Exam 13: Binomial Trees

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?

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.

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?

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?

In a binomial tree created to value an option on a stock,what is the expected return on the option?

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%.

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?

In a binomial tree created to value an option on a stock,the expected return on stock is

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?

Which of the following describes how American options can be valued using a binomial tree?

Which of the following are NOT true

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 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?

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?

Which of the following is true for a call option on a stock worth $50

Which of the following is NOT true in a risk-neutral world?

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?

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?

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?

Which of the following describes delta?