Exhibit 14-3
USE THE FOLLOWING INFORMATION TO ANSWER THE NEXT QUESTION(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, a call option on the stock has an exercise price of $65. The stock is equally likely to rise by 15% or fall by 15% during each six month period. The one-year risk free rate is 3%.
-Refer to Exhibit 14-3. Calculate the price of the call option after the stock price has already moved up in value once (C_d) .

Question

Quizplus · Accepted Answer

Current stock price = $60 Exercise price = $65 Risk free rate = 3% or 1.49% per six month period = (1.03)^0.5 - 1 = 0.0149 Price in six months if stock rises 15% = 60(1.15) = $69 Price in six months if stock falls 15% = 60(0.85) = $51 Price in one year if stock rises 15% per six month period = 60(1.15)(1.15) = $79.35 Price in one year if stock rises 15%, then falls 15% = 60(1.15)(0.85) = $58.65 Price in one year if stock declines 15% per period = 60(0.85)(0.85) = $43.35 Intrinsic value of call option if stock rises to $79.35 = Max[0, 79.35 - 65] = $14.35 Intrinsic value of call option if stock falls to $58.65= Max[0, 58.65 - 65] = $0 Intrinsic value of call option if stock falls to $43.35 = Max[0, 43.35 - 65] = $0 Estimate the number calls needed by constructing a hedge portfolio. The hedge portfolio will consist of one share of stock held long plus some number of call options written. At the end of the first six month period: Value of hedge portfolio if stock rises = Value of hedge portfolio if stock falls 79.35 + (14.35)(n) = 58.65 + (0)(n) n = -1.44251 Value of hedge portfolio at the end of first six months = 69 - (1.44251)(C_u) = 58.65/(1.0149) C_u = $7.7719

Exhibit 14-3 USE THE FOLLOWING INFORMATION TO ANSWER THE NEXT QUESTION(S)