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. 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?
2. 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.