Why Derivatives Pricing Dominates Bank Interviews
Sell-side quant interviews - Goldman Strats, JPMorgan QR, Morgan Stanley quant, Barclays QA - are dominated by derivatives pricing questions. The reason is straightforward: that's what these teams actually do day-to-day. Pricing model maintenance, volatility surface construction, and risk computation are the lion's share of bank quant work, and the interview content reflects that. Even at hedge funds and prop firms, derivatives knowledge appears regularly because options and futures positions are part of nearly every strategy.
This guide collects 20 worked examples drawn from real recent Goldman Sachs Strats, JPMorgan QR, Morgan Stanley, Barclays QA, Deutsche Bank QR, and SIG interviews. For broader context, see our stochastic calculus finance, option pricing models explained, and Greeks and volatility in options guides.
Section 1: Black-Scholes and Greeks (Questions 1-7)
1. Black-Scholes assumptions
What are the key assumptions behind the Black-Scholes formula?
Answer: (1) Geometric Brownian motion for the underlying. (2) Constant volatility. (3) Constant risk-free rate. (4) No dividends (or known constant dividend yield). (5) European exercise only. (6) Continuous trading. (7) No transaction costs. (8) Frictionless borrowing and lending. The interviewer often follows up: "which of these assumptions matters most?" Answer: constant volatility - this is what implied volatility surfaces explicitly violate, and what most derivative-pricing extensions try to fix.
2. Derive Black-Scholes from PDE
Sketch the derivation of Black-Scholes via the heat equation.
Answer: Set up the no-arbitrage portfolio (long option, short Δ shares). Apply Ito's lemma to the option value V(S, t). The dS dW terms cancel, leaving a PDE (\frac{\partial V}{\partial t} + \frac{1}{2}σ^2 S^2 \frac{\partial^2 V}{\partial S^2} + rS\frac{\partial V}{\partial S} - rV = 0). With boundary condition for European call (V(S, T) = max(S - K, 0)), substitute (τ = T - t), (x = \ln S), and the PDE becomes the heat equation, which has a known closed-form solution.
3. Vega for ATM call
Compute approximate vega for an at-the-money call on a $100 stock with 30% vol and 1 year to expiry.
Answer: Vega ≈ (S \sqrt{T/2π} ≈ 100 / 2.5 ≈ 40) per 1.0 (i.e., 100 vol-point) change. So per 1 vol point: $0.40 per share.
4. Delta for ATM put
Compute the delta of an at-the-money put.
Answer: Delta of ATM put ≈ -0.5 (varies slightly with rate and div). Put-call parity: Δ_call + |Δ_put| = 1. ATM call has Δ ≈ 0.5, so ATM put has Δ ≈ -0.5.
5. Gamma intuition
Gamma is largest for which options? Why?
Answer: Gamma is largest for ATM options near expiry - the option value is most sensitive to changes in delta when the option is on the cusp of being in or out of the money. Far from ATM, gamma is small (deep ITM acts like the stock; deep OTM acts like nothing). Far from expiry, gamma is also small (delta changes slowly).
6. Theta of a long call
Why is theta of a long call always negative?
Answer: Time decay. Each day that passes, the option has less time for the stock to move favourably. The option's "time value" decays toward zero as expiry approaches. The decay accelerates near expiry (theta becomes increasingly negative).
7. Why doesn't Black-Scholes fit the market?
Why does the implied volatility surface have skew and term structure if Black-Scholes assumes constant vol?
Answer: Black-Scholes' constant-vol assumption is wrong. Real markets exhibit (1) volatility smile - OTM options trade at higher implied vol than ATM. (2) Volatility skew - puts have higher implied vol than calls of equivalent moneyness (in equity index options). (3) Term structure - longer-dated options often have lower implied vol than near-dated. The market is pricing tail risk, jump risk, and stochastic volatility, none of which Black-Scholes models.
Section 2: Volatility and Skew (Questions 8-12)
8. Implied vs realised vol
What is the relationship between implied and realised volatility?
Answer: Implied volatility is what option prices imply about future realised volatility. They typically differ: implied vol > realised vol on average for equity index options (variance risk premium). Buying volatility (long options) has historically been a losing strategy on average because of this premium.
9. Trade volatility skew
You think SPX implied skew (puts higher IV than calls) is too steep. How do you trade it?
Answer: Sell the OTM put, buy the OTM call (a "risk reversal"). Skew bets are notoriously path-dependent - if the index drops, your short put loses; if vol surges across the surface, you're in trouble. Mitigations: hedge delta dynamically, use a smaller size, or trade the variance swap differential.
10. Smile vs skew
What's the difference between volatility "smile" and "skew"?
Answer: Smile is symmetric - both OTM puts and OTM calls have higher implied vol than ATM. Smile is most prominent in FX options. Skew is asymmetric - typically OTM puts have higher implied vol than OTM calls (true for equity index options). Other markets (e.g., crude oil) sometimes show "reverse skew" with OTM calls priced at higher vol.
11. Term structure of vol
Term structure is upward-sloping. What does this typically mean?
Answer: Markets are pricing higher uncertainty further into the future. Most common in calm markets - near-term implied vol is low because realised vol is low, but longer-dated vol is higher to reflect the unknown. After a vol spike, term structure often inverts (short-end IV very high, long-end lower) because the market expects vol to mean-revert.
12. Vega risk
You're long a portfolio of options across multiple expiries and strikes. How do you manage vega risk?
Answer: Compute vega per vol point per strike per expiry (the "vega bucket"). Aggregate to a single vega number for portfolio-level reporting, but always keep the buckets to understand exposure to specific parts of the surface. Hedge the largest buckets with offsetting trades; smaller buckets often unhedgeable economically.
Section 3: Exotic Options (Questions 13-16)
13. Barrier option types
What's the difference between a knock-in and knock-out barrier option?
Answer: Knock-in: the option becomes alive only if the underlying touches the barrier. Knock-out: the option dies if the underlying touches the barrier. Knock-in + knock-out (with same barrier and strike) = vanilla option. So knock-out = vanilla - knock-in.
14. Asian options
An Asian option pays based on the average price over a period, not the terminal price. Compared to a vanilla European with the same strike, why is the Asian usually cheaper?
Answer: Averaging reduces variance. The standard deviation of an average over n samples is σ/√n. So the volatility "seen" by the Asian option payoff is lower than the underlying's true volatility, making the option cheaper. Approximation: Asian price ≈ vanilla price with vol scaled by 1/√3 (for arithmetic average).
15. Variance swap pricing
A variance swap pays the realised variance over a period. How do you replicate it?
Answer: Static replication via a continuum of OTM puts and calls. Specifically, the fair strike of a variance swap equals (\frac{2}{T}\int \frac{C(K, T) + P(K, T)}{K^2} dK) (in continuous limit). In practice, replicate with a discrete portfolio of liquid strikes weighted by 1/K². The replication is delta-hedged dynamically.
16. Cliquet options
What's a cliquet option and why is it hard to price?
Answer: A cliquet (or "ratchet") option pays the cumulative return locked in periodically (e.g., monthly), often with caps and floors at each reset. Pricing is difficult because the payoff is path-dependent - you need to know the price at every reset, not just at terminal. Models that can handle this include Monte Carlo with path simulation, or PDE methods on a 2D lattice (price × time).
Section 4: Fixed Income and Other (Questions 17-20)
17. DV01 / PV01
What is DV01, and how do you compute it for a 5-year bond?
Answer: DV01 = "dollar value of a basis point" - the change in bond price for a 1 bp change in yield. For a 5-year zero-coupon bond at 5% yield, DV01 ≈ price × duration × 0.0001 ≈ 100 × 5 × 0.0001 = $0.05 per $100 face. For coupon bonds, use modified duration, which is shorter than maturity for high-coupon bonds.
18. Yield curve interpolation
Given quoted yields at 1Y, 2Y, 5Y, 10Y, how do you interpolate to get the 7Y yield?
Answer: Several approaches. (1) Linear interpolation between 5Y and 10Y. (2) Cubic spline through all points. (3) Bootstrapped from zero curve. (4) Parametric models (Nelson-Siegel-Svensson). Bank quant teams typically use bootstrapped zero curves with smooth interpolation (cubic spline or monotone Hermite).
19. Swaption pricing
How does a 2x10 swaption differ from a 2y option on a 10y bond?
Answer: Both have 2y option expiry. The 2x10 swaption gives the right to enter a 10y interest rate swap at a fixed rate. The 2y option on the 10y bond is similar but on bond price (not swap). Pricing-wise: the swaption is typically priced via Black's model with swap rate as the "underlying"; the bond option uses Black's model with bond price (and convexity adjustments). Dealers track both.
20. CDS spread
A 5-year CDS on a corporate bond trades at 200 bps. What does this mean?
Answer: The buyer of protection pays 200 bps per year (200 basis points = 2%) of the notional, usually quarterly. In return, if the bond defaults during the 5 years, the seller pays the buyer the loss given default (LGD). The 200 bps approximately equals the market's expected loss rate per year (LGD × annual default probability), plus risk premium and liquidity premium.
How to Use This Guide
For bank-track candidates, work through all 20 questions thoroughly - derivatives pricing is the dominant interview topic at Goldman Strats, JPMorgan QR, Barclays QA, Morgan Stanley quant. For prop trading and hedge fund tracks, focus on Sections 1 and 2 (Black-Scholes, Greeks, vol surface) - these come up consistently even when the firm doesn't trade many derivatives.
For broader prep:
- Quant interview questions hub
- Stochastic calculus finance
- Option pricing models explained
- Greeks and volatility in options
For firm-specific interview content:
Practise the questions Derivatives Pricing Interview Questions: 20 Real Examples 2026 actually asks
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