1) CH4 trading stock price is $100 and in each 3-month period will either increase by 25 percent or fall by 20 percent. A 6-month call on CH4 stock has an exercise price of $90. The risk-free 3-months interest rate is 1 percent.
a. What is the value of the CH4 call?
b. Now calculate the option deltas for the second 3-month period if the stock price rises to $125 or falls to $80.
c. Does the call option delta vary with the level of the stock price? Explain intuitively why.
d. Suppose that in month 3 the CH4 stock price is $80. How at that point could you replicate an investment in the stock by a combination of call options and risk-free lending? Show that our strategy does indeed produce the same returns as from an investment in the stock.
2) Suppose that you own an American put option on CH4 stock with an exercise price of $110.
a. Would you ever want to exercise the put early?
b. Calculate the value of the put.
c. Now compare the value with that of an equivalent European put option.
3) Recalculate the value of the CH4 call option, assuming that the option is American and that at the end of the first 3 months the company pays a dividend of $7.00. How would your answer change if the option were European?