week 9 MCQ's Flashcards
The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. An investor sells six-month call options with a strike price of $32. Which of the following hedges the position?
Select one:
a. Short 0.4 shares for each call option sold
b. Short 0.6 shares for each call option sold
c. Buy 0.6 shares for each call option sold
d. Buy 0.4 shares for each call option sold
Buy 0.4 shares for each call option sold
The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. What is the risk-neutral probability of that the stock price will be $36?
Select one:
a. 0.4
b. 0.6
c. 0.5
d. 0.3
0.4
The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume the risk-free rate is zero. An investor sells call options with a strike price of $32. What is the value of each call option?
Select one:
a. $2.0
b. $3.0
c. $2.4
d. $1.6
$1.6
The current price of a non-dividend-paying stock is $40. Over the next year it is expected to rise to $42 or fall to $37. An investor buys one-year put options with a strike price of $41. Which of the following is necessary to hedge the position?
Select one:
a. Sell 0.2 shares for each option purchased
b. Buy 0.8 shares for each option purchased
c. Buy 0.2 shares for each option purchased
d. Sell 0.8 shares for each option purchased
Buy 0.8 shares for each option purchased
The current price of a non-dividend-paying stock is $40. Over the next year it is expected to rise to $42 or fall to $37. An investor buys put options with a strike price of $41. What is the value of each option? The risk-free interest rate is 2% per annum with continuous compounding.
Select one:
a. $1.93
b. $2.93
c. $3.93
d. $0.93
$0.93
Which of the following describes how American options can be valued using a binomial tree?
Select one:
a. Check whether early exercise is optimal at the final nodes
b. Check whether early exercise is optimal at all nodes where the option is in-the-money
c. None of the above
d. Check whether early exercise is optimal at the penultimate nodes and the final nodes
Check whether early exercise is optimal at all nodes where the option is in-the-money
In a binomial tree created to value an option on a stock, the expected return on stock is
Select one:
a. It is impossible to know without more information
b. The risk-free rate
c. The return required by the market
d. Zero
The risk-free rate
In a binomial tree created to value an option on a stock, what is the expected return on the option?
Select one:
a. The risk-free rate
b. The return required by the market
c. Zero
d. It is impossible to know without more information
The risk-free rate
Which of the following is true for a call option on a stock worth $50
Select one:
a. As a stock’s expected return increases the price of the option decreases
b. As a stock’s expected return increases the price of the option on the stock stays the same
c. As a stock’s expected return increases the price of the option might increase or decrease
d. As a stock’s expected return increases the price of the option increases
As a stock’s expected return increases the price of the option on the stock stays the same
Which of the following are NOT true
Select one:
a. A hedge set up to value an option does not need to be changed
b. Risk-neutral valuation involves assuming that the expected return is the risk-free rate and then discounting expected payoffs at the risk-free rate
c. All of the above
A hedge set up to value an option does not need to be changed
The current price of a non-dividend paying stock is $30. Use a two-step tree to value a European call option on the stock with a strike price of $32 that expires in 6 months. Each step is 3 months, the risk free rate is 8% per annum with continuous compounding. What is the option price when u = 1.1 and d = 0.9?
Select one:
a. $1.49
b. $1.69
c. $1.89
d. $1.29
$1.49
Which of the following is NOT true in a risk-neutral world?
Select one:
a. Investors expect higher returns to compensate for higher risk
b. The expected return on a stock is the risk-free rate
c. The discount rate used for the expected payoff on an option is the risk-free rate
d. The expected return on a call option is independent of its strike price
Investors expect higher returns to compensate for higher risk
If the volatility of a non-dividend paying stock is 20% per annum and a risk-free rate is 5% per annum, which of the following is closest to the Cox, Ross, Rubinstein parameter u for a tree with a three-month time step?
Select one:
a. 1.09
b. 1.07
c. 1.11
d. 1.05
1.11
Which of the following describes delta?
Select one:
a. The ratio of a change in the stock price to the corresponding change in the option price
b. The ratio of a change in the option price to the corresponding change in the stock price
c. The ratio of the stock price to the option price
d. The ratio of the option price to the stock price
The ratio of a change in the option price to the corresponding change in the stock price
A tree is constructed to value an option on an index which is currently worth 100 and has a volatility of 25%. The index provides a dividend yield of 2%. Another tree is constructed to value an option on a non-dividend-paying stock which is currently worth 100 and has a volatility of 25%. Which of the following are true?
Select one:
a. The parameters p and u are the same for both trees
b. The parameter u is the same for both trees but p is not
c. The parameter p is the same for both trees but u is not
d. None of the above
The parameter u is the same for both trees but p is not
