AIFB Certified Computational Finance CCFP Exam
**Question 1.** Which condition is required for the Central Limit Theorem to hold when aggregating
daily log‑returns of a stock?
A) Returns must be normally distributed.
B) Returns must be independent and identically distributed with finite variance.
C) Returns must be positively skewed.
D) Returns must follow a Poisson process.
Answer: B
Explanation: The CLT requires i.i.d. variables with a finite second moment; normality of the individual
observations is not required.
**Question 2.** In a multi‑variable calculus setting, the Hessian matrix of a twice‑differentiable function
is used to determine:
A) The function’s gradient direction.
B) The convexity or concavity at a stationary point.
C) The optimal step size in gradient descent.
D) The correlation between variables.
Answer: B
Explanation: The Hessian’s eigenvalues indicate whether a stationary point is a local minimum (positive
definite), maximum (negative definite), or saddle point.
**Question 3.** The Lagrange multiplier associated with a budget constraint in portfolio optimization
represents:
A) The marginal increase in expected return per unit of risk.
B) The shadow price of the budget, i.e., the change in the objective per additional unit of budget.
C) The correlation between assets.
D) The variance of the optimal portfolio.
Answer: B
, AIFB Certified Computational Finance CCFP Exam
Explanation: In constrained optimization, the multiplier measures the sensitivity of the optimal value to
a change in the constraint bound.
**Question 4.** Which matrix decomposition is most appropriate for generating correlated normal
random variables in Monte‑Carlo simulation?
A) QR decomposition.
B) LU decomposition.
C) Cholesky decomposition.
D) Singular Value Decomposition.
Answer: C
Explanation: Cholesky factorizes a positive‑definite covariance matrix into a lower‑triangular matrix,
enabling transformation of independent normals into correlated ones.
**Question 5.** In the context of stochastic calculus, Ito’s Lemma is used to:
A) Approximate the price of a European option via binomial trees.
B) Transform a deterministic differential equation into a stochastic one.
C) Derive the differential of a function of a stochastic process.
D) Compute the expected value of a jump‑diffusion process.
Answer: C
Explanation: Ito’s Lemma provides the stochastic differential of a twice‑differentiable function of an Itô
process, accounting for the diffusion term.
**Question 6.** The Ornstein‑Uhlenbeck process is a mean‑reverting model. Which parameter controls
the speed of reversion?
A) The drift μ.
B) The volatility σ.
C) The mean level θ.
, AIFB Certified Computational Finance CCFP Exam
D) The reversion rate κ.
Answer: D
Explanation: κ (often denoted λ) determines how quickly the process pulls back toward its long‑run
mean θ.
**Question 7.** An AR(1) model for log‑returns is given by rₜ = ϕ r₍ₜ₋₁₎ + εₜ. For stationarity, the
parameter ϕ must satisfy:
A) ϕ = 0.
B) |ϕ| < 1.
C) ϕ > 1.
D) ϕ ≤ 0.
Answer: B
Explanation: Stationarity of an AR(1) requires the absolute value of the autoregressive coefficient to be
less than one.
**Question 8.** In a GARCH(1,1) model, the unconditional variance of the series equals:
A) ω / (1 – α – β).
B) ω + α + β.
C) (α + β) / ω.
D) ω × (α + β).
Answer: A
Explanation: For GARCH(1,1) with variance equation σ²ₜ = ω + α ε²₍ₜ₋₁₎ + β σ²₍ₜ₋₁₎, the long‑run variance is
ω/(1‑α‑β) provided α+β<1.
**Question 9.** Cointegration between two asset price series implies:
A) Both series are stationary.
, AIFB Certified Computational Finance CCFP Exam
B) The linear combination of the series is stationary even though each series is non‑stationary.
C) The series have identical autocorrelation structures.
D) The series cannot be used in a pairs‑trading strategy.
Answer: B
Explanation: Cointegration means a weighted sum of non‑stationary I(1) series yields a stationary I(0)
series, useful for statistical arbitrage.
**Question 10.** When back‑testing a trading strategy, a p‑value of 0.03 indicates:
A) A 3 % probability that the observed performance is due to random chance.
B) The strategy is 97 % profitable.
C) The Type II error rate is 3 %.
D) The null hypothesis cannot be rejected.
Answer: A
Explanation: A p‑value of 0.03 means there is a 3 % chance of observing results as extreme as those
obtained, assuming the null hypothesis (no skill) is true.
**Question 11.** The fundamental theorem of asset pricing states that a market is free of arbitrage if
and only if:
A) There exists at least one risk‑free asset.
B) All assets have the same expected return.
C) There exists an equivalent martingale (risk‑neutral) measure.
D) The market follows a normal distribution.
Answer: C
Explanation: Absence of arbitrage is equivalent to the existence of a probability measure under which
discounted asset prices are martingales.
**Question 1.** Which condition is required for the Central Limit Theorem to hold when aggregating
daily log‑returns of a stock?
A) Returns must be normally distributed.
B) Returns must be independent and identically distributed with finite variance.
C) Returns must be positively skewed.
D) Returns must follow a Poisson process.
Answer: B
Explanation: The CLT requires i.i.d. variables with a finite second moment; normality of the individual
observations is not required.
**Question 2.** In a multi‑variable calculus setting, the Hessian matrix of a twice‑differentiable function
is used to determine:
A) The function’s gradient direction.
B) The convexity or concavity at a stationary point.
C) The optimal step size in gradient descent.
D) The correlation between variables.
Answer: B
Explanation: The Hessian’s eigenvalues indicate whether a stationary point is a local minimum (positive
definite), maximum (negative definite), or saddle point.
**Question 3.** The Lagrange multiplier associated with a budget constraint in portfolio optimization
represents:
A) The marginal increase in expected return per unit of risk.
B) The shadow price of the budget, i.e., the change in the objective per additional unit of budget.
C) The correlation between assets.
D) The variance of the optimal portfolio.
Answer: B
, AIFB Certified Computational Finance CCFP Exam
Explanation: In constrained optimization, the multiplier measures the sensitivity of the optimal value to
a change in the constraint bound.
**Question 4.** Which matrix decomposition is most appropriate for generating correlated normal
random variables in Monte‑Carlo simulation?
A) QR decomposition.
B) LU decomposition.
C) Cholesky decomposition.
D) Singular Value Decomposition.
Answer: C
Explanation: Cholesky factorizes a positive‑definite covariance matrix into a lower‑triangular matrix,
enabling transformation of independent normals into correlated ones.
**Question 5.** In the context of stochastic calculus, Ito’s Lemma is used to:
A) Approximate the price of a European option via binomial trees.
B) Transform a deterministic differential equation into a stochastic one.
C) Derive the differential of a function of a stochastic process.
D) Compute the expected value of a jump‑diffusion process.
Answer: C
Explanation: Ito’s Lemma provides the stochastic differential of a twice‑differentiable function of an Itô
process, accounting for the diffusion term.
**Question 6.** The Ornstein‑Uhlenbeck process is a mean‑reverting model. Which parameter controls
the speed of reversion?
A) The drift μ.
B) The volatility σ.
C) The mean level θ.
, AIFB Certified Computational Finance CCFP Exam
D) The reversion rate κ.
Answer: D
Explanation: κ (often denoted λ) determines how quickly the process pulls back toward its long‑run
mean θ.
**Question 7.** An AR(1) model for log‑returns is given by rₜ = ϕ r₍ₜ₋₁₎ + εₜ. For stationarity, the
parameter ϕ must satisfy:
A) ϕ = 0.
B) |ϕ| < 1.
C) ϕ > 1.
D) ϕ ≤ 0.
Answer: B
Explanation: Stationarity of an AR(1) requires the absolute value of the autoregressive coefficient to be
less than one.
**Question 8.** In a GARCH(1,1) model, the unconditional variance of the series equals:
A) ω / (1 – α – β).
B) ω + α + β.
C) (α + β) / ω.
D) ω × (α + β).
Answer: A
Explanation: For GARCH(1,1) with variance equation σ²ₜ = ω + α ε²₍ₜ₋₁₎ + β σ²₍ₜ₋₁₎, the long‑run variance is
ω/(1‑α‑β) provided α+β<1.
**Question 9.** Cointegration between two asset price series implies:
A) Both series are stationary.
, AIFB Certified Computational Finance CCFP Exam
B) The linear combination of the series is stationary even though each series is non‑stationary.
C) The series have identical autocorrelation structures.
D) The series cannot be used in a pairs‑trading strategy.
Answer: B
Explanation: Cointegration means a weighted sum of non‑stationary I(1) series yields a stationary I(0)
series, useful for statistical arbitrage.
**Question 10.** When back‑testing a trading strategy, a p‑value of 0.03 indicates:
A) A 3 % probability that the observed performance is due to random chance.
B) The strategy is 97 % profitable.
C) The Type II error rate is 3 %.
D) The null hypothesis cannot be rejected.
Answer: A
Explanation: A p‑value of 0.03 means there is a 3 % chance of observing results as extreme as those
obtained, assuming the null hypothesis (no skill) is true.
**Question 11.** The fundamental theorem of asset pricing states that a market is free of arbitrage if
and only if:
A) There exists at least one risk‑free asset.
B) All assets have the same expected return.
C) There exists an equivalent martingale (risk‑neutral) measure.
D) The market follows a normal distribution.
Answer: C
Explanation: Absence of arbitrage is equivalent to the existence of a probability measure under which
discounted asset prices are martingales.
