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. 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?
2. 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?
3. 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?
4. 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?
5. 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?
6. 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?
7. 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?

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.