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**** 8002 Description | 8002 Syllabus | 8002 Exam Objectives | 8002 Course Outline ****
**** SAMPLE II- Mathematical Foundations of Risk Measurement 2021 Dumps ****
QUESTION: 124
What is a Hessian?
A. Correlation matrix of market indices
B. The vector of partial derivatives of a contingent claim
C. A matrix of second derivatives of a function
D. The point at which a minimum of a multidimensional function is achieved
Answer: C
QUESTION: 125
The Newton-Raphson method
A. is based on finding a middle point between left and right end of the search interval
B. is based on Taylor series and uses the first derivative
C. can be used for continuous but not differentiable functions
D. does provide an error bound along with every iteration
Answer: B
QUESTION: 126
The gradient of a smooth function is
A. a vector that shows the direction of fastest change of a function
B. matrix of second partial derivatives of a function
C. infinite at a maximum point
D. a matrix containing the function’s second partial derivatives
Answer: A
QUESTION: 127
The gradient of a function f(x, y, z) = x + y2 — x y z at the point x = y = z = 1 is
A. (0, 2, 1)
B. (0, 0, 0)
39
C. (1, 1, 1)
D. (0, 1, -1)
Answer: D
QUESTION: 128
Variance reduction is:
A. A technique that is applied in regression models to improve the accuracy of the
coefficient estimates
B. A numerical method for finding portfolio weights to minimize the variance of a
portfolio that has a given expected return
C. A numerical method for finding the variance of the underlying that is implicit in a
market price of an option
D. A method for reducing the number of simulations required in a Monte Carlo
simulation
Answer: D
QUESTION: 129
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. 11.82
B. 12.33
C. 12.49
D. 12.78
Answer: C
QUESTION: 130
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:
40
A. 0.5290
B. 0.5292
C. 0.5286
D. 0.5288
Answer: D
QUESTION: 131
A 2-step binomial tree is used to value an American put option with strike 105, given that
the underlying price is currently 100. At each step the underlying price can move up by
10 or down by 10 and the risk-neutral probability of an up move is 0.6. There are no
dividends paid on the underlying and the continuously compounded risk free interest rate
over each time step is 1%. What is the value of the option in this model?
A. 7.12
B. 6.59
C. 7.44
D. 7.29
Answer: A
QUESTION: 132
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
Answer: C
41
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