Binomial Trees

Chapter 12: Binomial Trees

 

1. A stock price is currently $50. It is known that at the end of two months it will be either $53 or $48. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a two-month European call option with a strike price of $49?

 

 

1. Solve the long form using portfolios with binomial tree drawing
2. Solve the formula-based calculation (both a and b answers should be same for the price of option)

Answer:  2.23

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2. A stock price is currently $40. It is known that at the end of three months it will be either $45 or $35. The risk-free rate of interest with quarterly compounding is 8% per annum. Calculate the value of a three-month European put option on the stock with an exercise price of $40.

 

1. Solve the long form using portfolios with binomial tree drawing
2. Solve the formula-based calculation (both a and b answers should be same for the price of option)

Answer: 2.06

3. Two stage Binomial problem (PUT, class slides)

 

4. Two step binomial problem.  A stock price is currently $50. Over each of the next two three-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a six-month European call option with a strike price of $51?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Chapter 7: Swaps

Companies X and Y have been offered the following rates per annum on a $5 million 10-year investment:

 

	Fixed Rate	Floating Rate
Company X	8.0%	LIBOR
Company Y	8.8%	LIBOR

 

Company X requires a fixed-rate investment; company Y requires a floating-rate investment. Design a swap that will net a bank, acting as intermediary, 0.2% per annum and will appear equally attractive to X and Y.

What is the NET after SWAP is completed for company X and Y?

The spread between the interest rates offered to X and Y is 0.8% per annum on fixed rate investments and 0.0% per annum on floating rate investments. This means that the total apparent benefit to all parties from the swap is 0.8% per annum.  Of this 0.2% per annum will go to the bank. This leaves 0.3% per annum for each of X and Y. In other words, company X should be able to get a fixed-rate return of 8.3% per annum while company Y should be able to get a floating-rate return LIBOR + 0.3% per annum. The required swap is shown in Figure S7.1. The bank earns 0.2%, company X earns 8.3%, and company Y earns LIBOR + 0.3%.

 

 

 

 

 

 

 

 

 

 

 

Chapter 11 Trading Strategies

Problem1

An investor believes that there will be a big jump in a stock price, but is uncertain as to the direction. Identify different strategies the investor can follow and explain the differences among them.

Possible strategies are: Strangle; Straddle; Strip; Strap

The strategies all provide positive profits when there are large stock price moves. A strangle is less expensive than a straddle, but requires a bigger move in the stock price in to provide a positive profit. Strips and straps are more expensive than straddles but provide bigger profits in certain circumstances. A strip will provide a bigger profit when there is a large downward stock price move. A strap will provide a bigger profit when there is a large upward stock price move. In the case of strangles, straddles, strips and straps, the profit increases as the size of the stock price movement increases.

 

Problem 2

Suppose that put options on a stock with strike prices $30 and $35 cost $4 and $7, respectively. How can the options be used to create (a) a bull spread and (b) a bear spread?

Draw the payoff diagram and show all the data on the diagram.

Construct a table that shows the profit and payoff for both spreads.

 

Problem 3

A call with a strike price of $60 costs $6. A put with the same strike price and expiration date costs $4.

Draw the payoff diagram and show all the data on the diagram.

Construct a table that shows the profit from a straddle.

For what range of stock prices would the straddle lead to a loss?