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

質問 1

What is the indefinite integral of the function f(x) = ln(x), where ln(x) denotes the natural logarithmic function?

（A）ln(x) - x

（B）1/x

（C）exp(x)

（D）x ln(x) - x

正解：D 解答を投票する

質問 2

If A and B are two events with P(A) = 1/4, P(B) = 1/3 and P(A intersection B) =1/5, what is P(Bc | Ac) i.e. the probability of the complement of B when the complement of A is given?

（A）12/29

（B）3/4

（C）37/45

（D）None of these

正解：C 解答を投票する

質問 3

A 2-step binomial tree is used to value an American put option with strike 104, given that the underlying price is currently 100. At each step the underlying price can move up by 20% or down by 20% and the risk-neutral probability of an up move is 0.55. There are no dividends paid on the underlying and the discretely compounded risk free interest rate over each time step is 2%. What is the value of the option in this model?

（A）12.78

（B）12.33

（C）12.49

（D）11.82

正解：C 解答を投票する

質問 4

Variance reduction is:

（A）A numerical method for finding portfolio weights to minimize the variance of a portfolio that has a given expected return

（B）A technique that is applied in regression models to improve the accuracy of the coefficient estimates

（C）A method for reducing the number of simulations required in a Monte Carlo simulation

（D）A numerical method for finding the variance of the underlying that is implicit in a market price of an option

正解：C 解答を投票する

質問 5

When a number is written with a fraction as an exponent, such as , which of the following is the correct computation?

（A）Square 75, then take the fifth root of it

（B）Take the square-root of 75 and raise it to the 5th power

（C）Divide 75 by 2, then raise it to the 5th power

（D）Multiply 75 by 2.5

正解：B 解答を投票する

質問 6

What is the total derivative of the function f(x,y) = ln(x+y), where ln() denotes the natural logarithmic function?

（A）(x + y) / (x+y)

（B）1 / (x+y)

（C）-x/(x+y) - y/(x+y)

（D）ln(x+y) x + ln(x+y) y

正解：A 解答を投票する

質問 7

Bond convexity is closely related to ...

（A）The sensitivity of the bond's present value with respect to yield

（B）The second derivative 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 integral of the bond's present value with respect to yield

正解：B 解答を投票する

質問 8

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 9

Calculate the determinant of the following matrix:

（A）4.25

（B）4

（C）-4.25

（D）2

正解：D 解答を投票する

質問 10

Maximum likelihood estimation is a method for:

（A）Estimating the implied volatility of a simple European option

（B）Solving a portfolio optimization problem

（C）Finding parameter estimates of a given density function

（D）Estimating the solution of a partial differential equation

正解：C 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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