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. 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?
2. 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?
3. 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?
4. 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.