Problem 1:

A trader wants to construct a top vertical combination: she sells a call option with a strike price of $60 and a put option with a strike price of $40. Both options have the same maturity. The call costs $5 and the put costs $7.

1. Construct a table showing the payoff from the strategy. (3 pts)
2. Construct a table showing the profit from the strategy. (3 pts)
3. What is the profit/loss achieved on the strategy if the stock price at the option expiry is equal to S20? (1 pts)
4. What is the profit/loss achieved on the strategy if the stock price at the option expiry is equal to $50? (1 pts)
5. What is the profit/loss achieved on the strategy if the stock price at the option expiry is equal to S80? (1 pts)
6. What stock level(s) will result in zero profits? (2 pts)
7. Draw the profit diagram of such a strategy for different ranges of stock prices? (2 pts)
8. What is the possible risk that the trader is facing? (1 pt)

Problem 2 (10 pts)

The current price of a non-dividend-paying stock is $100 with a volatility of 45%. The risk-free rate of interest with continuous compounding is 5% per annum. The stock pays no dividend.

For a three-month time step:

1. What is the percentage up movement? (1 pt)
2. What is the percentage down movement? (1 pt)
3. What is the probability of an up movement in a risk-neutral world? (1 pt)
4. What is the probability of a down movement in a risk-neutral world? (1 pt)
5. Use a two-step tree to value a six-month European call option with the strike price is $111. (6 pt)

Problem 3 (10 pts)

A stock price is currently $100. It is known that at the end of three months it will be either $120 or $80.

The risk-free rate of interest with continuous compounding is 6% per annum. The stock pays no dividend.

1. What is the percentage up movement? (1 pt)
2. What is the percentage down movement? (1 pt)
3. What is the probability of an up movement in a risk-neutral world? (1 pt)
4. What is the probability of a down movement in a risk-neutral world? (1 pt)
5. Use a two-step tree to value a six-month American put option with the strike price is $90. (6 pt)