Question

You writes a three-year 150-strike European put with a premium of$12. The continuously compounded risk-free interest rate is 5%. Calculate the difference between the maximum profit and the minimum profit.

Answer 1

Assume that premium is paid upfront, therfore there is effect of time value of money.

Premium amount after 3 years= premium now * continous compounding rate

= $ 12 * ( e^0.05*3 )

= $ 12 * ( e^0.015 )

= $ 12 * 1.1618

= $ 13.94

Maxmium Profit = As a put writter maximum profit will be get, when the holder lapses the option. In that case maximum profit will be the premium received.

= $ 13.94

Minimum Profit = As a put writter minimum profit or we can say maximum loss will be incurred, when the holder exercise the option and price in the market is zero. In that case minimum profit will be exercise price reduced by premium received

= $ 150 - $ 13.94

= $ 136.06

Difference between the maximum profit and the minimum profit = $ 136.06 - $ 13.94

= $ 122.12