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

1. When calculating the implied volatility from an option price we use the bisection method and know initially that the volatility is somewhere between 1% and 100%. How many iterations do we need in order to determine the implied volatility with accuracy of 0.1%?

A) 25
B) 100
C) 10
D) 5

2. For the function f(x) =3x-x3 which of the following is true?

A) x = 0 is a minimum
B) x = 2 is a maximum
C) None of these
D) x = -3 is a maximum

3. The Newton-Raphson method

A) is based on finding a middle point between left and right end of the search interval
B) can be used for continuous but not differentiable functions
C) is based on Taylor series and uses the first derivative
D) does provide an error bound along with every iteration

4. Which of the following statements is true for symmetric positive definite matrices?

A) If a is its eigenvalue, then is also its eigenvalue
B) If a is its eigenvalue, then -a is also its eigenvalue
C) One of its eigenvalues equals 0
D) Its eigenvalues are all positive

5. The natural logarithm of x is:

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

Solutions: