Question 1) How many nodes are there at the end of a Cox-Ross-Rubinstein five-step binomial tree?

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 a Cox, Ross, Rubinstein tree?

A) Make u a function of time

B) Make p a function of time

C) Make u and p a function of time

D) Make the lengths of the time steps unequal

8) What is the recommended way of making volatility a function of time in a Cox, Ross, Rubinstein tree?

A) Make u a function of time

B) Make p a function of time

C) Make u and p a function of time

D) Make the lengths of the time steps unequal

9) A binomial tree prices an American option at $3.12 and the corresponding European option at $3.04. The Black-Scholes price of the European option is $2.98. What is the control variate price of the American option?

A) $3.06

B) $3.18

C) $2.90

D) $3.08

10) The chapter discusses an alternative to the Cox, Ross, Rubinstein tree. In this alternative, which of the following are true?

A) The relationship between u and d is: u=1/d

B) The relationship between u and d is: u-1=1-d

C) The probabilities on the tree are all 0.5

D) None of the above

11) Which of the following cannot be valued by simulating paths through a tree in the way described in the chapter?

A) European options

B) American options

C) Asian options (i.e., options on the average stock price)

D) An option which provides a payoff of $100 if the stock price is greater than the strike price at maturity

12) For an option on futures, the volatility is 35%, the time step is three months, and the risk-free rate is 5%. What is the Cox, Ross, Rubinstein parameter, u?

A) 1.34

B) 1.29

C) 1.09

D) 1.19

13) For an option on futures, the volatility is 35%, the time step is three months, and the risk-free rate is 5%. What is the Cox, Ross, Rubinstein parameter, p?

A) 0.52

B) 0.46

C) 0.48

D) 0.50

14) When the volatility of an option increases from 30% to 32% the value of the option increases from $2.00 to $2.40. What is the vega of the option?

A) 0.20 dollars per %

B) 0.50 dollars per %

C) 0.80 dollars per %

D) 2.00 dollars per %

15) The values of a stock price at the end of the second time step are $80, $100, $125. The corresponding values of an option are $0, $5, and $20 respectively. What is an estimate of gamma?

A) 0.136

B) 0.146

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