Exam 18: Binomial Trees in Practice

A European option on a stock with 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.A second price can be obtained using the tree building procedure in the chapter.Which of the following is true when a very large number of time steps are used in the tree?

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?

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 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?

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

What is the recommended way of making interest rates a function of time in a Cox,Ross,Rubinstein tree?

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?

Which of the following is possible in a modified Cox,Ross,Rubinstein binomial tree?

Which of the following is true for u in a Cox-Ross-Rubinstein binomial tree?

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

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?

Which of the following describes the way that the parameters in a binomial tree are chosen?

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

Which of the following cannot be estimated from a single binomial tree?

Which of the following can be valued without using a numerical procedure such as a binomial tree?

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

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?

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?

How many different paths are there through a Cox-Ross-Rubinstein tree with four-steps?

What is the difference between valuing an American and a European option using a tree?