1. The common stock of Texas Energy Company is selling at $90. A 1-year call option written on Texas’s stock is selling for $8. The call’s exercise price is $100. The risk-free interest rate is 1% per year. Suppose that puts on Texas stock are not tradable, but you want to buy one. How would you do it? Suppose that puts are traded, what should a 1- year put with an exercise price of $100 sell for?
2. The CEO of an Energy company has been offered an incentive scheme. She will receive a bonus of $500,000 if the stock price at the end of the year is $120 or more; otherwise she will receive nothing. Draw a position diagram illustrating the payoffs from such a scheme. What combination of options would provide these payoffs?
3. Go to finance yahoo. Check out the delayed bid-ask quotes for a public energy company with options for different exercise prices and maturities. Plot the mid bid-ask quote as a function of exercise prices for one maturity date. Confirm that put-call parity approximately holds for at least one put/call option with the same strike price.
4. A stock price of Anadarko is currently $70. Over each of the next two 1-year periods it is expected to go up by 20% or down by 20%. The risk-free interest rate is 1% per annum. What is the value of a 2 year European and American put option with strike price of $72? Estimate how high the strike price has to be for it to be optimal to exercise the option immediately.
5. Consider the Exxon stock discussed in class, which can go up or down 20% per year and has an initial value of $82. The current annual risk free rate is 5%, compounded annually. You are offered a 5-year European “hybrid” option with strike price $80. This option can be declared, after exactly 3 years, by the purchaser, to be either a call or a put. Find the value of this “hybrid” option. Use binomial trees with annual periods to solve this value.