Session 14: Determinants of Option Value
Read: Chapter 21
1. CH4 Trading’s stock price is £110 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
interest rate is 1 percent per month, or about 3 percent for 3 months.
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
£137.50 or falls to £88.
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 £88. 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 £12.50. (Thus, the price at
the end of 3 months is either 25 percent above or 20 percent below the ex-dividend price in
month 3.) How would your answer change if the option were European?
4. The current price of United Carbon stock is $200. The standard deviation is 22.3 percent a
year, and the interest rate is 21 percent a year. A one-year call option on United Carbon
stock has an exercise price of $180. Use the Black-Scholes model to value the call option
on United Carbon.
