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Free PRMIA 8007 Practice Exam with Questions & Answers | Set: 2

Questions 11

Maximum likelihood estimation is a method for:

Options:
A.

Finding parameter estimates of a given density function

B.

Estimating the solution of a partial differential equation

C.

Solving a portfolio optimization problem

D.

Estimating the implied volatility of a simple European option

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Questions 12

Calculate the determinant of the following matrix:

Options:
A.

4.25

B.

-4.25

C.

4

D.

2

Questions 13

An underlying asset price is at 100, its annual volatility is 25% and the risk free interest rate is 5%. A European put option has a strike of 105 and a maturity of 90 days. Its Black-Scholes price is 7.11. The options sensitivities are: delta = -0.59; gamma = 0.03; vega = 19.29. Find the delta-gamma approximation to the new option price when the underlying asset price changes to 105

Options:
A.

6.49

B.

5.03

C.

4.59

D.

4.54

Questions 14

Consider the following distribution data for a random variable X: What is the mean and variance of X?

Options:
A.

3.6 and 7.15

B.

3.4 and 3.84

C.

3.5 and 3.45

D.

None of these

Questions 15

The correlation between two asset returns is 1. What is the smallest eigenvalue of their correlation matrix?

Options:
A.

1

B.

0.5

C.

0

D.

None of the above

Questions 16

Let N(.) denote the cumulative distribution function of the standard normal probability distribution, and N' its derivative. Which of the following is false?

Options:
A.

N(0) = 0.5

B.

N'(0) ≥ 0

C.

N(x) → 0 as x → ∞

D.

N'(x) → 0 as x → ∞

Questions 17

When the errors in a linear regression show signs of positive autocorrelation, which of the statements below is true?

Options:
A.

The regression coefficient will be too high and the standard error of the regression coefficient will be understated

B.

The regression coefficient will be too low and the standard error of the regression coefficient will be overstated

C.

The regression coefficient will be unbiased, but the standard error of the regression coefficient will be understated

D.

The regression coefficient will be unbiased, but the standard error of the regression coefficient will be overstated

Questions 18

Let E(X ) = 1, E(Y ) = 3, Corr(X, Y ) = -0.2, E(X2 ) = 10 and E(Y2 ) = 13. Find the covariance between X and Y

Options:
A.

-2.8

B.

1.3

C.

-1.2

D.

None of the above

Questions 19

Variance reduction is:

Options:
A.

A technique that is applied in regression models to improve the accuracy of the coefficient estimates

B.

A numerical method for finding portfolio weights to minimize the variance of a portfolio that has a given expected return

C.

A numerical method for finding the variance of the underlying that is implicit in a market price of an option

D.

A method for reducing the number of simulations required in a Monte Carlo simulation

Questions 20

Find the roots, if they exist in the real numbers, of the quadratic equation

Options:
A.

4 and -2

B.

-4 and 2

C.

1 and 0

D.

No real roots

Exam Code: 8007
Certification Provider: PRMIA
Exam Name: Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
Last Update: Jul 13, 2025
Questions: 132
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