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NEW QUESTION 56
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. 12.78
- D. 12.49
Answer: D
NEW QUESTION 57
What is the maximum value of the function F(x, y)=x2+y2 in the domain defined by inequalities x 1, y -2, y-x 3 ?
- A. 0
- B. 1
- C. 2
- D. 3
Answer: D
NEW QUESTION 58
You intend to invest $100 000 for five years. Four different interest payment options are available. Choose the interest option that yields the highest return over the five year period.
- A. a continuously-compounded rate of 4%
- B. a lump-sum payment of $22 500 on maturity (in five years)
- C. a quarterly-compounded rate of 4.1%
- D. an annually compounded rate of 4.15%
Answer: C
NEW QUESTION 59
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)) = 0.6065
- C. E(exp(X)) = 1
- D. E(exp(X)) = 2.7183
Answer: A
NEW QUESTION 60
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. 0.5290
- B. 0.5286
- C. 0.5292
- D. 0.5288
Answer: D
NEW QUESTION 61
In statistical hypothesis tests, 'Type I error' refers to the situation in which...
- A. Both null hypothesis and alternative hypothesis are rejected
- B. The null hypothesis is rejected when in fact it should have been accepted
- C. The null hypothesis is accepted when in fact it should have been rejected
- D. Both null hypothesis and alternative hypothesis are accepted
Answer: B
NEW QUESTION 62
The gradient of a function f(x, y, z) = x + y2 - x y z at the point x = y = z = 1 is
- A. (0, 1, -1)
- B. (0, 0, 0)
- C. (1, 1, 1)
- D. (0, 2, 1)
Answer: A
NEW QUESTION 63
In a multiple linear regression, the significance of R2 can be tested using which distribution?
- A. Binomial distribution
- B. Student's t distribution
- C. Normal distribution
- D. F-distribution
Answer: D
NEW QUESTION 64
When a number is written with a fraction as an exponent, such as , which of the following is the correct computation?
- A. Multiply 75 by 2.5
- B. Take the square-root of 75 and raise it to the 5th power
- C. Square 75, then take the fifth root of it
- D. Divide 75 by 2, then raise it to the 5th power
Answer: B
NEW QUESTION 65
Which of the following statements are true about Maximum Likelihood Estimation?
(i) MLE can be applied even if the error terms are not i.i.d. normal.
(ii) MLE involves integrating a likelihood function or a log-likelihood function.
(iii) MLE yields parameter estimates that are consistent.
- A. (i), (ii), and (iii)
- B. (i) only
- C. (i) and (ii)
- D. (i) and (iii)
Answer: D
NEW QUESTION 66
Suppose we perform a principle component analysis of the correlation matrix of the returns of 13 yields along the yield curve. The largest eigenvalue of the correlation matrix is 9.8. What percentage of return volatility is explained by the first component? (You may use the fact that the sum of the diagonal elements of a square matrix is always equal to the sum of its eigenvalues.)
- A. Cannot be determined without estimates of the volatilities of the individual returns
- B. 98%
- C. 64%
- D. 75%
Answer: D
NEW QUESTION 67
I have a portfolio of two stocks. The weights are equal. The one volatility is 30% while the other is 40%. The minimum and maximum possible values of the volatility of my portfolio are:
- A. 5% and 35%
- B. 10% and 70%
- C. 30% and 40%
- D. 10% and 40%
Answer: A
NEW QUESTION 68
Let f(x) = c for x in [0,4] and 0 for other values of x.
What is the value of the constant c that makes f(x) a probability density function; and what if f(x) = cx for x in
[0,4]?
- A. 1/4 and 1/6
- B. 1/7 and 1/9
- C. 1/4 and 1/7
- D. None of the above
Answer: D
NEW QUESTION 69
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. 0.14
- B. 0.25
- C. 0.50
- D. 0.02
Answer: A
NEW QUESTION 70
Newton-Raphson iteration is used to find a solution of x5 - x3 + x = 1. If xn = 2, what is xn+1?
- A. 1.623
- B. 0.377
- C. 2.362
- D. 1.638
Answer: D
NEW QUESTION 71
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