Chapter 12 Introduction to Binomial Trees

1) 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. Which of the following hedges the position?

A) Buy 0.6 shares for each call option sold

B) Buy 0.4 shares for each call option sold

C) Short 0.6 shares for each call option sold

D) Short 0.4 shares for each call option sold

2) 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?

A) 0.6

B) 0.5

C) 0.4

D) 0.3

3) 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?

A) $1.6

B) $2.0

C) $2.4

D) $3.0

4) 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. Which of the following is necessary to hedge the position?

A) Buy 0.2 shares for each option purchased

B) Sell 0.2 shares for each option purchased

C) Buy 0.8 shares for each option purchased

D) Sell 0.8 shares for each option purchased

5) 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.

A) $3.93

B) $2.93

C) $1.93

D) $0.93

6) Which of the following describes how American options can be valued using a binomial tree?

A) Check whether early exercise is optimal at all nodes where the option is in-the-money

B) Check whether early exercise is optimal at the final nodes

C) Check whether early exercise is optimal at the penultimate nodes and the final nodes

D) None of the above

7) In a binomial tree created to value an option on a stock, the expected return on stock is

A) Zero

B) The return required by the market

C) The risk-free rate

D) It is impossible to know without more information