A given stock is currently priced at $100. Historically, its annual return has been 12 percent with a standard deviation of 15 percent. Build a spreadsheet simulation model for the stock price, using the option pricing model described in the text. Build the model to simulate the stock price over 126 days. Assume that the risk-free rate of return is 6 percent.
a. A particular European call option gives the owner the right to purchase this stock after six months at a strike price of $105. What is the price of the option?
b. Create a graph of the option price as a function of the strike price, for strike prices from $100 to $110 in increments of $1.
c. A particular European put option gives the owner the right to sell this stock after six months at a strike price of $95. What is the price of the put?
d. A look back call option on this stock has an exercise price given by the minimum price observed over its six-month term. What is the price of the look back option?
e. An Asian option on this stock has a strike price set by the average value of the stock during its term. What is the price of the Asian option?
f. A knockout call option on this stock terminates if the stock price reaches or exceeds $125 (that is, the option cannot be exercised). Otherwise, it has the same structure as the normal call. What is the price of the knockout option?