$1.$ An investor buys a European put on a share for $$5.$ The stock price is $$55$ and the strike price is $$50.$ Draw a graph to show the variation of the investor's profit with the stock price at the maturity of the option. Under what circumstances does the investor make a profit? Under what circumstances will the option be exercised?

$2.(20$ points$)$ An investor takes the position below on the same stock with a strike price of $$100$ and the same maturity:

Buy $1$ XYZ call at $$3\mathrm{.}30$

Buy $1$ XYZ put at $$3\mathrm{.}20$

i$.(3$ points$)$ What is the name of this strategy?

ii$.(3$ points$)$ What is the aim of this investor?

iii. $(12$ points$)$ Draw a graph to show the possible profit and loss. $($don$$t forget to show break$-$even points, strike price etc.$)$

iv$.(2$ points$)$ At which stock price maximum loss is realized and what will be the maximum loss?