Graded Discussion Questions $4$: Options

Create a new thread and answer the questions listed below. Make sure you answer all questions in a single thread. Answer the questions in the sequence they are asked. Once you post your first thread, you will be able to see the answers of every other student. So$,$ from an evaluation perspective, it does not make sense if you look at the answers and post again. Only your first post will be used for grading purposes. You should not send any files to the instructors regarding this. Neither should you upload any file to answer these questions. Questions should be answered as if you are trying to use Excel to answer these questions. If you use calculators to solve these and just put the answers, you will get no points for that question. Show detailed calculations for numerical questions.

$1.$ What is the difference between the two primary kinds of options $($puts and calls$)?$ What is the difference between European and American options?

$2.$ What is the difference between payoff and profit of an option? Which line $($payoff$/$profit$)$ should be lower when you draw the two lines on the graph for a long call option? Which line $($payoff$/$profit$)$ should be lower when you draw the two lines on the graph for a short put option?

$3.$ How can a protective put strategy be formed? What is the maximum profit when a straddle is sold?

$4.$ The price of a put option with $3$ months to maturity and a strike price of $57\mathrm{.}5$ is $4\mathrm{.}5.$ The underlying asset of the put option is currently trading at $55\mathrm{.}17.$ Assume the risk$-$free rate to be $7\%.$ What is the price of a call option with a strike price of $57\mathrm{.}5$ with a $3-$month maturity on the same asset? Show calculations.

$5.$ Suppose Jane bought a put option with a strike price of $$30\mathrm{.}00$ by paying $$2\mathrm{.}00$ two months ago. On the expiration day, the price of the stock is $$28\mathrm{.}62.$ What should she do$?$ What is her total profit or loss on this trade?