Hull: Options, Futures, and other Derivatives, Ninth EditionChapter 21: Basic Numerical Procedures Multiple Choice Test Bank: Questions 1. How many nodes are there at the end of a Cox-Ross-Rubinstein five-step binomial tree? A. 4 B. 5 C. 6 D. 7 2. Which of the following cannot be estimated from a single binomial tree? A. delta B. gamma C. theta D. vega 3. Which of the following is true for u in a Cox-Ross-Rubinstein binomial tree? A. It depends on the interest rate and the volatility B. It depends on the volatility but not the interest rate C. It depends on the interest rate but not the volatility D. It depends on neither the interest rate nor the volatility 4. How many different paths are there through a Cox-Ross-Rubinstein tree with four-steps? A. 5 B. 9 C. 12 D. 16 5. When we move from assuming no dividends to assuming a constant dividend yield, which of the following is true for a Cox, Ross, Rubinstein tree? A. The parameters u and p change B. p changes but u does not C. u changes but p does not D. Neither p nor u changes 6. When the stock price is 20 and the present value of dividends is 2, which of the following is the recommended way of constructing a tree? A. Draw a tree for an initial stock price of 20 and subtract the present value of future dividends at each node B. Draw a tree for an initial stock price of 22 and subtract the present value of future dividends at each node C. Draw a tree with an initial stock price of 18 and add the present value of future dividends at each node D. Draw a tree with an initial stock price of 18 and add 2 at each node 7. What is the recommended way of making interest rates a function of time in The implicit finite difference method relates prices at one node to three prices at nodes at the same time D. $3. Make u and p a function of time D. The Black-Scholes price of the European option is $2. The implicit finite difference method relates prices at one node to three prices at nodes at a later time B. Rubinstein tree? A. None of the above 13. None of the above 11. Make p a function of time C.e. The relationship between u and d is: u=1/d B.a Cox.18 C. Make the lengths of the time steps unequal 9. European options B. What is the recommended way of making volatility a function of time in a Cox. Ross.90 D. Ross. The probabilities on the tree are all 0.08 10.12 and the corresponding European option at $3. The implicit finite difference method relates prices at one node to three prices at nodes at an earlier time C. $2.Which of the following cannot be valued by Monte Carlo simulation A. Rubinstein tree? A. What is the control variate price of the American option? A. Make u a function of time B. Rubinstein tree.04. Make p a function of time C. Ross. which of the following are true: A. $3.5 D. $3.The chapter discusses an alternative to the Cox.Which of the following is true? A. Make u and p a function of time D. A binomial tree prices an American option at $3. An option which provides a payoff of $100 if the stock price is greater than the strike price at maturity 12. The relationship between u and d is: u-1=1-d C.Which of the following is true? A.06 B. Asian options (i. Make u a function of time B. The implicit finite difference method is equivalent to using a trinomial tree .. options on the average stock price) D. American options C. Make the lengths of the time steps unequal 8.98. In this alternative. 045 D. Rubinstein binomial tree? A. The first price is sometimes higher and sometimes lower than the second price D.A European option on a stock with a known dollar dividend is valued by setting the stock price variable equal to the stock price minus the present value of the dividend in the Black-Scholes-Merton formula.5 B. $125. 0.45 C. The interest rate and volatility must be constant . The first price is higher than the second price B. The interest rate can be a function of time but the volatility cannot D.156 D. 0. The time steps for American options are not equal D. Neither method is equivalent to using a trinomial tree 14. $5. The interest rate or the volatility can be a function of time. A second price can be obtained using the tree building procedure in the chapter. The explicit finite difference method is equivalent to using a trinomial tree C.What is the difference between valuing an American and a European option using a tree? A. 0. 0. The value of u is higher for American options B. The interest rate and volatility can both be functions of time B. Which of the following is true when a very large number of time steps are used in the tree? A. The first price is lower than the second price C. 0.The standard deviation of the values of an option calculated using 10.5. and $20 respectively. What is an estimate of gamma? A. The two prices are almost exactly the same 18. The average of the values is 20. The corresponding values of an option are $0. 0.0045 15.The values of a stock price at the end of the second time step are $80.B.136 B.166 16. Ross. but not both C.Which of the following is possible in a modified Cox. $100.000 Monte Carlo trials is 4. It is necessary to do two calculations at nodes where the option is in the money 17.146 C. What is the standard error of this as an estimate of the option price? A. 0. The value of u is lower for American options C. 4. Both methods are equivalent to using a trinomial tree D. American put options on futures . All of the above 20. American call options on a currency D. The tree recombines D. The expected return during each time step is the risk-free rate B. American put options on a non-dividend paying stock B. The standard deviation of the return in each time step is. for small time steps.19. almost exactly equal to the volatility per annum times the square root of the length of the time step in years C. American call options on a non-dividend paying tock C.Which of the following describes the way that the parameters in a binomial tree are chosen? A.Which of the following can be valued without using a numerical procedure such as a binomial tree? A.