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Question 1

Score: 0/0

Longstaff-Schwartz (LSM) is primarily used to price:

Foreign exchange forwards

European options under stochastic volatility

Bermudan caplets in HJM

American-style options by regression on cross-sectional Monte Carlo paths

to track

2026 Statistics

Key Facts: CQF Exam

6 months

Program Length

CQF program structure

6 + 2

Core Modules + Electives

CQF qualification page

$24,695

Full Program Fee (2026)

CQF program fees page

June 25, 2026

Next Intake

CQF.com

60%

Module Exam Pass Mark

CQF assessment policy

Online

Delivery Format

CQF Institute

The CQF is a 6-month online part-time quant finance qualification from the CQF Institute (Fitch Learning). The next intake is June 25, 2026, with tuition of $24,695 for the full program (Level I + Level II) or $13,095 per level. Assessment uses take-home module exams in modules 2-4 plus a written capstone project after module 6, with a 60% passing mark per exam. The syllabus covers stochastic calculus, portfolio theory, Black-Scholes derivatives, machine learning, deep learning, fixed income, and credit risk.

Sample CQF Practice Questions

Try these sample questions to test your CQF exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Which of the following best describes a standard Brownian motion W(t)?

A.W(0)=0, continuous paths, independent increments, and W(t)-W(s) ~ N(0, t-s) for t>s

B.W(0)=1, differentiable paths, and W(t)-W(s) ~ N(0, t-s)

C.A continuous-time Markov chain on a finite state space

D.A deterministic process with linear drift and unit variance

Explanation: Standard Brownian motion starts at 0, has continuous (but nowhere differentiable) paths, independent increments, and increments W(t)-W(s) are normally distributed with mean 0 and variance t-s.

2For a process dX = a(X,t) dt + b(X,t) dW, Ito's lemma gives df(X,t) equal to which expression?

A.(f_t + a f_x + 0.5 b^2 f_xx) dt + b f_x dW

B.(f_t + a f_x) dt + b f_x dW

C.(f_t + a f_x + 0.5 b f_xx) dt + b f_x dW

D.f_t dt + b f_x dW

Explanation: Ito's lemma adds a 0.5 b^2 f_xx term to the ordinary chain rule because (dW)^2 = dt to leading order. The full drift is f_t + a f_x + 0.5 b^2 f_xx and the diffusion is b f_x.

3Geometric Brownian motion dS = mu S dt + sigma S dW has which solution?

A.S(t) = S(0) exp((mu - 0.5 sigma^2) t + sigma W(t))

B.S(t) = S(0) exp(mu t + sigma W(t))

C.S(t) = S(0) (1 + mu t + sigma W(t))

D.S(t) = S(0) + mu t + sigma W(t)

Explanation: Applying Ito's lemma to f(S) = log(S) gives d(log S) = (mu - 0.5 sigma^2) dt + sigma dW. Exponentiating yields S(t) = S(0) exp((mu - 0.5 sigma^2) t + sigma W(t)). The -0.5 sigma^2 t is the convexity correction.

4What does Girsanov's theorem accomplish in quant finance?

A.Changes the probability measure so that a discounted asset becomes a martingale under the new measure

B.Transforms a non-Markov process into a Markov process

C.Converts a stochastic differential equation into an ordinary differential equation

D.Removes the diffusion term from an SDE

Explanation: Girsanov's theorem provides the Radon-Nikodym derivative that lets us change measures from the real-world P to the risk-neutral Q. Under Q, drift shifts so discounted asset prices are martingales, enabling risk-neutral pricing.

5A discrete-time process M(n) is a martingale with respect to a filtration F(n) if which condition holds?

A.E[M(n+1) | F(n)] = M(n) and E[|M(n)|] is finite for all n

B.E[M(n+1) | F(n)] >= M(n) for all n

C.Var[M(n+1) | F(n)] = Var[M(n)] for all n

D.M(n+1) and M(n) are independent for all n

Explanation: A martingale satisfies E[M(n+1) | F(n)] = M(n) (no expected drift conditional on the past) and the integrability condition E[|M(n)|] < infinity. The first inequality defines a submartingale, not a martingale.

6What is the quadratic variation of standard Brownian motion W on [0,T]?

A.T

B.0

C.sqrt(T)

D.T^2

Explanation: The quadratic variation of Brownian motion on [0,T] equals T almost surely. This fact is encoded in the heuristic (dW)^2 = dt that underlies Ito's lemma.

7Under risk-neutral measure Q, what is the drift of a non-dividend-paying stock S in a Black-Scholes world?

A.The risk-free rate r

B.The expected real-world return mu

C.Zero

D.The dividend yield q

Explanation: Under Q, dS = r S dt + sigma S dW^Q. The real-world drift mu is replaced by the risk-free rate r so that the discounted price e^(-rt) S is a martingale.

8Which integral makes sense in the Ito calculus but not in classical (Riemann-Stieltjes) calculus?

A.Integral of f(t) dW(t) where W is Brownian motion

B.Integral of f(t) dt with continuous f

C.Integral of f(t) dg(t) where g has bounded variation

D.Integral of polynomial functions

Explanation: Brownian motion has unbounded variation on every interval, so integral with respect to dW cannot be defined as a Riemann-Stieltjes integral. The Ito construction defines it as an L^2 limit using left-endpoint evaluation.

9The Ornstein-Uhlenbeck process dX = theta(mu - X) dt + sigma dW exhibits which key behavior?

A.Mean reversion to mu at speed theta

B.Pure random walk with no mean reversion

C.Exponential growth toward mu

D.Cyclical oscillation around mu

Explanation: The drift theta(mu - X) pulls X back toward the long-run mean mu, with theta controlling the speed. This makes OU a standard model for interest rates (Vasicek) and other mean-reverting series.

10For GBM dS = mu S dt + sigma S dW, what is E[S(t)] given S(0)?

A.S(0) exp(mu t)

B.S(0) exp((mu - 0.5 sigma^2) t)

C.S(0) exp(mu t + 0.5 sigma^2 t)

D.S(0) exp(sigma^2 t)

Explanation: The expected value of GBM is S(0) exp(mu t). The Ito correction -0.5 sigma^2 appears inside the exponential of the path, but when you take E[exp(sigma W(t))] = exp(0.5 sigma^2 t), the corrections cancel.

About the CQF Exam

The Certificate in Quantitative Finance (CQF) is a six-month, online, part-time master's-level qualification delivered by the CQF Institute, part of Fitch Learning. The program covers stochastic calculus, portfolio theory and risk, Black-Scholes derivatives pricing, machine learning and deep learning applied to finance, fixed income, and credit risk. Assessment is via module exams in modules 2 through 4 plus a final capstone project after module 6. The next intake starts June 25, 2026.

Questions

100 scored questions

Time Limit

Take-home module exams; final project ~3 months

Passing Score

60% per module exam plus pass on final project

Exam Fee

$24,695 full program (CQF Institute (part of Fitch Learning))

CQF Exam Content Outline

16%

Module 1: Building Blocks of Quantitative Finance

Brownian motion, Ito's lemma, stochastic differential equations, geometric Brownian motion, martingales, Girsanov's theorem, and change of measure

16%

Module 2: Quantitative Risk & Return

Markowitz mean-variance optimization, efficient frontier, CAPM, APT, Sharpe and Sortino ratios, parametric, historical, and Monte Carlo VaR, expected shortfall, and coherent risk measures

18%

Module 3: Equities & Currencies (Black-Scholes)

Black-Scholes PDE derivation, risk-neutral pricing, put-call parity, the Greeks (Delta, Gamma, Vega, Theta, Rho), volatility smile and surface, binomial trees, and exotic options including Asian, barrier, lookback, and American (Longstaff-Schwartz)

14%

Module 4: Data Science & Machine Learning I

Supervised learning, linear and logistic regression, generalized linear models, support vector machines, decision trees, random forests, gradient boosting, regularization (Ridge, Lasso, ElasticNet), cross-validation, and feature engineering for finance

14%

Module 5: Data Science & Machine Learning II

Unsupervised learning (K-means, hierarchical clustering, PCA, autoencoders), deep learning (MLP, CNN, RNN, LSTM, transformers), NLP for finance (sentiment, embeddings), and reinforcement learning (Q-learning, deep Q, policy gradient) for execution and portfolio problems

12%

Module 6: Fixed Income & Credit

Short-rate models (Vasicek, CIR, Hull-White), HJM framework, LIBOR market model, Merton structural model, reduced-form hazard rate models, CDS pricing, Gaussian copula correlation, and Basel III/IV capital requirements

Numerical Methods

Finite differences (explicit, implicit, Crank-Nicolson), Monte Carlo simulation, variance reduction (antithetic, control variate, importance sampling), quasi-Monte Carlo, and Fourier transform (FFT) option pricing

Time Series & Volatility

ARMA models, GARCH family (GARCH, EGARCH, GJR-GARCH), EWMA, stochastic volatility (Heston model), and realized volatility estimation

How to Pass the CQF Exam

What You Need to Know

Passing score: 60% per module exam plus pass on final project
Exam length: 100 questions
Time limit: Take-home module exams; final project ~3 months
Exam fee: $24,695 full program

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

CQF Study Tips from Top Performers

1Internalize Ito's lemma: for dX = a dt + b dW, df(X,t) = (f_t + a f_x + 0.5 b^2 f_xx) dt + b f_x dW; reach for it on every SDE problem

2Derive Black-Scholes once by hand from the delta-hedged portfolio so the Greeks and risk-neutral measure feel intuitive rather than memorized

3Practice all three VaR methods (parametric, historical, Monte Carlo) on the same return series so you understand when each one breaks

4Use Python notebooks for every module: simulate Brownian paths, fit GARCH, calibrate Heston, train an LSTM, and price a CDS to make the math concrete

5Schedule the final capstone project at the start of module 5 - candidates who leave it until after module 6 routinely run out of time

Frequently Asked Questions

What is the CQF and who administers it?

The Certificate in Quantitative Finance (CQF) is a six-month online, part-time, master's-level qualification in quantitative finance, machine learning, and risk management. It is delivered by the CQF Institute, part of Fitch Learning, and was founded by Dr. Paul Wilmott. The program is recognized globally on the buy side, sell side, and in fintech for quant and risk roles.

What is the format of the CQF assessment?

CQF assessment uses take-home module exams in modules 2, 3, and 4 plus a written final capstone project after module 6. Each module exam combines multiple-choice questions with applied modeling and Python coding exercises submitted online. The pass mark per module exam is 60%, and the final project is graded pass, merit, or distinction by CQF faculty.

How much does the CQF cost in 2026?

The full CQF program (Level I plus Level II) is $24,695 for the June 2026 intake, with individual levels priced at $13,095 each. Tuition includes pre-program primers, all lectures and materials, software access, alumni network membership, and a Wilmott Magazine subscription. UK and EU residents pay 20% VAT on top of the listed fees.

When is the next CQF intake?

The CQF runs two intakes per year, in January and June. The next cohort begins on June 25, 2026, with the following intake in January 2027. Candidates can complete the full six-month program in one go or split it as Level I and Level II across separate cohorts.

What topics are covered in the CQF syllabus?

The CQF syllabus has six core modules: Building Blocks of Quantitative Finance (stochastic calculus), Quantitative Risk and Return (portfolio theory and VaR), Equities and Currencies (Black-Scholes and derivatives), Data Science and Machine Learning I and II, and Fixed Income and Credit. Candidates also select two advanced electives from a catalog covering algorithmic trading, advanced risk, ESG, behavioral finance, and more.

What background do I need to start the CQF?

Most CQF candidates have a quantitative undergraduate or master's degree in finance, mathematics, physics, computer science, or engineering. You need fluency in calculus, linear algebra, probability and statistics, and basic Python. Free pre-program primers cover math, finance, statistics, and Python so candidates can refresh prerequisites before module 1 starts.

How long should I plan to study for the CQF?

Plan for roughly 350 to 450 hours of study over the six-month program, or about 12 to 15 hours per week. Lecture hours are fixed by the schedule, but extra time is needed for exercises, the three module exams, and the capstone project. Splitting the program into Level I and II spreads this load over a longer calendar but the total effort stays similar.