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Hull: Options, Futures, and other Derivatives, Ninth Edition Chapter 21: Basic Numerical Procedures Multiple Choice Test Bank: Questions with Answers 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 Answer: C The number of nodes at the end of one time step is 2; the number of nodes at the end of two time steps is 3; and so on. 2. Which of the following cannot be estimated from a single binomial tree? To calculate vega it is necessary to increase volatility slightly and construct a new tree. The other three can be estimated from a single tree. 3. Which of the following is true for u in a Cox-Ross-Rubinstein binomial tree? . t e u It therefore depends on volatility but not the interest rate. 4. How many different paths are there through a Cox-Ross-Rubinstein tree with four-steps?

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There are two choices for the path chosen at the initial node, two choices at the node reached at the end of the first time step, and so on. The total number of paths is 2 4 = 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 Answer: B The formula for u does not change but the formula for p does change. 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? We first subtract the present value of dividends from the initial stock price. We then draw the
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