Options, Futures and Other Derivatives, Hull

Hull: Options, Futures, and Other Derivatives, Ninth Edition Chapter 13: Introduction to Binomial Trees Multiple Choice Test Bank: Questions 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 Hull: Options, Futures, and Other Derivatives, Ninth Edition Chapter 14: Wiener Processes and Ito's Lemma Multiple Choice Test Bank: Questions 1. A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz where time is measured in years. If a = 2 and b =3 what is the expected value after 3 years? A. 12 B. 14 C. 16 D. 18 2. A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz where time is measured in years. If a = 3 and b =4 what is the standard deviation of the value in 4 years? A. 4 B. 8 C. 12 D. 16 3. A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz If a = 3 and b =4 what is the standard deviation of the value in three months? A. 1 B. 2 C. 3 D. 4 4. The variance of a Wiener process in time t is A. t B. t squared C. the square root of t D. t to the power of 4 5. The process followed by a variable X is dX = mX dt+sX dz What is the coefficient of dz in the process for the square of X. A. sX B. sX2 C. 2sX2 D. msX 6. The process followed by a variable X is dX = mX dt+sX dz What is the coefficient of dt in the process for the square of X. A. 2mX2+s2X2 B. 2mX2 C. mX2+2s2X2 D. mX2+s2X2 7. Which of the following is true when the stock price follows geometric Brownian motion A. The future stock price has a normal distribution B. The future stock price has a lognormal distribution C. The future stock price has geometric distribution D. The future stock price has a truncated normal distribution 8. If a stock price follows a Markov process which of the following could be true A. Whenever the stock price has gone up for four successive days it has a 70% chance of going up on the fifth day. B. Whenever the stock price has gone up for four successive days there is almost certain to be a correction on the fifth day. C. The way the stock price moves on a day is unaffected by how it moved on the previous four days. D. Bad years for stock price returns are usually followed by good years. 9. A variable x starts at zero and follows the generalized Wiener process dx = a dt + b dz where time is measured in years. During the first two years a=3 and b=4. During the following three years a=6 and b=3. What is the expected value of the variable at the end of 5 years A. 16 B. 20 C. 24 D. 30 10. A variable x starts at zero and follows the generalized Wiener process dx = a dt + b dz where time is measured in years. During the first two years a=3 and b=4. During the following three years a=6 and b=3. What the standard deviation of the value of the variable at the end of 5 years A. 6.2 B. 6.7 C. 7.2 D. 7.7 11. If a variable x follows the process dx = b dz where dz is a Wiener process, which of the following is the process followed by y = exp(x). A. dy = by dz B. dy = 0.5b2y dt+by dz C. dy =( y+0.5b2y) dt+by dz D. dy = 0.5b2y dt+b dz 12. If the risk-free rate is r and price of a nondividend paying stock grows at rate mwith volatility s, at what rate does a forward price of the stock grow for a forward contract maturing at a future time T. A. m B. ms2/2 C. mr D. rs2/2 13. When a stock price, S, follows geometric Brownian motion with mean return m and volatility s what is the process follows by X where X = ln S. A. dX = m dt + s dz B. dX = (mr) dt + s dz C. dX = (ms2) dt + s dz D. dX = (m s2/2) dt + s dz 14. Which of the following gives a random sample from a standard normal distribution in Excel? A. =NORMSINV() B. =NORMSINV(RAND()) C. =RND(NORMSINV()) D. =RAND() 15. Which of the following defines an Ito process? A. A process where the drift is non-constant and can be stochastic B. A process where the coefficient of dz is non-constant and can be stochastic C. A process where either the drift or the coefficient of dz or both are non-constant and can be stochastic D. A process where proportional changes follow a generalized Wiener process 16. A stock price is $20. It has an expected return of 12% and a volatility of 25%. What is the standard deviation of the change in the price in one day. (For this question assume that there are 365 days in the year.) A. $0.20 B. $0.23 C. $0.26 D. $0.29 17. A stock price is $20. It has an expected return of 12% and a volatility of 25%. What is the stock price that has a 2.5% chance of being exceeded in one day? (For this question assume that there are 365 days in the year.) A. $20.41 B. $20.51 C. $20.61 D. $20.71 18. Which of the following is NOT a property of a Wiener process? A. The change during a short period of time dt has a variance dt B. The changes in two different short periods of time are independent C. The mean change in any time period is zero D. The standard deviation over two consecutive time periods is the sum of the standard deviations over each of the periods 19. If e is a random sample from a standard normal distribution, which of the following is the change in a Wiener process in time dt . A. e times the square root of dt B. e times dt C. dt times the square root of e D. The square root of e times the square root of dt 20. For what value of the correlation between two Wiener processes is the sum of the processes also a Wiener process? A. 0.5 B. 0.5 C. 0 D. 1