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. 028What is theta, and is collecting theta a strategy?The GreeksCoretechnicalIndian broking

   Say this

   Theta is the change in option value from one day passing, all else equal. For a long option it is negative — you lose a little every day. Collecting theta is not a strategy on its own; it is the premium you receive for being short gamma and short vega, and you only keep it if realised volatility comes in below implied.

   Then walk it

   1. Theta is largest in absolute terms for at-the-money options close to expiry, and it accelerates in the final week. A one-week ATM option can lose a fifth of its value a day near the end.
   2. The relationship to remember: theta and gamma are two sides of one trade. In Black-Scholes, theta is approximately minus half gamma times spot squared times variance. That identity says you are paid theta in exact proportion to the gamma you are short.
   3. So the break-even is not the passage of time, it is a volatility comparison. If you sell an option at 20 implied and the stock realises 15, you keep money. Realise 25 and you lose, no matter how much theta accrued on the way.
   4. This is why 'theta decay strategies' marketed to retail are misleading. Selling weekly index options collects theta reliably and looks like a bond until the week it does not, and one bad week removes many months of accrual. SEBI's own studies on Indian index option traders point at exactly this pattern of losses.
   5. The honest version of a short-theta business is the market maker's: sell options, delta hedge continuously, and earn the implied-minus-realised spread while keeping gamma small and diversified across names and expiries.
   6. Also note theta is not uniform through the day or week. Weekend decay is priced in on Friday, and on a low-realised-volatility day the effective bleed is higher than the model number suggests, because you also fail to earn the gamma.

   Where candidates lose it

   Presenting theta as free income. The interviewer's follow-up is always 'so you would just sell options every week?' Name the theta-gamma identity and say plainly that theta is compensation for short convexity, not a yield.

   Expect next

   • Write down the relationship between theta and gamma.
   • Why do weekly-expiry sellers in India lose money on average?
   • When is theta actually your friend?
2. 029What is vega, and where on the surface is it biggest?The GreeksIntermediatetechnicalEquity derivativesVolatility trading

   Say this

   Vega is the change in option value for a one-point move in implied volatility. It is biggest for long-dated at-the-money options, and it scales roughly with the square root of time. That is the key structural fact: gamma lives at the front of the curve, vega lives at the back.

   Then walk it

   1. Both calls and puts have positive vega, because higher volatility widens the distribution and both are convex payoffs. Being long options is being long volatility, full stop.
   2. Magnitude: vega is proportional to spot times root time times the standard normal density at d1. Root time means a two-year option has about five times the vega of a one-month option on the same notional.
   3. So the division of labour on a desk: if you want to trade the level of volatility you use long-dated options or variance swaps. If you want to trade the movement of the underlying you use short-dated options, where gamma dominates and vega is almost irrelevant.
   4. Vega is not one risk, it is a surface of risks. A book can be vega-flat in total and still be badly exposed if it is long front-month and short back-month volatility — that is vega term structure risk, and desks bucket vega by expiry rather than summing it.
   5. Numbers: an at-the-money one-year index option with 10 million of notional might carry 40,000 of vega, so a three-point volatility spike is 120,000. In March 2020 index implied volatility went from 15 to 80 in three weeks. That is the scale of the risk.
   6. The limitation: vega assumes a parallel shift in implied volatility, and real surfaces do not shift in parallel. Front-month volatility moves far more than back-month, and the skew steepens as the level rises. So you need vanna and volga — the cross-sensitivities to spot and to volatility itself — before your vega number means anything on a skewed book.

   Where candidates lose it

   Saying vega is biggest at the money and stopping, without the root-time scaling. The distinction that matters is that gamma is a short-dated risk and vega a long-dated one; if you cannot say which instrument to use for which view, you have not answered a trading question.

   Expect next

   • So which option would you buy to express a pure view on the level of volatility?
   • Why is a vega-neutral book still exposed to volatility?
   • What are vanna and volga, and when do they matter?
3. 030Rho gets ignored. When does it actually matter?The GreeksIntermediatetechnicalRates derivativesEquity derivatives

   Say this

   Rho is the sensitivity of an option's value to the interest rate. It is negligible on short-dated equity options, which is why nobody talks about it, and it is first-order on long-dated options, on FX, and on anything with a large strike relative to spot. It came back into focus when rates went from zero to five percent.

   Then walk it

   1. Sign: calls have positive rho, puts negative. A higher rate lowers the present value of the strike you will pay, which helps the call and hurts the put.
   2. Size: rho scales with time and with the discounted strike. On a one-month at-the-money option a 25 basis point rate move is a rounding error. On a five-year option it can be worth more than a volatility point.
   3. So where it bites: long-dated structured products, LEAPS, and the embedded options in insurance and pension liabilities. Anyone running a long-dated book in 2022 saw their option values move on rates as much as on volatility.
   4. In FX, rho is not one number but two, because you have the rate on each currency. The forward points are the rate differential, so an FX option's exposure to rates is really an exposure to the carry, and on a high-differential pair like USD/INR that dominates.
   5. Rates also change behaviour, not just value. Early exercise on American puts becomes optimal at higher rates, and the cost of carrying a delta hedge is a financing cost that grows with the rate. At five percent, financing a one-million-share hedge is a real line item in the profit and loss.
   6. The honest caveat: for the typical short-dated index option trade, rho is genuinely ignorable and pretending otherwise is false precision. The judgement being tested is whether you know which Greeks to care about for which instrument, rather than whether you can list five of them.

   Where candidates lose it

   Dismissing rho entirely, or over-claiming its importance. The right answer is a judgement about maturity and instrument: irrelevant for weekly index options, first-order for a five-year structured note and for FX carry. And name the financing cost of the hedge, which most candidates miss.

   Expect next

   • How does rho work differently in FX?
   • What did the 2022 rate cycle do to long-dated option books?
   • How does a higher rate change your delta hedging cost?
4. 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?
5. 036What is the difference between implied and realised volatility, and which one are you actually trading?VolatilityCoretechnicalVolatility tradingProp trading firms

   Say this

   Realised volatility is what the underlying actually did — measured from historical returns. Implied volatility is what the option market is charging, backed out of the price. When you buy an option and delta hedge it, you are long realised and short implied: you make money if the world turns out more volatile than the price you paid.

   Then walk it

   1. Realised is backward-looking and measurable: annualise the standard deviation of log returns, typically by multiplying the daily figure by root 252. The answer depends on your window, which is why people argue about it.
   2. Implied is forward-looking and is a price, not a forecast. It contains the market's expectation plus a risk premium plus supply and demand for that specific strike and expiry.
   3. The trade: buying a delta-hedged option is long realised volatility, short implied. The profit over the life is roughly the gamma-weighted difference between the two, which is why a variance swap — whose payoff is exactly realised variance minus a strike — is the clean expression of the view.
   4. A number to anchor it: Nifty realised volatility runs in the low teens in calm periods while India VIX often sits a few points above. That gap is the premium, and it is persistent enough that systematic short-volatility strategies exist to harvest it.
   5. The two are not even measuring the same object. Implied is a risk-neutral expectation over the option's remaining life. Realised is a sample statistic over a past window. Comparing them requires matching horizons, and most casual comparisons do not.
   6. The limitation to volunteer: implied above realised does not mean options are expensive. It means you are being paid for taking crash risk, and the payment looks generous right up to the point where you find out why it existed. February 2018 and March 2020 are the two reference points.

   Where candidates lose it

   Treating implied volatility as the market's forecast of realised volatility. It is a price with a risk premium in it, and a persistent gap is compensation rather than mispricing. Saying so is what separates an answer from a definition.

   Expect next

   • So is a persistent gap between them an inefficiency?
   • How would you measure realised volatility, and over what window?
   • What is the cleanest instrument for trading realised against implied?
6. 037Why is implied volatility usually higher than subsequent realised volatility?VolatilityIntermediatetechnicalVolatility tradingHedge funds

   Say this

   Because options are insurance and insurance is sold above expected loss. Investors are structurally long equities and want protection, protection pays off when everything else is losing, and that correlation makes buyers willing to overpay. The gap is the variance risk premium.

   Then walk it

   1. The demand side: pension funds, insurers and long-only managers are natural buyers of downside protection and natural sellers of upside. That flow is one-directional and persistent, which pushes put implied volatility above fair value.
   2. The risk-premium argument: a payoff that is positive exactly when markets crash has a negative beta to the market, so in any asset pricing framework it should earn a negative expected return. Someone has to be paid to supply it.
   3. Supply is constrained by capital and by the shape of the risk. Selling volatility has a fat left tail and requires margin that rises exactly when you are losing, so the pool of people willing to do it in size is limited. Limited supply against persistent demand means a price above fair value.
   4. Empirically the gap averages two to four volatility points on major indices and is much wider in the puts than in the calls, which is the skew. It is one of the most robust findings in empirical finance.
   5. But the premium is not free money. The return distribution of harvesting it is negatively skewed: many small gains, rare enormous losses. A Sharpe ratio computed on a short-volatility strategy over a calm sample is one of the most misleading numbers in the industry.
   6. And the premium varies. In calm markets it compresses to almost nothing, and that is precisely when short-volatility positioning is largest — because the recent track record looks best. That reflexivity is why the unwinds are violent, and it is what happened on 5 February 2018.

   Where candidates lose it

   Saying 'because option sellers need a profit'. The real answer is a risk premium argument: the payoff has negative beta, so it earns a negative expected return, so buyers pay above expectation. And you must volunteer the negative skew of harvesting it, or you sound like someone about to sell naked options.

   Expect next

   • So why doesn't everyone sell volatility?
   • When is the premium largest, and when is it smallest?
   • How would you harvest it without blowing up?
7. 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?
8. 039The FX smile looks symmetric, the equity smile is a downward smirk and commodities often smirk upward. Why the different shapes?VolatilityIntermediatesuperdayFX derivativesCommodities trading

   Say this

   Because the shape encodes which direction is the scary one for that asset, and that differs by market. Equities crash down, so the put wing is bid. Commodities spike up on supply shocks, so the call wing is bid. A currency pair is somebody's up and somebody else's down, so the tails are more balanced and you get a smile rather than a smirk.

   Then walk it

   1. Equities: gaps are downward and correlated. Leverage amplifies falls, and the entire institutional base is long and buys puts. Result is a steep left wing — a 25-delta put can trade five or more volatility points above the at-the-money.
   2. Commodities: the supply shock is the tail. A hurricane, a refinery fire, a war, an export ban — all push price up violently, and the downside is floored by the cost of production. So calls are bid, and you get inverse skew. Natural gas in winter is the purest example.
   3. FX on a G10 pair: both sides are a major economy, so a fall in one currency is a rise in the other and there is no structural short. You get a roughly symmetric smile driven by kurtosis, and the market quotes it as a butterfly — the average wing over the body.
   4. But an emerging market currency is skewed, and USD/INR is the clean case. The rupee depreciates in jumps and appreciates slowly, partly because the central bank manages it, so USD calls and rupee puts carry a premium. The risk reversal is persistently one-sided.
   5. Rates are their own case. With yields near zero the smile shape changed entirely, and desks moved to normal rather than lognormal volatility to allow negative rates at all. Shape follows what the market believes the tail looks like.
   6. The general principle worth naming: the smile is a picture of where the market thinks the gap risk is, plus who needs the hedge. If you know the structural position of the participants and the physics of the underlying, you can predict the shape before you look at a screen.

   Where candidates lose it

   Describing three shapes without a unifying mechanism. The answer is 'the bid wing is the tail direction plus the hedging demand'. Get USD/INR in there — an India-facing interviewer will expect you to know that the rupee's skew is one-sided and why.

   Expect next

   • What shape would you expect in USD/INR and why?
   • Why does natural gas skew change with the season?
   • How do you quote a smile in FX conventions?
9. 040What does the volatility term structure normally look like, and what does it mean when it inverts?VolatilityIntermediatetechnicalVolatility tradingHedge funds

   Say this

   Normally upward sloping — front-month implied volatility below the longer dates — because volatility mean-reverts and the near term is usually calmer than the long-run average. An inversion means the market is pricing near-term stress: an event, a crisis, or a known catalyst inside the front expiry.

   Then walk it

   1. The mean-reversion logic: if spot volatility is 12 and the long-run mean is 18, then the average over the next two years should be closer to 18 than to 12. So the curve slopes up from a low starting point and slopes down from a high one.
   2. Inversions are therefore a stress signal. In March 2020 the front month went to 80 while one-year implied was in the 30s — the market said the next month is chaos and then it normalises.
   3. There is a milder, non-crisis inversion too: a known event inside the front expiry. An earnings date, an election, a central bank meeting, a court ruling. That produces a local bump in the specific expiry that contains it, not a whole-curve inversion.
   4. Trading it: a calendar spread expresses a view on the slope. Long the back month and short the front is long the term structure and short near-term gamma — that is a bet on mean reversion, and it is the standard trade after a spike.
   5. The carry side of the same fact: an upward-sloping VIX curve means long-volatility ETPs bleed on the roll, which is why products like the short-term futures trackers lose value over time even when spot volatility is unchanged. Roll cost has historically dominated their returns.
   6. The limitation: an inverted curve is information, not a signal. It usually resolves by front-month volatility collapsing, which is why selling the spike works most of the time — and the times it does not, it goes much higher first, which is enough to end a career. Knowing the base rate is not the same as being able to hold the position.

   Where candidates lose it

   Saying inverted means fear and stopping. Add the two distinct causes — systemic stress versus a datable event inside one expiry — and add the roll-cost consequence for volatility ETPs. And be honest that selling an inverted curve is a high-base-rate, high-tail-risk trade.

   Expect next

   • How would you trade an inversion, and how would you size it?
   • Why do long-volatility ETPs lose money in a normal market?
   • What does a bump in one single expiry tell you?
10. 041What is the VIX, and how is it actually computed?VolatilityIntermediatetechnicalVolatility tradingIndian derivatives desks

    Say this

    It is the market's 30-day expected volatility on the S&P 500, expressed annualised in percentage points. It is not an average of implied volatilities — it is built from a strip of out-of-the-money option prices across all strikes, which makes it a model-free estimate of the square root of expected variance.

    Then walk it

    1. The construction: take all reasonably liquid out-of-the-money puts and calls in the two expiries that straddle 30 days, weight each by one over its strike squared, sum, interpolate to exactly 30 days, take the square root and annualise.
    2. The one-over-strike-squared weighting is the part worth knowing. It comes from the mathematics of replicating a variance swap: a portfolio of options weighted that way has a payoff equal to realised variance. So the VIX is the fair strike of a 30-day variance swap, quoted as a volatility.
    3. That is why it is called model-free. It does not use Black-Scholes at all — it reads variance straight off prices. The older VIX methodology up to 2003 did use at-the-money Black-Scholes implieds, and the change matters when you compare long histories.
    4. Because it uses every strike, it is sensitive to the wings. A bid in deep out-of-the-money puts lifts the VIX even if at-the-money implied volatility has not moved, which is why the VIX can rise on a flat day.
    5. You cannot trade the index. You trade VIX futures and options, and the futures are priced off forward variance rather than spot VIX, so they do not track it one for one. In a spike, the front future will lag spot VIX substantially.
    6. India's equivalent is the India VIX, built on Nifty options with the same methodology adapted by the NSE. It matters for the same reason: it is the reference for weekly-expiry positioning and it inverts in exactly the same way in a stress event.

    Where candidates lose it

    Calling it 'an average of option implied volatilities'. It is a variance-swap strike, and the one-over-K-squared weighting is the specific thing the interviewer is checking. Also expect the follow-up on why VIX futures do not track spot VIX — have the forward-variance answer ready.

    Expect next

    • Why doesn't a VIX future track spot VIX?
    • Why can VIX rise on a day when at-the-money implied is unchanged?
    • What is India VIX built on?

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.