Indicate detailed solution for each:

1. A one-year call option on a stock with a strike price of $50 costs $4; a one-year put option on the stock with a strike price of $50 costs $3. Suppose that a trader buys one call option and two put options. What should be the stock price for the trader to make a profit?

2. You own 200 shares of XYZ traded at $42 each. What would be the breakeven points if you write three 45 call contracts at $4?

3. An asset is trading for $45. Three month American 40 puts are selling for $ The risk free rate is 10% per annum. What are the boundaries of an American 40 call on the same asset with the same expiration date as the put to avoid arbitrage opportunities?
4. European two-month 50 and 55 puts are trading for $2 and $8, respectively. What do you do if the risk free rate is 10% per year and you think you have an arbitrage opportunity? Justify your answer

5. You have a stock trading at $60. You expect the stock to go to either 70 or 50 in one period. The risk free rate for the period is 3%. What is the value of a 60 call on the stock? Justify your answer.

6. The price of a stock is $54. A trader sells 50 put option contracts on the stock with a strike price of $50 when the option price is $4. The options are exercised when the stock price is $49. What is the traders net profit or loss? Justify your answer.

7. Assume that you purchase 100 shares of EBAY at $100. You observe 2-month $100 calls trading at $5 and 2-month $105 calls trading at $3.

If you add a 1:3 call ratio spread (that is buying one $100 call contract and writing three $105 call contracts), what would be the characteristics of your position?