Question

Bob writes a two-year 100-strike European put with a premium of $10. The continuously compounded risk-free interest rate is 4%. Calculate the difference between Bob’s maximum profit and his minimum profit

Answer 1

Time to Maturity = 2 Years

Risk Free Rate = 4%

Strike Price = $100

Put Option Premium = $10.

Since, Bob has written i.e. sold this put option, he would collect the premium for selling a right of selling to other party. Thus, he would incur maximum gain if its right expire worthless i.e. Other party don't come to him to excercise his option. And minimum gain i.e. maximum loss would happen if the stock price falls to 0 i.e. Other party would sell a thing worth 0 for $100 to Bob.

Payoff on a Put Option = Max (Strike Price - Stock Price, 0)

Profit for Bob can be written as = Premium Collected - Max (Strike Price - Stock Price, 0)

Profit for Bob = $10 - Max ($100 - Stock Price, 0)

Maximum Gain = $10 - 0 (If Stock Price >= 100)

Minimum Gain (Maximum Loss) = $10 - $100 (If Stock Price = 0)

Difference = Maximum Gain - Minimum Gain

Difference = $10 - $100 = $90

The differnce between maximum and minimum gain is $90.