Question

You buy a stock at $200 and buy an at-the-money 8-month European put option on the stock at a price of $15. The continuously compounded risk-free interest rate is 4%. Calculate the 8-month profit if the 8-month stock price is $180.

Answer 1

Long on Stock = 200

European Put Option (At the money) Strike Price = 200

European Put Option Premium Paid = (15)

Stock price at expiration = 180

Loss on Stock = Stock Price after 8 months - Stock price at time of purchase=  200-180 = 20

Gain on Put Option = Strike price - Stock Price at expiration = 200-180= 20

Future Value of Premium Paid = Premium Paid * (1+(int%*8/12)) = 15 * (1+ (4%*8/12))

Future Value of Premium Paid = 15 * (1.026667)

Future Value of Premium Paid = 15.4

Total Profit / Loss = Gain/loss on stock + Gain/Loss on Put Option - Value of premium paid on 8th Month

Total Profit / Loss = -20 + 20 - 15.4

Total Loss = $-15.4