Looking for the book? “A Practical Guide to Quantitative Finance Interviews” is also the title of Xinfeng Zhou’s book, known as the Green Book. It was published by CreateSpace in 2008, and Amazon describes more than 200 real interview problems across brain teasers, calculus, linear algebra, probability, stochastic processes and stochastic calculus, finance and programming. This page is an independent guide. It isn’t affiliated with the author or publisher, and it doesn’t reproduce the book’s problems. Buy or borrow the book through a legitimate retailer or library.
What is a practical guide to quantitative finance interviews? Quant interviews test probability, mental math, decision-making under uncertainty and coding, and formats differ by firm and role. Prepare by role: traders drill probability, speed and market-making games, researchers add statistics and coding, and developers focus on algorithms. Use the Green Book as a foundation, then practice out loud, timed and firm-specific.
Key takeaways
- Formats vary. Jane Street describes a conversation. Citadel Securities’ campus quant research first round centers on programming. Optiver stresses speed and composure.
- The Green Book is a strong probability foundation but doesn’t cover timed mental-math tests, market-making games or modern coding and machine learning.
- Method and communication matter more than memorized answers.
- Applications for summer 2027 roles reportedly opened in August 2026, so start now.
- Skip proxy and “ghostwriting” services. They put your candidacy at risk.
What quant interviews actually test
Five skills show up across firms:
- Probability and expected value.
- Speed and accuracy with numbers.
- Decisions under uncertainty, such as market-making and betting games.
- Programming and data, with statistics and machine learning added for research roles.
- Communication. Interviewers want to hear how you reason.
Finance knowledge matters less at prop firms than people expect. Bank and derivatives roles test more of it.
How the process works, from the firms’ own pages
Jane Street (trading)
- The process starts with phone interviews and ends with in-person interviews. The final round may include problem solving, probability and statistics, coding in any language, data analysis and general interests.
- Quantitative traders conduct the interviews, and the firm says they feel more like a conversation than a quiz, with no prior finance knowledge or complicated math required.
- Its tips: approach the problem methodically, communicate clearly, correct your mistakes and ask why. It also publishes a mock interview video.
- There is no GPA or degree requirement.
Citadel Securities (campus quantitative research)
- The process typically takes four to five weeks.
- The first round is a 45- to 60-minute remote interview on technical and behavioral skills, focused on programming, data structures and algorithms, and problem-solving. Python and C++ are the core languages, but any language is welcome.
- The second round is onsite, usually three to five 60-minute interviews, followed by a final team-fit review.
- Its advice: take time to assess a problem before coding, ask clarifying questions, share your thought process, discuss trade-offs and take hints.
Optiver
- Optiver says mental math is necessary but not sufficient. It also assesses quick decision-making and composure under pressure, and says final interviews don’t require technical preparation.
- For engineers, it expects confident knowledge of a major object-oriented language (C++, Java or Python), standard libraries and algorithms, and data structures with their time and space complexity.
- Candidate reports (not official) describe a sequences test, working-memory and reaction games, probability-approximation questions and a market-making game. The widely reported 80 arithmetic questions in 8 minutes varies: formats change over time and differ by office and role.
Third-party guides disagree on stage counts, pass rates and pay. Use official pages first, and treat unsourced numbers cautiously.
Prep map by role
| Role | Core topics | Where the Green Book helps | Add |
|---|---|---|---|
| Quant trader | Probability, EV, mental math, trading games, options basics | Probability, brain teasers | Timed arithmetic, market-making practice, core options chapters of Hull (Black-Scholes, Greeks, hedging) |
| Quant researcher | Probability, statistics, linear algebra, coding | Probability, linear algebra, stochastic processes | Python, statistics, ML basics |
| Quant developer | Algorithms, data structures, C++/Python | Little | LeetCode-style practice, language mastery |
| Bank quant | Derivatives, stochastic calculus | Stochastic processes, finance | Shreve, Hull, Joshi |
For banks, reviewers note that product knowledge and market-making games aren’t fully covered by the book.
What the Green Book covers, and what it doesn’t
Strengths. It’s broad, and readers most often praise the probability and brain teaser sections. Goodreads reviewers call those sections good, while saying better resources exist for other chapters.
Limitations reviewers cite:
- It gives solutions but doesn’t teach a systematic method for reaching them.
- Its programming section is dated, and modern coding, machine learning and trading-game questions aren’t covered.
- It doesn’t cover mental-math speed tests, sequence tests or market-making simulations, and established firms write original questions knowing candidates use the book.
Verdict: essential for probability and math fundamentals, insufficient alone. Pair it with role-specific practice.
A repeatable problem-solving method
- Clarify the question and assumptions.
- Simplify: use symmetry, small cases, and drop irrelevant outcomes.
- Model: define states or a recursion.
- Compute.
- Sanity-check with bounds, extreme cases or simulation.
Worked example 1: symmetry
A fair die is rolled until a 6 appears. What’s the probability no 1 appeared first?
Only 1s and 6s matter. The first of those is equally likely to be either, so the answer is 1/2.
Worked example 2: backward induction
You may roll a die up to three times and stop any time, taking that number in dollars. What’s the fair price?
- One roll: $3.50.
- Two rolls: keep the first roll only if it beats $3.50 (4, 5 or 6). Value = 15/6 + (3/6)(3.5) = $4.25.
- Three rolls: keep the first roll only if it beats $4.25 (5 or 6). Value = (5 + 6 + 4×4.25)/6 = 28/6 ≈ $4.67.
Check it with a quick simulation:
python
import random
def play(n_rolls=3):
thresholds = [3.5, 4.25] # continuation values with 1 and 2 rolls left
for left in range(n_rolls, 1, -1):
x = random.randint(1, 6)
if x > thresholds[left - 2]:
return x
return random.randint(1, 6)
print(sum(play() for _ in range(1_000_000)) / 1_000_000) # ≈ 4.667Worked example 3: mental math
- 47 × 23 = 50×23 − 3×23 = 1,150 − 69 = 1,081.
- 47 × 53 = 50² − 3² = 2,491.
- 15% of 240 = 24 + 12 = 36.
Worked example 4: making a market
Make a market on the sum of two dice. Fair value is 7 and the standard deviation is about 2.4. Start wide (for example, 6 at 8). If someone keeps buying your offer, they may know something, so shift both sides up. If nobody trades, tighten. Interviewers look at your fair value, spread logic and updating, not one “correct” spread.
Practice plans
| Timeline | Focus |
|---|---|
| 4 weeks (interview scheduled) | Week 1: probability and EV plus daily timed mental math. Week 2: your firm’s format and market-making practice. Week 3: coding and algorithms (developers and researchers) or options basics (traders). Week 4: timed mocks, error-log review, rest. |
| 8 weeks | Weeks 1–3: probability and brain teasers. Weeks 4–5: calculus, linear algebra, statistics. Week 6: finance or stochastic processes. Week 7: coding and simulation. Week 8: mocks. |
| 12 weeks | Add a Python project, ML fundamentals for research roles, and two or three full mock loops. |
Daily habits: 15–20 minutes of timed mental math, an error log, and explaining solutions out loud. Candidates report at least three to four weeks of daily practice for timed arithmetic screens.
Timing: Quantt reports that top firms opened summer 2027 internship and 2027 full-time applications in August 2026. Check each firm’s careers page.
Communicate the way firms ask
- Restate the problem and state your assumptions.
- Think out loud, and say when you’re stuck.
- Take hints gracefully.
- State confidence honestly (“about 70% sure”) instead of bluffing.
- Check your answer before you finish.
Integrity, AI and pirated PDFs
- Don’t use “OA proxy” or ghostwriting services. They defeat the purpose of the test and put your candidacy at risk.
- Check each firm’s AI policy. For example, Goldman Sachs has told campus applicants it wants to hear from them in their own voice.
- One reviewer says the author hasn’t released an official free PDF. Buy or borrow the book instead of using unofficial copies.
Free official resources
- Jane Street’s trading interviews page, including a mock interview video.
- Citadel Securities’ interview-process and candidate FAQ pages.
- Optiver’s campus FAQs and engineering interview tips.
It’s Xinfeng Zhou’s book, nicknamed the Green Book. The author is a CFA charterholder and FRM with a Ph.D. from MIT.
No. It covers probability and math fundamentals well but not mental-math speed tests, market-making simulations or modern coding and ML.
The Green Book leans toward quant finance topics, stochastic calculus and harder probability, while Heard on the Street has broader coverage, including statistics and financial economics. Many candidates use both.
Four weeks if you’ve been invited, and eight to twelve if you’re starting early. Adjust for your role and background.
Jane Street says its trading interviews don’t require prior finance knowledge. Market makers benefit from options basics, and bank roles test more.
Jane Street lets you code in any language. Citadel Securities names Python and C++, and Optiver names C++, Java and Python.
Bottom line
Match your prep to the role and the firm’s own process. Build probability and math fundamentals with the Green Book, add role-specific practice, and rehearse out loud and timed. Start early and keep it honest.
This is general information, not career or legal advice. Firm processes change, so verify on each firm’s site. Company and book names are used for identification only, and this page isn’t affiliated with any of them.