives

   Say this

   Price it off the vanilla surface using the in-out parity relationship, then adjust for the fact that a barrier is enormously sensitive to skew and to the dynamics near the barrier. The hard part is not the price, it is that delta and gamma become discontinuous at the barrier, so the hedge is unstable exactly where you need it.

   Then walk it

   1. Start with the identity: a down-and-in put plus a down-and-out put with the same strike and barrier equals a vanilla put. That gives you a sanity check and lets you price the harder one from the easier one.
   2. The naive route is a closed form under Black-Scholes with constant volatility. It is wrong in a specific direction, because a barrier payoff depends on the whole distribution near the barrier, which is precisely where the skew lives. You have to price it on a model calibrated to the smile — local volatility at minimum, stochastic volatility if the book is big.
   3. Then the risk. Just above the barrier the knock-in has almost no value; just below it is a live vanilla put. So delta jumps, and gamma is effectively infinite at the barrier. Hedging through it means trading a large amount of stock in a market that is already moving.
   4. That discontinuity is why desks apply a barrier shift — pricing as if the barrier were slightly further away — to build in the cost of the hedging error. It is a reserve dressed up as a model input, and it should be sized to the liquidity of the underlying.
   5. Pin risk near expiry compounds it. A barrier close to spot in the last days combines the discontinuity with almost no time to hedge, which is when the losses actually happen.
   6. The commercial context worth naming: these sit inside autocallable notes sold to retail and private banking clients, which is where most barrier risk in the world lives. The client is short a knock-in put and often does not know it, and in a sharp drawdown the whole book knocks in at once — the dealers end up with correlated, one-way risk, which is exactly what happened to Korean autocallable books in early 2020.

   Where candidates lose it

   Pricing it with a Black-Scholes closed form and stopping. The interviewer wants the two hard parts: skew dependence, because a barrier reads the wing of the distribution, and hedge instability at the barrier. Naming the barrier shift shows you have seen how a desk actually handles it.

   Expect next

   • Why is a barrier option so much more skew-sensitive than a vanilla?
   • How do you hedge through the barrier in an illiquid name?
   • Where does barrier risk actually sit in the market, and why does it correlate?

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.