$4.($a$)$ Suppose that you can trade calls and puts in the market. You want to generate the to payoff structure, where $\backslash ($ S$\_\{$T$\}\backslash )$ is the underlying stock price in year $\backslash ($ T $\backslash ).$

Figure $1.$ Payoff diagram

$($i$)$ Create a trading strategy that replicates the payoff by trading calls only.

$($ii$)$ Create a trading strategy that replicates the payoff by trading puts only.