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. 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?
2. 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?
3. 031You have sold a call and you are delta hedging it. Walk me through what you actually do over the option's life.The GreeksIntermediatetechnicalMarket makingEquity derivatives

   Say this

   You buy delta shares against the short call and rebalance as spot moves. Because you are short gamma, every rebalance means buying higher and selling lower, so you lose money on the hedge and you are paid theta to compensate. Over the life, your profit is the premium you collected less what the hedging actually cost you.

   Then walk it

   1. Day one: sell the 100-strike call at, say, 4.00 with a 0.5 delta, so buy 50 shares per contract. You are locally flat.
   2. Stock rises to 105. Delta is now 0.65, so you buy 15 more shares at 105. Stock falls back to 100, delta is 0.5, so you sell 15 shares at 100. You have just bought at 105 and sold at 100. That loss is what being short gamma means, and it is unavoidable.
   3. Do that repeatedly and the total hedging loss is roughly proportional to the realised variance of the stock. You keep money only if the stock realises less volatility than the 20-ish implied you sold at.
   4. So the profit and loss decomposition is clean: premium received, minus the realised variance cost, plus or minus the error from hedging discretely rather than continuously, minus bid-offer and financing on the share position.
   5. How often to rebalance is a real decision, not a technicality. Hedge too often and transaction costs eat you; too rarely and you run naked gamma between hedges. Desks usually hedge on a delta band — rebalance when delta moves more than some threshold — rather than on a clock.
   6. The failure mode to state: a gap. If the stock jumps from 100 to 130 overnight on a takeover, no rebalancing schedule saves you, because you were hedged for the 0.65 delta and you needed 1.0. Delta hedging manages diffusion risk, not jump risk, and that is exactly the assumption Black-Scholes makes and reality does not.

   Where candidates lose it

   Describing the mechanics without ever stating that the hedge loses money. Short gamma means the rebalancing is systematically adverse, and the theta you collect is the payment for it. If your answer does not contain 'buy high, sell low', you have not understood the trade.

   Expect next

   • How often would you rebalance, and what decides it?
   • Decompose your final profit and loss into its pieces.
   • The stock gaps 30 percent overnight. What happens to you?
4. 035You have just taken over a derivatives book from someone who left suddenly. What do you look at, in what order?The GreeksIntermediatesuperdayEquity derivativesRisk management

   Say this

   Directional exposure first, then convexity, then the things that cannot be hedged. Concretely: net delta, then gamma and where it is concentrated by strike and expiry, then vega bucketed by maturity, then the operational calendar — expiries, ex-dividend dates, barriers and any physically settled contract.

   Then walk it

   1. Net delta first, because it is the biggest and the easiest to neutralise. I want to be able to say in one number how much I make or lose on a 1 percent market move, and I would hedge any large residual with futures within the hour.
   2. Then gamma, and not just the total — where it sits. A book that is gamma-flat overall but long gamma at 24,000 and short at 25,000 is a different animal from a genuinely flat one, and the strike concentration tells you where the pain is.
   3. Then vega by expiry bucket. A summed vega number hides term structure risk. I want front month, second month, and beyond separately, because they do not move together.
   4. Then the calendar risks, which is where inherited books actually blow up: what expires this week, what has a barrier near spot, which names go ex-dividend, and whether anything settles physically rather than in cash.
   5. Then the stress grid. Profit and loss under spot down 10 and volatility up 10, spot down 20 and volatility up 25, and a single-name gap. Greeks are local; the grid is what tells me if there is a hole.
   6. And the unglamorous parts, said out loud because they are what catch people: does the position in the risk system reconcile with the clearing house, is there any trade with a manual mark, and what are the margin requirements if the market moves against me. I would rather find an unreconciled position on day one than on the day it matters.

   Where candidates lose it

   Listing all the Greeks in textbook order with no prioritisation. The question is about triage under uncertainty. Lead with 'hedge the delta first because it is the biggest and cheapest to fix', and include the operational checks — reconciliation and the expiry calendar — which is what someone who has actually held a book says.

   Expect next

   • What would you hedge in the first hour, and what would you leave?
   • Why does bucketing vega by expiry matter?
   • What operational risk would worry you most on a book you have not seen before?

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.