PRMIA 8002 P R M Exam Practice Test Instant Access

Question 1

A quadratic form is

Adefined as a positive definite Hessian matrix.

Ban algebraic expression in two variables, x and y, involving , and terms.

Ca specific solution of the Black-Scholes pricing formula

Dan algebraic expression in two variables, x and y, involving , , and terms.

Answer : B

Question 2

Evaluate the derivative of exp(x2 + 2x + 1) at the point x = -1

A0.5

Answer : B

Question 3

Which of the following statements about variance and standard deviation are correct?

1. When calculated based on a sample of the population data, one has to correct for any bias in the result by using the number of degrees of freedom in the calculation

2. Variance is in square root units of the underlying data, whereas standard deviation is in units of the underlying data

3. When considering independent variables, variance is additive, while standard deviation is not

AAll three statements are correct

BStatements 1 and 2 are correct

CStatements 1 and 3 are correct

DStatements 2 and 3 are correct

Answer : C

Question 4

Which of the following statements is not correct?

AEvery linear function is also a quadratic function.

BA function is defined by its domain together with its action.

CFor finite and small domains, the action of a function may be specified by a list.

DA function is a rule that assigns to every value x at least one value of y.

Answer : D

Question 5

You work for a brokerage firm that charges its client x per share. The volume of trade of a client of type A depends on the per share commission in the following manner. If the commission is x, the client of type A will trade e-ax shares on average each week. What is the optimal commission x that maximizes the income from client A, noting that a is greater than zero?

C42

Da2

Answer : C

Question 6

Every covariance matrix must be positive semi-definite. If it were not then:

ASome portfolios could have a negative variance

BOne or more of its eigenvalues would be negative

CThere would be no Cholesky decomposition matrix

DAll the above statements are true

Answer : D

Question 7

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.

A5.19

B5.66

C6.31

D4.18

Answer : C

PRMIA 8002 Mathematical Foundations of Risk Measurement :II P R M Exam Practice Test