8007無料問題集「PRMIA Exam II: Mathematical Foundations of Risk Measurement

質問 1

Which of the following statements is true?

（A）Discrete and continuous compounding produce the same results if the discount rate is positive.

（B）Continuous compounding can be thought as making the compounding period infinitesimally small.

（C）The constant plays an important role in the mathematical description of continuous compounding.

（D）Continuous compounding is the better method because it results in higher present values compared to discrete compounding.

正解：B 解答を投票する

質問 2

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

（A）x = -3 is a maximum

（B）None of these

（C）x = 0 is a minimum

（D）x = 2 is a maximum

正解：B 解答を投票する

質問 3

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）5

（B）10

（C）100

（D）25

正解：B 解答を投票する

質問 4

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

（A）Statements 2 and 3 are correct

（B）Statements 1 and 2 are correct

（C）Statements 1 and 3 are correct

（D）All three statements are correct

正解：C 解答を投票する

質問 5

In a binomial tree lattice, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of . The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. The risk neutral probability for an up move is:

（A）0.5286

（B）0.5288

（C）0.5292

（D）0.5290

正解：B 解答を投票する

質問 6

The first derivative of a function f(x) is zero at some point, the second derivative is also zero at this point. This means that:

（A）f has necessarily neither a minimum nor a maximum at this point

（B）f has necessarily a maximum at this point

（C）f has necessarily a minimum at this point

（D）f might have either a minimum or a maximum or neither of them at this point

正解：D 解答を投票する

質問 7

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 2

（B）arithmetic sequence, common ratio 2

（C）geometric sequence, common ratio 3

（D）arithmetic sequence, common difference 2

正解：A 解答を投票する

質問 8

Two vectors are orthogonal when:

（A）their scalar product (sum product) is zero

（B）their determinant is zero

（C）one is a scalar multiple of the other

（D）their components are linearly dependent

正解：A 解答を投票する

質問 9

Kurtosis(X) is defined as the fourth centred moment of X, divided by the square of the variance of X.
Assuming X is a normally distributed variable, what is Kurtosis(X)?

（A）3

（B）1

（C）2

（D）0

正解：A 解答を投票する

質問 10

Let X be a random variable normally distributed with zero mean and let . Then the correlation between X and Y is:

（A）zero

（B）positive

（C）not defined

（D）negative

正解：A 解答を投票する

8007 無料問題集「PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition」

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