What is the result corresponding to that in Problem 9.23 for European put options? 9.15.

Suppose that you are the manager and sole owner of a highly leveraged company. All the debt will mature in 1 year. If at that time the value of the company is greater than the face value of the debt, you will pay off the debt. If the value of the company is less than the face value of the debt, you will declare bankruptcy and the debt holders will own the

(a) Express your position as an option on the value of the company.

(b) Express the position of the debt holders in terms of options on the value of the company.

(c) What can you do to increase the value of your position? 9.26 Consider an option on a stock when the stock price is $41, the strike price is $40, the risk- free rate is 6%, the volatility is 38%, and the time to maturity in 1 year. Assume that a dividend of $0.50 is expected after 6 months.

(a) Use DerivaGem to value the option assuming it is a European call.

(b) Use DerivaGem to value the option assuming it is a European pat.

(c) Verify that put-call parity holds.

(d) Explore using DerivaGem what happens to the price of the options as the time to maturity becomes very large. For this purpose, assume there are no dividends. Explain the results you get.