1. Today’s price of a non-dividend paying stock is $60. Use a two-step tree to value a European call option on the stock with a strike price of $60 that expires in 6 months. Each step is 3 months. The risk free rate is 5% per annum with continuous compounding. Assume that the option is written on 100 shares of stock, and that u = 1.15 and d = 0.85.

What is the option price today?

How would you hedge a position where you buy the call option today?

2. Today’s price of a non-dividend paying stock is $60. Use a two-step tree to value a European call option on the stock with a strike price of $60 that expires in 6 months. Each step is 3 months. The risk free rate is 5% per annum with continuous compounding. Assume that the option is written on 100 shares of stock, and that u = 1.15 and d = 0.85.

What is the option price today?

How would you hedge a position where you buy the call option today?

3. The exercise price of the options is $100 per share, all options are European and the stock does not pay any dividend. The call price is $10 per share and the put price is $3 per share. Both options mature in 1 year. Finally the annual rate of interest is 5% with continuous compounding. What is the share price today?

For questions 4 and 5, use the following information: stock price is $95 per share, exercise price of the options is $100 per share, all options are European and the stock does not pay any dividend.Option contracts are written on 100 shares of stock and mature in 3 months.The call price is $2 per share and the put price is $6 per share.

4. Use the put and call options and the underlying stock to create a portfolio which will be equivalent to lending $10,000 (face amount) for 3 months.

5. What is the rate of interest that you receive on the money that you have lent in 9). Give this rate per annum with continuous compounding.