Question $5$: contains $5$ parts, $($a$),($b$),($c$),($d$),$ and $($e$).$

While at a party you overhear a $$frenemy$$ saying $$You$$d have to be foolish not to

sell a call option on stock you own. You don$$t really lose anything because if the

stock is called, you own it and just have to give it up$.$ In return you receive fee

income that you get to keep no matter what the buyer of the call option does. This is

a no$-$lose proposition in my opinion.$$

Question $5($a$)$: What type $($describe$)$ of strategy your frenemy is suggesting?

Assuming you own $100$ shares and write $100$ call options on the shares, with a

call premium of $$3,$ and a strike price of $$15.$ Draw a clearly labeled diagram

to illustrate the payoff of this strategy as a function of stock price at

expiration.

Question $5($b$)$: Is this view of call options correct?

Question $5($c$)$: Calculate the profit$/$loss at expiration $[$ignore time value of

money$]$ from owning the shares and writing the call options if the stock price

at maturity is $$19.$ Is the call option $$in the money$$ or $$out of the money$$ at

maturity? Is the owner of the stock better or worse off than without the call

option transaction? By how much?

Question $5($d$)$: Instead of writing $100$ call options, assume the investor in part

$($a$)$ bought $100$ put options with the same strike price of $$15.$ The price of each

put option is $$3.$ Draw a diagram of the payoff of this strategy and describe

why someone might pursue this strategy.

Question $5($e$)$: Suppose today$$s stock price is $$15$ and assume the stock does not

pay dividend before the expiration date of the options. Is there an arbitrage

opportunity based on the call and put prices in parts $($a$)$ and $($d$)?$