USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
The following information is provided in the context of a two-period (two six-month periods) binomial option pricing model. A stock currently trades at $60 per share, and a call option on the stock has an exercise price of $65. The stock is equally likely to rise by 15 percent or fall by 15 percent during each six-month period. The one-year risk free rate is 3 percent.
-Refer to Exhibit 16.2. Calculate the price of the call option after the stock price has already moved up in value once (C_u) .

Question

Quizplus · Accepted Answer

Using the binomial option pricing model, we can calculate the price of the call option as follows: - First, determine the possible stock prices in six months: - If the stock rises by 15%, the price will be: 60 x 1.15 = $69 - If the stock falls by 15%, the price will be: 60 x 0.85 = $51 - Next, calculate the probability of each stock price: - There is a 50% chance the stock will rise to $69. - There is a 50% chance the stock will fall to $51. - Calculate the payoffs of the call option at each possible stock price: - If the stock price is $69, the call option is in-the-money and has a payoff of $4 ($69 - $65). - If the stock price is $51, the call option is out-of-the-money and has a payoff of $0. - Calculate the expected payoff of the call option: - Expected payoff = (0.5 x $4) + (0.5 x $0) = $2 - Calculate the present value of the expected payoff: - Present value = $2 / (1 + 0.03/2) = $1.94 - Finally, add the present value of the expected payoff to the current price of the stock option (C_u): - Price of call option = $5.83 + $1.94 = $7.77