1) Consider a 2-year European put with a strike price of $60 on a stock whose current price is $57. We assume that there are two time steps of 1 year, and in each time step the stock price either moves up by 15% or moves down by 15%. Let the risk-free interest rate be 4%. What will be the value of this put?

a. 3.25

b. 2.25

c. None is correct

d. 0

e. 4.25

f. 1.25

2) Consider a European put option on a non-dividend-paying stock when the stock price is $40, the strike price is $42, the time to maturity is 3 months, and the risk-free rate of interest is 8% per annum. Find a lower bound for the option price.

a. 2.85

b. 1.17

c. -2.85

d. 1.89

e. This info is not sufficient.

f. 2.65

3) Let L=x²t³. Using Its Lemma, find the value of p.

a. Several options are correct.

b. t(2ax+b²)+x²

c. 2axt³ + 3x²t² + t²b²

d. 2axt+x²+bt

e. 3ax²t² + 2x³t + 3bxt²

f. b + 2xt³

g. None is correct.

4) Let the current price of a stock be 25 . Now suppose that the change in its value during one year is f(0,1). Here, f(x,y) denotes a probability distribution which is normally distributed with mean x and standard deviation y. What is the probability distribution of the stock price at the end of 1/3 years?

a. Several answers are correct.

b. Normal distribution

c. The information is not sufficient.

d. None of the above

5) Let the current price of a stock be 25 . Now suppose that the change in its value during one year is f(0,1). Here, f(x,y) denotes a probability distribution which is normally distributed with mean x and standard deviation y. What is the probability distribution of the stock price at the end of 1/3 years?

a. Several answers are correct.

b. Normal distribution

c. The information is not sufficient.

d. None of the above

e. Beta distribution

f. Standard normal distribution

g. Log-normal distribution

e. Beta distribution

f. Standard normal distribution

g. Log-normal distribution

6) Consider the position of an investor who shorts 400 shares in March when the price per share is $104 and closes out the position by buying them back in June when the price per share is $99. Suppose that a dividend of $2 per share is paid in April. What would be his/her net gain (in dollars) when the position is closed out in June?

a. 915

b. 1255

c. 790

d. 850

e. 0

f. 660

g. All are wrong