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PRMIA 8007 - Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition

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Total 132 questions

An operational risk analyst models the occurrence of computer failures as a Poisson process with an arrival rate of 2 events per year. According to this model, what is the probability of zero failures in one year?

A.

0.02

B.

0.14

C.

0.25

D.

0.50

At what point x does the function f(x) = x3 - 4x2 + 1 have a local minimum?

A.

-0.666666667

B.

0

C.

2.66667

D.

2

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.

5.19

B.

5.66

C.

6.31

D.

4.18

Which of the following properties is exhibited by multiplication, but not by addition?

A.

associativity

B.

commutativity

C.

distributivity

D.

invertibility

A quadratic form is

A.

defined as a positive definite Hessian matrix.

B.

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

C.

a specific solution of the Black-Scholes pricing formula

D.

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

Consider the linear regression model for the returns of stock A and the returns of stock B. Stock A is 50% more volatile than stock B. Which of the following statements is TRUE?

A.

The stocks must be positively correlated ( )

B.

Beta must be positive ( )

C.

Beta must be greater in absolute value than the correlation of the stocks ( )

D.

Alpha must be positive ( )

What is the probability of tossing a coin and getting exactly 2 heads out of 5 throws?

A.

8/15

B.

9/23

C.

10/32

D.

None of these

If a time series has to be differenced twice in order to be transformed into a stationary series, the original series is said to be:

A.

non-linear

B.

integrated of order 2

C.

differential

D.

non-functional

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

A.

1

B.

0.5

C.

0

D.

None of the above

Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?

A.

E(exp(X)) = 1.6487

B.

E(exp(X)) = 1

C.

E(exp(X)) = 2.7183

D.

E(exp(X)) = 0.6065