Citi Interview Questions
74 problems from Citi quant and strat loops: fixed-income derivatives pricing, rates and curve risk, probability and expectation puzzles, and clean algorithmic coding.
Inside the Citi interview
Citi is a global investment bank whose quant and strategist interviews lean heavily into fixed-income and rates derivatives, the curve and covariance risk behind a desk's book, and the probability and algorithmic coding that screen for clean quantitative reasoning.
What they test
The largest block is derivatives and options pricing — swaptions and caplets under Black's model, FX forwards and digitals, CDS and defaultable-bond spreads, and arbitrage-free implied-vol surfaces. Around it sits a strong algorithmic coding core (streaming medians, DAG scheduling, subarray DP) and a deep well of probability, expectation, and Bayesian updating puzzles. Rounding it out: linear algebra for PCA and covariance work, plus time-series and optimization for portfolio and hedging questions.
The recurring shapes
Rates and curve risk recur constantly: DV01 and key-rate hedging, duration/convexity, and bootstrapping discount or OIS curves from par swap rates. Pricing questions hinge on no-arbitrage and risk-neutral valuation, while the covariance side asks you to fix a nearly-PSD matrix, shrink a correlation estimate, or explain why the top PCA eigenvector of a rates covariance is flat. The probability set favors pattern races, exchangeability, and posterior updates over macro regimes.
How to approach
Reach for the canonical tool first: put-call parity and replication before a model, memorylessness and exchangeability before brute-force counting, and Bayes with explicit priors on signal questions. On rates, always tie a hedge back to a sensitivity (DV01, vega, convexity) and a no-arbitrage constraint. On coding, state the data structure that makes the streaming or graph problem linear before writing it.
The mix is roughly a third hard, half medium, and a handful of easy warm-ups — weighted toward the medium-to-hard rates-and-derivatives questions that define a Citi quant loop.
Citi options pricing questions (17)
- Extracting Convenience Yield from the Forward Curve
- Defaultable Zero-Coupon Bond Pricing with Constant Hazard Rate
- CDS Par Spread Derivation Under Constant Hazard Rate
- FX Digital Call Pricing and Delta Blow-Up
- Implied Dividend Yield from Put-Call Parity
- Caplet Pricing and Delta Under Black's Model
- Extracting Risk-Neutral Density From a Volatility Smile
- FX Forward Pricing and Covered Interest Parity
- Forward-Starting Zero-Coupon Bond Pricing and Arbitrage
- DV01 Hedge With Treasury Futures and Convexity Matching
- European Option on a Zero-Coupon Bond
- Key-Rate DV01 Hedging and Curve Risk
- Building an Arbitrage-Free Implied Volatility Surface for Futures Options
- Callable Bond Negative Convexity and Embedded Option Decomposition
- Payer Swaption Pricing and Vega Under Black's Model
- FX Smile Calibration from Delta Quotes
- Bootstrapping an OIS Discount Curve
Citi coding questions (15)
- Maximum Product Subarray
- Stable Sorting Under Worst-Case and Space Constraints
- Maximum Sum Circular Subarray
- DAG Reachability Queries with Preprocessing
- Longest Valid Parentheses Substring With One Flip
- Tick Data Cleaning Pipeline with Midprice Returns
- Heap Operations and K Largest Elements
- Reverse a Linked List and Implement Square Root
- VWAP and Last-Trade Price per Symbol per Day
- Longest Increasing Subsequence
- Rolling Median in a Streaming Window
- Dynamic Set Operations with Efficient Median
- Bellman-Ford: Shortest Paths with Negative Edge Weights
- Critical Path Scheduling on a DAG
- Maximum Non-Overlapping Interval Scheduling
Citi probability questions (12)
- Tightest Moment Bound on a Tail Probability
- Race Between Two Patterns on a Fair Die
- HHT Before THH in Coin Flips
- Three Boxes: Conditional Probability of a White Ball
- Bayesian Posterior Over Macro Regimes: Single and Matched Signals
- Stopping by Pattern vs. Number on a Die
- Aces Before Kings: Probability via Exchangeability
- First Three Decimal Digits of 0.99^100
- Bayesian Update with Three Binary Signals
- Probability No One Gets Their Own Hat
- Posterior Return Probability with Binary Regime Indicators
- One-Sided Chebyshev Bound vs. Markov's Inequality
Citi linear algebra questions (7)
- Vectorized Factor Return Series and Covariances
- Top-k Eigenvectors of a Large Sparse Symmetric Matrix
- PCA Factor Model for Yield Curve Risk
- Why the Top PCA Eigenvector of a Rates Covariance Matrix Is Flat
- Shrinkage Estimator for Correlation Matrix
- Streaming PCA on Large Return Matrices
- Fixing a Nearly-PSD Covariance Matrix
Citi expected value questions (5)
Citi optimization questions (4)
Citi time series questions (4)
Citi finance questions (4)
Citi random variables questions (2)
Citi regression questions (2)
Citi stochastic processes questions (1)
Citi statistics questions (1)
Citi interview FAQ
What kind of questions does Citi ask in quant interviews?
Candidates most often report options pricing, coding and probability questions. This page collects 74 of them, 74 stamped with the month they were last reported — each with a full worked solution.
How hard are Citi interview questions?
The set spans 4 easy, 40 medium and 30 hard problems. Most sit at medium difficulty — solvable in a few minutes with clean reasoning — with a harder tail that rewards knowing the canonical tricks.
How do I prepare for the Citi quant interview?
Work through this set by topic (use the sidebar), starting from your weakest area. 12 problems are free to open with their full solution, so you can judge the quality before anything else. Then broaden out with the related firms below — the question families overlap heavily.
Are these the actual Citi interview questions?
They are built from candidate-reported Citi questions. We rewrite each prompt for clarity and author the worked solutions ourselves — we don't claim the wording is verbatim, and we never invent questions or recycle generic lists. 74 of 74 carry the month they were last reported.