Belvedere Trading Interview Questions
60 real Belvedere Trading interview questions for Quant Trader and Quant Researcher roles: options pricing, probability, expected value, market microstructure, fast mental math, and brain-teasers.
Inside the Belvedere Trading interview
Belvedere Trading is a Chicago-based options market maker specializing in equity-index options. Its interviews probe whether you can price under uncertainty and quote fast — leaning on probability, expected value, and the mechanics of a two-sided market rather than memorized formulas.
What they test
The core is probability and expected value — dice, card, and coin setups, posterior updates, and pattern-race problems — paired with a market-making block on reading fair value off the order book, adverse selection, and quoting under flow. A genuine options-pricing strand covers Black-Scholes, butterfly/convexity arbitrage, and the forward curve, with a steady run of brain-teasers and fast mental math.
The recurring shapes
Expect to compute an expectation by conditioning (expected tosses to a pattern, balls left in a match box, coins after pairing), update a posterior after an observation (double-headed coin, a buy print moving fair value), and reason about convexity and no-arbitrage in option prices across strikes. The coding questions are interview-floor data-structure work: order-book ladders, as-of joins, and running best-trader aggregations.
How to approach
Quote a number with a tight, defensible range and say how you'd update it — that mirrors making a market. State your assumptions out loud, lean on linearity of expectation and conditioning before brute force, and for the microstructure and options problems, anchor on no-arbitrage and adverse selection rather than reaching for a closed form.
A medium-leaning set with a meaningful hard tail in options pricing, game theory, and stochastic reasoning, plus easy mental-math warmups to build speed.
Belvedere Trading probability questions (14)
- Ten of Spades Before All Face Cards
- Posterior Probability of a Double-Headed Coin
- Will the Resting Offer Get Hit? Overlapping Random Time Windows
- Probability of Strictly Increasing Dice Rolls
- First-to-Roll-Six Dice Game
- Posterior Probability of a Double-Headed Coin
- Convergence in Probability vs. Almost Sure Convergence
- Symmetric Random Binary Tree
- Pattern Race: HHT vs THH
- Top Two Meeting in the Final
- Generalized Monty Hall: n Doors
- Conditional Marble Draw with Three Colors
- Probability of No Ace in a 13-Card Hand
- Hungry Bear Catching Fish
Belvedere Trading coding questions (13)
- Max Profit with At Most K Trades, Fewest Trades on Ties
- Trade Aggregator: Running Best Trader by Edge Score
- Order Book Price Ladder with Add, Delete, and Level Clear
- Bundle Arbitrage Across Nested Stock Baskets
- Weighted Average Trade Price Over a Window
- Segment Tree with Lazy Propagation for Range Add and Range Min
- First Missing Positive in O(n) Time and O(1) Space
- Trade-to-Quote As-Of Join
- All-Pairs Two-Sum With Stable Ordering
- BFS on a Grid with Alternating Obstacles
- Minimum Insertions to Make a String a Palindrome
- Next Lexicographic Permutation In Place
- Minimum Swaps to Move All Evens Ahead of Odds
Belvedere Trading expected value questions (7)
- Single Die vs. Average of 100 Dice: Which Game to Play?
- Expected Balls Left in the Banach Match Problem
- Uniformly Decreasing Chain
- Expected Circular Mismatches
- Expected Tosses for Three Consecutive Heads
- Expected Coins Remaining After Removing Heads-Tails Pairs
- Conditional Uniform Selection: Expected Value
Belvedere Trading combinatorics questions (6)
Belvedere Trading brain teasers questions (5)
Belvedere Trading game theory questions (4)
Belvedere Trading options pricing questions (4)
Belvedere Trading market microstructure questions (3)
Belvedere Trading stochastic processes questions (1)
Belvedere Trading optimization questions (1)
Belvedere Trading statistics questions (1)
Belvedere Trading random variables questions (1)
Belvedere Trading interview FAQ
What kind of questions does Belvedere Trading ask in quant interviews?
Candidates most often report probability, coding and expected value questions. This page collects 60 of them, 22 stamped with the month they were last reported — each with a full worked solution.
How hard are Belvedere Trading interview questions?
The set spans 14 easy, 30 medium and 16 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 Belvedere Trading quant interview?
Work through this set by topic (use the sidebar), starting from your weakest area. 8 problems are free to open with their full solution, so you can judge the quality before anything else. Then walk the full Belvedere Trading interview guide for the round-by-round funnel and the online assessment.
Are these the actual Belvedere Trading interview questions?
They are built from candidate-reported Belvedere Trading 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. 22 of 60 carry the month they were last reported.