[OFOD10e13] Binomial Trees

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* 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 six-month 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 one-year 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

* 8. In a binomial tree created to value an option on a stock, what is the expected return on the option?

A.Zero
B.The return required by the market
C.The risk-free rate
D.It is impossible to know without more information

* 9. A stock is expected to return 10% when the risk-free rate is 4%. What is the correct discount rate to use for the expected payoff on an option in the real world?

A.4%
B.10%
C.More than 10%
D.It could be more or less than 10%

* 10. Which of the following is true for a call option on a stock worth $50

A.As a stock’s expected return increases the price of the option increases
B.As a stock’s expected return increases the price of the option decreases
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 on the stock stays the same

* 11. Which of the following are NOT true

A.Risk-neutral valuation and no-arbitrage arguments give the same option prices
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.A hedge set up to value an option does not need to be changed
D.All of the above

* 12. 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?

A.$1.29
B.$1.49
C.$1.69
D.$1.89

* 13. The current price of a non-dividend paying stock is $30. Use a two-step tree to value a European put option on the stock with a strike price of $32 that expires in 6 months with u = 1.1 and d = 0.9. Each step is 3 months, the risk free rate is 8%.

A.$2.24
B.$2.44
C.$2.64
D.$2.84

* 14. Which of the following is NOT true in a risk-neutral world?

A.The expected return on a call option is independent of its strike price
B.Investors expect higher returns to compensate for higher risk
C.The expected return on a stock is the risk-free rate
D.The discount rate used for the expected payoff on an option is the risk-free rate

* 15. 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?

A.1.05
B.1.07
C.1.09
D.1.11

* 16. 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 p for a tree with a three-month time step?

A.0.50
B.0.54
C.0.58
D.0.62

* 17. The current price of a non-dividend paying stock is $50. Use a two-step tree to value an American put option on the stock with a strike price of $48 that expires in 12 months. Each step is 6 months, the risk free rate is 5% per annum, and the volatility is 20%. Which of the following is the option price?

A.$1.95
B.$2.00
C.$2.05
D.$2.10

* 18. Which of the following describes delta?

A.The ratio of the option price to the stock price
B.The ratio of the stock price to the option price
C.The ratio of a change in the option price to the corresponding change in the stock price
D.The ratio of a change in the stock price to the corresponding change in the option price

* 19. When moving from valuing an option on a non-dividend paying stock to an option on a currency which of the following is true?

A.The risk-free rate is replaced by the excess of the domestic risk-free rate over the foreign risk-free rate in all calculations
B.The formula for u changes
C.The risk-free rate is replaced by the excess of the domestic risk-free rate over the foreign risk-free rate for discounting
D.The risk-free rate is replaced by the excess of the domestic risk-free rate over the foreign risk-free rate when p is calculated

* 20. 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?

A.The parameters p and u are the same for both trees
B.The parameter p is the same for both trees but u is not
C.The parameter u is the same for both trees but p is not
D.None of the above