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PRMIA 8007 Exam Syllabus Topics:

Section	Weight	Objectives
Numerical Methods & Financial Mathematics	15%	- Root finding and approximation - Basics of risk modeling - Time value of money
Statistics and Regression Analysis	20%	- Linear regression 1. Hypothesis testing and confidence intervals 2. Simple and multiple regression - Descriptive statistics 1. Correlation and covariance 2. Measures of location and dispersion
Probability Theory	25%	- Random variables and distributions 1. Expected value, variance, covariance 2. Discrete and continuous distributions - Basic probability concepts 1. Conditional probability and independence 2. Axioms and rules
Calculus and Functions	20%	- Single-variable calculus 1. Limits and continuity 2. Derivatives and applications 3. Integrals and applications - Multivariable calculus 1. Optimization 2. Partial derivatives
Linear Algebra and Matrix Theory	20%	- Matrix operations 1. Addition, multiplication, inversion 2. Determinants and trace - Vectors and eigenvalues 1. Diagonalization 2. Eigenvalues and eigenvectors

PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:

1. The natural logarithm of x is:

A) the inverse function of exp(x)
B) always greater than x, for x>0
C) 46
D) log(e)

2. Identify the type and common element (that is, common ratio or common difference) of the following sequence: 6, 12, 24

A) geometric sequence, common ratio 3
B) geometric sequence, common ratio 2
C) arithmetic sequence, common ratio 2
D) arithmetic sequence, common difference 2

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

A) 4 and -2
B) 1 and 0
C) No real roots
D) -4 and 2

4. Bond convexity is closely related to ...

A) The integral of the bond's present value with respect to yield
B) The sensitivity of the bond's present value with respect to yield
C) The derivative of the bond's present value with respect to yield
D) The second derivative of the bond's present value with respect to yield

5. In a 2-step binomial tree, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of d = 1/u. The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. Use the Cox, Ross, Rubinstein parameterization to find the risk neutral probability and hence find the value of a European put option with strike 102, given that the underlying price is currently 100.

A) 5.66
B) 4.18
C) 5.19
D) 6.31

Solutions:

Question # 1
Answer: A

Question # 2
Answer: B

Question # 3
Answer: C

Question # 4
Answer: D

Question # 5
Answer: D