Interview case patterns

~10 min read

🎯 Interview frequent

Why it matters

Quant/FE interviews recycle a small number of shapes: price this, hedge that, find the arb, size the risk, explain the P&L. If you recognize the pattern, you can spend the 8–12 minutes on the actual model choice instead of flailing. This page is a map of those shapes, not a new theory — it pulls together TVM through hedging.

Core concepts

Pattern A — “What’s the fair price?” Always: (1) write the payoff, (2) pick the measure and the discount, (3) name the dynamics, (4) name the method (closed form / tree / PDE / MC), (5) list the risks the model misses. Example: Asian call → MC under \(Q\), GBM or local vol, control = geometric Asian.
Pattern B — “There’s an arb — or is there?” Compare a quoted price to a replicating portfolio. Cash-and-carry, put-call parity, curve bootstrap consistency, CDS vs. bond basis. If it looks like free money, hunt friction: borrow, haircuts, CTD, early exercise, taxes, you cannot short the asset.
Pattern C — “Hedge this.” Translate the position into Greeks, then neutralize in order: delta with the underlier, gamma/vega with other options, residual curve with swaps/futures. State what is left (jump, skew, liquidity). “I’m delta-flat” is never the end of the answer.
Pattern D — “The book lost money overnight. Why?” Use the P&L explain: \(\Delta P \approx \Delta\cdot\Delta S + \tfrac12\Gamma(\Delta S)^2 + \text{vega}\,\Delta\sigma + \Theta + \text{carry} + \text{unexplained}\). Then match to a market move (spot, curve, smile, spread). Unexplained P&L is a mapping bug until proven otherwise.
Pattern E — “Risk this.” Horizon, P&L definition (clean vs. dirty), factors, method (parametric / hist / MC), and a stress that the quantile misses. Quote VaR and a coherent alternative or a stress. See VaR / risk measures.
Pattern F — “Build a curve / a vol surface.” Instruments, interpolation, what you discount vs. project, arbitrage checks (calendar, butterfly). Don’t invent a parametric form you cannot defend.
Numbers hygiene. Dimensions: bp vs percent vs vol points. Compounding. Day-count. Notional vs. PV. Sign of the position (long/short, payer/receiver, bought/sold protection). A wrong sign is a failed case even if the formula is right.
Talk like a desk, not a textbook. “I’d sell the 3m10y straddle, delta-hedge, and I’m short gamma into the event” is better than reciting Itô’s formula. Then be ready to go one level deeper if they push.

Mental model

  hear the case
       |
       v
  [ what is the product / payoff / position? ]
       |
       v
  [ which pattern: price | arb | hedge | P&L | risk | curve ]
       |
       v
  [ replicating story  +  what can break it ]
       |
       v
  [ a number or a Greek  +  the residual risks ]
       |
       v
  [ one thing I'd check in data / a stress ]

Start from the contract, not from the fanciest SDE you know. Complexity is a last resort.

Interview questions

A client wants a 1y at-the-money-forward call on a single stock. Walk the pricing case in 60 seconds. Answer: Payoff \(\max(S_T - F, 0)\) with \(F = S_0 e^{(r-q)T}\). Vanilla European → BS as quote, maybe a smile adjustment from listed options if they exist. Hedge: buy \(\Delta\) shares, finance, rebalance; residual vega/skew. Risks: dividends, borrow, jumps into earnings, discrete hedge. If they need an American, switch to a tree.
Quoted 1y forward is 2% through cash-and-carry. List three reasons you still might not arb it. Answer: You cannot actually short the asset (borrow fee, locates). Dividends/storage uncertain. Transaction costs + bid/ask on spot and forward. Corporate actions. For indexes, the replicating basket vs. the futures spec. “Through” might also be a quoting convention (premium vs. discount, day-count).
You are long a 10y receiver swap and short a 10y Treasury of matched DV01. Rates rally, you still lose. Give two plausible reasons. Answer: (1) Curve shape: swap spread widened (SOFR/LIBOR vs. Treasury) enough to swamp the parallel DV01. (2) Convexity mismatch / key-rate mismatch (the swap’s risk is not a bullet at 10y). Also: financing of the short Treasury, and any optionality if the Treasury was CTD into a future.
Overnight P&L on a short 1-month 25-delta put is very negative, spot barely moved. What do you look at first? Answer: Implied vol / skew (vega and vanna): a vol spike or put-skew steepener marks you down without a spot move. Then: theta vs. calendar, borrow, and whether the position was actually delta-flat under the right sticky rule. Last: a jump that reverted by the close (intraday gamma) that the EOD spot doesn’t show.
Design a 99% 1-day VaR for a book of listed equity options. Which method, and what will it miss? Answer: Full-reval historical or MC with a smile; delta-normal is insufficient (gamma). Misses: events not in the window, overnight jumps, liquidity/bid-ask on OTM, correlation breaks across names, and anything beyond the 99% quantile (add ES + a crash stress). Backtest exceptions.
The interviewer says ‘your Monte Carlo price is 2.13 ± 0.40.’ What do you say next? Answer: Standard error is unusable — widen \(N\), add a control variate (the European vanilla), maybe quasi-MC. Also ask: bias from \(\Delta t\)? American? Same seed for Greeks? Never ship a price whose error bar is 20% of the number.

Watch

There is no single “FE interview cases” lecture worth pretending is canonical. Use the topic videos earlier in this guide, then practice out loud with a timer:

Pricing: Black-Scholes, risk-neutral valuation (MIT 18.S096)
Arb / parity: Put-call parity
Risk: What is value at risk (VaR)?