What is the value of a European put option if the underlying stock price is $50,
ID: 2721432 • Letter: W
Question
What is the value of a European put option if the underlying stock price is $50, the strike price is $43, the underlying stock volatility is 55 percent, and the risk-free rate is 5.8 percent? Assume the option has 156 days to expiration. (Use 365 days in a year. Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.)
What is the value of a European put option if the underlying stock price is $50, the strike price is $43, the underlying stock volatility is 55 percent, and the risk-free rate is 5.8 percent? Assume the option has 156 days to expiration. (Use 365 days in a year. Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "$" sign in your response.)
Explanation / Answer
Current Stock Price - SP0 - $50 Exercise Price - EP - $43 Time - t - 156 days Risk Free Rate of Return - r - 5.8% Volatility - v - 55% Computation of Variables D1 = Ln (SP0/EP) + [(r + 0.50v^2)*t] / v*t = {Ln (50/43)+ [(0.058 + 0.50 * 0.55^2)*156/365]} / 0.55 * 156/365 = [Ln 1.1628 + 0.089433] / 0.359566 = (0.150823 + 0.089433) / 0.359566 = 0.240256 / 0.359566 = 0.668183 D2 = Ln (SP0/EP) + [(r - 0.50v^2)*t] / v*t = D1 - v*t = 0.668183 - 0.55 * 156/365 = 0.668183 - 0359566 = 0.308617 Value of Put = [EP * e^-rt * N(-D2)] - [SP0 * N(-D1)] where N(-D1) and N(-D2) are standard normal distribution probability factors. N(-D1) = 0.252008 N(-D2) = 0.378807 Value of Put Option = [43 * e^-0.058*156/365 * 0.378807] - [50 * 0.252008] = [16.28868 * e ^ -0.024789] - 12.60042 = 16.28868 * 0.975516 - 12.60042 = 15.88987 - 12.60042 = 3.289445 Value of Europen Put Option = $3.29
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