Options Pricing Interview Questions
This playlist takes you from the model-free foundations of derivatives all the way to the machinery quants actually use on a trading desk. You'll start with no-arbitrage anchors (put-call parity, payoff replication, the one-step binomial tree) and the central idea that prices come from risk-neutral
How to think about options pricing questions
Option pricing has one founding idea that makes everything else mechanical: a derivative is worth whatever it costs to replicate it. If you can build the same payoff from stock and cash, no-arbitrage forces the prices to match — and the model just bookkeeps that replication.
REPLICATE, THEN PRICE
Hedge the option with a position in the underlying so the combined book is riskless; that hedge ratio is the delta. Because the hedged portfolio can only earn the risk-free rate, the option's fair value is pinned — this is the engine behind binomial trees and Black–Scholes alike.
PRICE UNDER THE RISK-NEUTRAL MEASURE
The clean way to value any payoff: pretend the world drifts at the risk-free rate, take the expected payoff, and discount it. Real-world probabilities drop out entirely — what matters is volatility, which is why the Greeks (delta, gamma, vega) are the real vocabulary of the desk.
The thread through every problem: build the payoff from things you can already price, and let no-arbitrage do the rest.
Options Pricing questions (84)
- Option Payoffs at Expiration
- American vs. European Options and Time Value
- Option Pricing on a Dice Product
- Volatility in FX Markets
- One-Step Binomial Option Pricing
- Positive and Negative Parts, Put-Call Parity
- Binary Outcome Option Pricing
- Call Option Price via Probability Tree
- Put-Call Parity and Arbitrage Construction
- Binomial Tree Option Pricer
- Bond Price Change: Duration and Convexity
- FX Forward Pricing and Covered Interest Parity
- Straddle and Call Spread Pricing via Put-Call Parity
- Implied Volatility via Newton-Bisection
- ETF Creation/Redemption Arbitrage Threshold
- Put-Call Parity Arbitrage with Dividends
- Implied Dividend Yield from Put-Call Parity
- Delta of a Digital Call Option
- Delta-Gamma-Vega Hedging With Two Options
- Break-Even Implied Volatility with Adverse Selection
- Straddle Gamma Across Price Movement
- Time Horizons for Vega-Driven Option Appreciation
- American vs. European Call Arbitrage on a Non-Dividend Stock
- Bond Duration, Convexity, and Futures Hedging
- Vertical Call Spread Greeks Analysis
- Effect of Rising Risk-Free Rate on American Option Exercise
- Black-Scholes Assumptions, Greeks, and Short Straddle P&L
- Path-Dependent Delta: Sudden Jump vs. Gradual Decline
- Callable Bond Negative Convexity and Embedded Option Decomposition
- European Call Option With Infinite Maturity
- Hedging Autocallables, Volatility Product Pricing, and Mixed-Portfolio VaR
- Bachelier vs Black Volatility Mapping
- Deriving the Black-Scholes Formula from Risk-Neutral Expectation
- Crank-Nicolson Scheme for the Black-Scholes PDE
- Call Price Monotonicity in Time to Expiry and Gamma Comparison
- Discounted Stock as Martingale Under Risk-Neutral Measure
- Securitization Tranche Waterfall: Simulation and Analytic Loss
- Theta-Gamma Relationship and Delta-Hedged P&L
- Black-Scholes Monte Carlo Pricer
- Delta-Normal VaR with Correlation
- American Put Pricing via Projected SOR
- Black-Scholes PDE Derivation
- GARCH(1,1) with Student-t Innovations: VaR and Tail Risk
- Pricing a Call on the Dice-Cancellation Sum
- Forward Measure and Caplet Pricing
- Black-Scholes Assumptions and the American Call Delta
- Variance Reduction for Monte Carlo Option Pricing
- Defaultable Zero-Coupon Bond Pricing with Constant Hazard Rate
- American Option Early Exercise Analysis
- Monte Carlo Pricing of Arithmetic Asian Options with Variance Reduction
- CVA with Exposure Profile and Wrong-Way Risk
- Barrier Option In/Out Parity
- Barrier Digital Option via Brownian Bridge Correction
- CDS Par Spread Derivation Under Constant Hazard Rate
- Butterfly Arbitrage and Convexity of Call Prices in Strike
- Discrete Delta-Hedging Error
- Down-and-Out Call: Pricing and Monte Carlo
- Static Replication via the Breeden-Litzenberger Integral
- FX Put-Call Parity and Arbitrage
- Butterfly Spread Greeks and Smile Recentering
- Monte Carlo Pricing of an Arithmetic Asian Option
- Volatility Smile and Model Risk
- Pricing a Binary on a Compound Event with Partial Correlation Knowledge
- FX Digital Call Pricing and Delta Blow-Up
- Breeden-Litzenberger Formula
- Local Volatility vs Stochastic Volatility
- Merton Jump-Diffusion European Call Price
- Carr-Madan Formula for Option Pricing
- Static Arbitrage in Call Prices
- Bayesian Pricing of a Threshold Digital
- Replicating Arbitrary Payoffs with Calls and Puts
- Extracting Risk-Neutral Density From a Volatility Smile
- Dynamic Replication of Tournament Champion Contracts
- Black-Scholes Walkthrough: Assumptions, Failures, and Fixes
- Volatility Smile from Variance Mixtures
- Building an Arbitrage-Free Implied Volatility Surface for Futures Options
- Merton Structural Credit Model
- Numerical / Monte Carlo Greek Estimation
- Caplet Pricing and Delta Under Black's Model
- Feynman-Kac and Option Price Convexity
- Payer Swaption Pricing and Vega Under Black's Model
- FX Smile Calibration from Delta Quotes
- Variance Swap Fair Strike via Log-Contract Replication
- European Option on a Zero-Coupon Bond
Options Pricing interview questions FAQ
What kind of options pricing questions show up in quant interviews?
This page collects 84 options pricing problems that recur in quant trading and research interviews, each with a full worked solution and the intuition behind it. They range from quick warmups to the harder variants firms use to separate candidates.
How hard are options pricing interview questions?
The set spans 4 easy, 29 medium and 51 hard problems. Most sit at medium difficulty — a few minutes of clean reasoning — with a harder tail that rewards knowing the canonical approach rather than grinding.
How should I practice options pricing for quant interviews?
Work through them by difficulty, starting just below your level, and write the solution out before checking. 13 are free to open with the full worked solution, so you can judge the quality first. Focus on the recurring patterns rather than memorizing answers — the same handful of ideas generate most variants.
Are these real quant interview questions?
They are a curated set drawn from our problem bank — the kind of options pricing question that actually appears in quant interviews, rewritten for clarity with solutions we author ourselves. We don't claim any single wording is verbatim, and every problem carries a full solution.