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. 032You are long a one-month at-the-money straddle at 20 volatility. Under what conditions do you make money?The GreeksHardtechnicalVolatility tradingProp trading firms

   Say this

   If you delta hedge it, you make money when realised volatility over the month exceeds 20. If you do not hedge it, you make money only if the stock finishes far enough from the strike to cover the combined premium, which is a much harder bar. Those are two completely different trades and the distinction is the answer.

   Then walk it

   1. Unhedged: you paid, say, 4.6 percent of spot for the straddle, so the stock must move more than 4.6 percent in either direction by expiry. Direction does not matter, distance does — and crucially, the path does not help you at all.
   2. Hedged: you rebalance delta daily and harvest the moves. Now the path is everything. A stock that oscillates 2 percent a day and finishes flat pays you handsomely while the unhedged straddle expires worthless.
   3. The break-even in the hedged case is the realised-versus-implied comparison. Twenty percent annualised is about 1.25 percent a day. If the stock is genuinely moving more than that, gamma harvesting beats the theta you bleed.
   4. Arithmetic to make it concrete: 20 volatility on a 30-day option costs roughly 20 times root of 30 over 365, about 5.7 percent of spot for the straddle at a 0.8 scaling — call it 4.5 to 5 percent. So you need about a 5 percent move unhedged, or sustained daily moves above 1.25 percent hedged.
   5. Two things can still beat you even if you are right about realised volatility. Implied volatility can fall, which hits your vega mark immediately, and the realised moves can arrive as one gap rather than as daily oscillation — a gap gives you the payoff once rather than repeatedly.
   6. The honest limitation: long gamma is not a free option on chaos. You pay theta every day, and in a market that grinds quietly for three weeks and then explodes on day 25, you may have been stopped out of the position before the payoff arrives. Sizing and horizon matter as much as the volatility view.

   Where candidates lose it

   Answering only the unhedged version — 'the stock has to move more than the premium'. Any interviewer on a volatility desk is testing whether you know the hedged straddle is a bet on realised variance and the unhedged one is a bet on the terminal price. Say both, and say which one you meant.

   Expect next

   • What if the stock moves 5 percent but in one overnight gap?
   • You were right about realised volatility and still lost money. How?
   • Would you rather own the straddle or a variance swap for this view?
2. 033What is pin risk, and how do you manage a large position into expiry?The GreeksHardsuperdayMarket makingEquity derivatives

   Say this

   Pin risk is the risk that the underlying closes almost exactly at your strike, so you do not know whether you will be assigned. You go into the weekend not knowing whether you are flat or hugely long or short stock, and by the time you find out, the market has moved. It is a settlement risk, not a pricing risk.

   Then walk it

   1. The mechanism: you are short 1,000 at-the-money calls and the stock settles at the strike. If they are exercised you are short 100,000 shares; if not you are flat. You cannot hedge a position you do not know you have.
   2. Gamma explodes into expiry for at-the-money options, so your delta swings between near zero and near one on tiny price moves. The hedge you put on at 3:29 can be completely wrong at 3:30.
   3. How desks manage it: reduce the at-the-money position before the last hour, close out rather than let it go to assignment, and avoid being short large size at a strike where open interest is concentrated.
   4. Cash settlement solves it. Indian index options — Nifty and Bank Nifty — are cash-settled on a weighted average of the last half hour, so there is no assignment ambiguity. But cash settlement creates a different problem: settlement-price manipulation risk, which is exactly why SEBI moved to a VWAP of the closing period rather than a closing print.
   5. That closing-period mechanic is why you see the volume spike into the last thirty minutes on expiry day in India. Large positions need to hedge against the same average that determines their settlement.
   6. The broader lesson to volunteer: pin risk is one of a family of expiry-day operational risks — assignment, settlement price, and the exercise cut-off being after the market closes so you can be assigned on news that broke post-close. These are the risks that lose money on well-hedged books, and they are the reason expiry-day process discipline exists.

   Where candidates lose it

   Explaining pin risk as a pricing phenomenon. It is an operational and settlement risk, and the answer should include what you do about it — reduce size, close rather than assign, and know whether your contract is cash or physically settled. Naming the Indian cash-settlement mechanic shows local knowledge.

   Expect next

   • How does cash settlement change the problem, and what new problem does it create?
   • Why does volume spike in the last half hour of an Indian expiry day?
   • You are assigned on news that broke after the close. What is your exposure?
3. 034Beyond the five standard Greeks, which second-order sensitivities actually get managed?The GreeksHardsuperdayExotics tradingVolatility trading

   Say this

   Vanna and volga, mainly. Vanna is how delta changes when volatility moves, and it is the same thing as how vega changes when spot moves. Volga is the convexity of vega in volatility. On any book with skew — which is every real book — those two determine whether your vega hedge holds up.

   Then walk it

   1. Vanna matters because implied volatility and spot are correlated. In equities the correlation is strongly negative: spot falls, volatility rises. So a position with vanna gets a second hit at exactly the moment the first one arrives, and the two are not independent risks.
   2. Volga is the reason a vega-neutral book is not volatility-neutral for large moves. Wing options have positive volga, so a long-wings, short-body position is vega-flat and still profits from a volatility spike. Every risk reversal and butterfly carries it.
   3. Charm is the decay of delta with time, and it matters near expiry and on barrier books, where your delta changes overnight without the market moving at all.
   4. The FX market prices in these terms directly. The vanna-volga approach prices an exotic by taking the Black-Scholes value and adding the cost of hedging its vanna and volga with the market-quoted risk reversal and butterfly. It is not elegant, but it reproduces market prices better than a naive smile interpolation.
   5. How desks actually manage it: a risk report showing profit and loss under a grid of spot and volatility shocks, rather than a list of Greeks. The grid captures vanna and volga implicitly and does not require you to trust a Taylor expansion.
   6. And the limitation: these are still local derivatives. A scenario grid with a minus 20 percent spot and plus 30 volatility shock tells you more than any second-order Greek, because in a real dislocation the correlations you assumed break and the higher-order terms are no longer small.

   Where candidates lose it

   Rattling off exotic Greek names without connecting them to spot-volatility correlation. Vanna matters in equities specifically because the skew is one-sided and spot and volatility are negatively correlated. If you cannot say that, the names are decoration.

   Expect next

   • Why is vanna so important in equities specifically?
   • How can a vega-neutral book still profit from a volatility spike?
   • Would you rather have a Greek report or a scenario grid, and why?
4. 038Why does the volatility smile exist?VolatilityHardtechnicalVolatility tradingEquity derivatives

   Say this

   Because the real distribution of returns is not lognormal, and Black-Scholes assumes it is. The market corrects the model by charging a different implied volatility per strike. Fat tails make both wings expensive relative to the body, and in equities negative skewness makes the downside wing much more expensive than the upside — that asymmetry is why the smile is really a smirk.

   Then walk it

   1. Mechanically, implied volatility is just the number you plug into a wrong formula to get the right price. If the true distribution has more mass in the tails than a lognormal, you need a higher volatility input to reproduce the market price of a wing option.
   2. Two distinct effects. Kurtosis — fat tails on both sides — lifts both wings and gives you a symmetric smile, which is roughly what you see in FX on a major pair. Negative skew lifts the left wing only, which is what you see in equity indices.
   3. Why equities are skewed: leverage means falling equity raises the debt-to-equity ratio and therefore the volatility of the remaining equity. Crashes are correlated across names while rallies are not, so index skew is steeper than single-stock skew. And there is a real demand effect — everyone wants to buy puts and sell calls.
   4. So the skew is not purely a distributional statement. Part of it is the price of insurance, which means part of the steepness is a risk premium rather than a forecast of the crash probability.
   5. The models that generate it endogenously are stochastic volatility, where negative spot-volatility correlation produces skew, and jump-diffusion, where a downward jump component produces exactly the left-wing fat tail. Local volatility fits the observed surface exactly but has unrealistic dynamics.
   6. One thing to be careful about: the skew steepened permanently after the 1987 crash. Before it, index implied volatility was roughly flat across strikes. So a large part of the smile is a learned behaviour about crash risk, not a timeless property of returns — which means it can reprice when beliefs change.

   Where candidates lose it

   Explaining the smile as fat tails only. In equities the dominant feature is skew, not kurtosis, and it has three causes — leverage, correlated crashes, and put demand. Also worth saying that the shape post-dates 1987, because it makes clear you understand it is a market convention as much as a statistical fact.

   Expect next

   • Why is index skew steeper than single-stock skew?
   • What did the 1987 crash change about the surface?
   • Which model would you use if you had to price a barrier off this surface?
5. 042If you want pure exposure to volatility, why use a variance swap rather than a straddle?VolatilityHardsuperdayVolatility tradingHedge funds

   Say this

   Because a straddle's exposure to volatility changes as spot moves away from the strike, and a variance swap's does not. The variance swap pays realised variance minus a fixed strike, with constant exposure regardless of where spot goes. It is the clean instrument; the straddle is a path-dependent approximation to it.

   Then walk it

   1. The straddle problem: gamma and vega are concentrated at the strike. Spot moves 10 percent and your straddle is now a directional position with little volatility exposure left, so you have to keep re-striking to maintain the view.
   2. A variance swap pays the notional times realised variance less the strike variance. No re-striking, no delta to manage in the same way, and the payoff is linear in variance by construction.
   3. How it exists at all: you can replicate it statically with a portfolio of options across all strikes weighted by one over strike squared, plus a dynamic futures hedge. That replication is why it can be quoted without a model.
   4. The catch, and it is a big one: variance is the square of volatility, so the payoff is convex in volatility. A short variance position loses quadratically. At a 20 strike, realised of 60 is nine times the variance, not three times — which is how short variance books were destroyed in 2008.
   5. Which is why the market largely moved to capped variance swaps after 2008, typically capped at 2.5 times the strike. A volatility swap — linear in volatility rather than variance — is the other answer, but it needs a model to price because it is not statically replicable.
   6. And one practical limitation: the replication needs a continuum of strikes. In reality you have a finite strike grid, so a genuine jump produces a payoff the replicating portfolio did not deliver. Single-stock variance swaps on names with takeover risk are notorious for this, which is why dealers price them wide or refuse them.

   Where candidates lose it

   Saying 'variance swaps give pure volatility exposure' without naming the convexity. Variance is the square, so short positions lose non-linearly, and the 2008 blowups plus the move to capped structures are the evidence. That detail is what makes the answer sound like it came from a desk.

   Expect next

   • So why did the market start capping them?
   • What is the difference between a variance swap and a volatility swap?
   • Why are single-stock variance swaps dangerous for a dealer?
6. 050You think the skew is too steep. How do you trade that, and what are you exposed to?Option strategiesHardsuperdayVolatility tradingExotics trading

   Say this

   Sell the risk reversal: sell the out-of-the-money put and buy the out-of-the-money call, in vega-neutral ratio, and delta hedge. That is a direct bet that the put wing is expensive relative to the call wing. What you are exposed to is a crash, because you have sold exactly the insurance that pays off in one.

   Then walk it

   1. Structure: short the 25-delta put, long the 25-delta call, sized so the two vegas offset, then hedge the residual delta with futures. Now you are flat level of volatility and short skew.
   2. Why skew can be too steep: it contains a risk premium as well as a distributional forecast. After a shock the put wing often stays bid for months on hedging demand long after the realised tail risk has faded, which is when the trade has an edge.
   3. The exposures. You are short vanna, so a selloff that lifts volatility hits you twice. You are short the left tail outright, so a genuine crash is a large loss, not a marked one. And you have positive carry in a calm market, which is the seductive part.
   4. This is a classic picking-up-pennies trade, so the sizing rule matters more than the view: define the loss in a minus 20 percent, plus 25 volatility scenario before you put it on, and make that number survivable.
   5. The alternative expression is a put spread instead of an outright short put — sell the 25-delta put and buy the 10-delta. You keep most of the skew edge and cap the tail. You give up some premium and the trade becomes about the slope between two wing strikes rather than the whole wing.
   6. And the honest historical note: skew has been persistently 'too steep' on most measures since 1987, and shorting it has been profitable on average and career-ending in specific years. The trade is a volatility-of-volatility exposure as much as a skew view, and any backtest that does not include 2008, 2018 and 2020 is not telling you about the risk.

   Where candidates lose it

   Proposing a naked short put as the skew trade. The interviewer wants vega-neutral construction, a delta hedge, and an explicit statement of the tail. And you should volunteer the put-spread version, because capping the wing is what makes the trade institutional rather than reckless.

   Expect next

   • How do you make it vega-neutral, and why does that matter?
   • What does vanna do to you in a selloff?
   • Why has skew been persistently steep since 1987?
7. 051Structure a product for a client who wants equity upside with capital protection. What do you build and what are you not telling them?Option strategiesHardcase studyStructured productsWealth management

   Say this

   A zero-coupon bond plus a call option: put most of the money in a bond that matures at par to guarantee the principal, and spend the rest on index calls for the upside. What I would not hide is that the participation rate is set by how much premium the bond leaves over, that you forgo dividends, and that the protection is only as good as the issuer's credit.

   Then walk it

   1. The build on 100 rupees with a five-year horizon and rates at 7 percent: a zero-coupon bond maturing at 100 costs about 71. That leaves 29, less the dealer's margin, to buy five-year at-the-money index calls.
   2. If those calls cost 20, the participation rate is about 130 percent of the index move; if implied volatility is high and they cost 35, you cannot even get to 100 percent participation, and the structure has to be cheapened with a cap or a knock-out.
   3. So participation is a residual, not a feature. High rates make protection cheap and structures generous; low rates and high volatility make them mean. That is the single most useful thing to explain to a client who is comparing two notes.
   4. The things a sales deck buries: you receive no dividends over five years, which on an equity index is a substantial forgone return; the capital protection is an issuer obligation, not a segregated guarantee, which is what made 2008 Lehman notes worthless; and secondary liquidity is at the dealer's bid.
   5. The cheapening devices to watch for are where the real risk is: a knock-in put that turns protection into leveraged downside, an autocall that ends the trade just as it starts working, or a worst-of basket that sounds diversified and is actually short correlation.
   6. The comparison I would give honestly: for a client who can tolerate the volatility, a bond and equity blend replicates most of this at a fraction of the fee. The structure earns its keep when the client genuinely cannot bear a nominal loss, or has a regulatory or accounting reason to need a floor. Otherwise it is a well-packaged way of paying for behaviour.

   Where candidates lose it

   Building the bond-plus-call structure and presenting the participation rate as a design choice. It is arithmetic — it falls out of rates, volatility and fees. And you must name the issuer credit risk and the forgone dividends, because that is the disclosure test the interviewer is actually running.

   Expect next

   • What happens to the participation rate if rates fall to zero?
   • Where is the client short correlation in a worst-of basket?
   • Would a simple 70-30 portfolio do better, and when would it not?
8. 060A five-year CDS trades at 400 basis points. What does that tell you about the probability of default?Credit derivativesHardsuperdayCredit tradingRisk management

   Say this

   Roughly a 6 to 7 percent annual risk-neutral default probability, using the rule of thumb that spread equals default probability times loss given default. At a 40 percent recovery, 400 over 0.6 is about 667 basis points a year, so around 28 percent cumulative over five years. But that is a risk-neutral number, and it is meaningfully higher than the real-world probability.

   Then walk it

   1. The approximation: spread is approximately the hazard rate times one minus recovery. Invert it — hazard rate equals spread over loss given default. With 40 percent recovery assumed, 400 basis points implies about 6.7 percent a year.
   2. Cumulative over five years, compounding the survival probability: 0.933 to the fifth is about 0.71, so roughly a 29 percent chance of default over the life.
   3. The recovery assumption does a lot of work here. Assume 20 percent recovery instead and the implied hazard rate drops to 5 percent. So you cannot read a default probability out of a spread without a recovery view, and the two are jointly unidentified from the spread alone.
   4. The bigger point: this is a risk-neutral probability, which embeds a risk premium. Empirically risk-neutral default probabilities run perhaps two to three times realised default rates for investment grade credits, because investors demand compensation for default risk being correlated with bad times. Quoting 29 percent as the actual chance the company fails would be wrong.
   5. The spread also contains things that are not default risk: liquidity premium, the cost of dealer balance sheet, and for index CDS, the demand for macro hedges. In a stress event, spreads widen more than any credible reassessment of default odds justifies.
   6. So how I would use the number: as a market-implied ranking and a hedging cost, not as a forecast. If I wanted the real-world probability I would look at rating agency transition matrices or a structural model like Merton, and I would expect a considerably lower figure — and the gap between the two is itself the credit risk premium I might want to harvest.

   Where candidates lose it

   Quoting the risk-neutral number as the probability of default. The whole test is whether you know that the spread contains a risk premium, a liquidity component and a recovery assumption. Do the arithmetic, then correct it out loud.

   Expect next

   • How sensitive is your answer to the recovery assumption?
   • How would you get a real-world default probability instead?
   • Why do risk-neutral and real-world probabilities differ by so much?
9. 061What is the CDS-bond basis, and what does it mean when it goes negative?Credit derivativesHardsuperdayCredit tradingHedge funds

   Say this

   The basis is the CDS spread minus the bond's credit spread on the same issuer and maturity. In theory it should be near zero, because buying the bond and buying protection creates a near-riskless position. A negative basis — CDS cheaper than the cash bond spread — means the cash market is under stress and nobody has the balance sheet to arbitrage it.

   Then walk it

   1. The arbitrage in principle: buy the bond, buy CDS protection to the same maturity, and you have hedged default risk. The residual spread you earn should be roughly the risk-free rate, so a large positive residual is a negative basis trade.
   2. Why it does not get arbitraged away: the trade needs funding for the bond position and balance sheet at a dealer. In a crisis funding is expensive or unavailable, so the trade is theoretically profitable and practically impossible. That is why the basis went to hundreds of basis points negative in late 2008 and again in March 2020.
   3. So a deeply negative basis is a funding stress indicator, not a credit signal. It measures the scarcity of balance sheet rather than the probability of default.
   4. Structural reasons for a non-zero basis in normal times: the cheapest-to-deliver option in CDS makes protection worth slightly more than a specific bond's spread; CDS is unfunded so it attracts different investors; and CDS documentation covers restructuring events that a bond spread does not price identically.
   5. A positive basis usually reflects demand for protection that cannot easily be expressed in cash — for example when bonds are impossible to borrow, so the negative view has to be taken in CDS.
   6. The limitation for anyone thinking of the trade: it is not riskless. You carry the counterparty on the protection leg, you carry funding and margin risk that can force you out, and you carry basis risk on the exact maturity and deliverable. The 2008 version of this trade destroyed funds who were right about the convergence and could not survive the path.

   Where candidates lose it

   Calling a negative basis an arbitrage. The point is precisely that it is not — it persists because funding and balance sheet are the binding constraint, and that is why the size of the basis is a stress gauge. Say that, and name March 2020.

   Expect next

   • So why does the arbitrage not close?
   • What does a persistently positive basis tell you?
   • How would you fund and size a negative basis trade?
10. 062What section of the indenture deals with payment waterfalls, and how does cash actually move through a structured credit deal?Credit derivativesHardsuperdayNomuraStructured Products · New York · 2026

    Say this

    The priority of payments section of the indenture, usually Article 11 in a CLO indenture, with the interest and principal waterfalls set out separately. Cash from the loan portfolio is collected in interest and principal accounts and then paid out strictly in seniority order, subject to coverage tests that can divert cash upward if the deal is underperforming.

    Then walk it

    1. Two waterfalls, kept separate by design. Interest proceeds pay fees, then senior note interest, then down the stack. Principal proceeds are used during reinvestment to buy more loans, and after that to amortise notes top-down.
    2. The accounts matter and this is what the operational question is really about: a collection account split into interest and principal, an unfunded amounts or ramp-up account at new issue, an expense reserve, and often an interest reserve for the first payment date before the portfolio is fully ramped.
    3. The tests are the teeth. Overcollateralisation and interest coverage tests are measured at each payment date, and a failure diverts cash that would have gone to the junior tranches into paying down the senior notes until the test is cured. That is the structural protection the AAA buyer is paying for.
    4. There is usually also a reinvestment overcollateralisation test which, if failed, sends a portion of equity distributions to buy more collateral rather than pay the equity — a softer version of the same mechanism.
    5. At new issue settlement the account structure is what trips people up: the ramp-up account holds undrawn proceeds, loans settle over weeks with delayed compensation, and the first payment date often needs an interest reserve because the portfolio has not been earning for a full period.
    6. The honest framing: the waterfall is the product. Credit analysis of the underlying loans matters, but the reason the AAA has performed through two cycles is the diversion mechanics, and the reason equity returns are volatile is that it sits last in both waterfalls and absorbs every test failure first.

    Where candidates lose it

    Waving at 'senior gets paid first'. This question is asked to find out whether you have read a document. Name the priority of payments section, name the interest and principal waterfalls separately, and name the overcollateralisation test diversion — that is the mechanic that defines the product.

    Expect next

    • What happens to equity distributions when the overcollateralisation test fails?
    • Which accounts exist at a new issue settlement and why?
    • Why has the CLO AAA performed so well through credit cycles?

    Reported by candidates at Nomura (Structured Products, New York, 2026). 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.