Problem $17$: Option $(15\%)$

The stock price of Johnson & Johnson $($JNJ$)$ is trading at $$160$ per share in the beginning of Jan $2024.$ You heard that JNJ develop a new medicine for cancer. The medicine is very likely to be formally approved by FDA in $3$ months. It will cause a rise of JNJ share's price $($likely $$170$ $$180).$ Yet experts point out the effect of this medicine may be limited so it is not likely to increase JNJ share's price a lot $($larger than $$180).$ Suppose there are following European equity options $($with $3-$month maturity from now$)$ available in the market. Design an option strategy which is likely to utilize this opportunity.

$\backslash$table$[[$Option Type,Strike Price Premium$],[$TSLA March $160$ Call,$$160,$$$14\mathrm{.}2,],[$TSLA March $180$ Call,$$180,$$$10\mathrm{.}2,],[$TSLA March $200$ Call,$$200,$$$5\mathrm{.}3,],[$TSLA March $160$ Put,$$160,$$$3\mathrm{.}4,],[$TSLA March $180$ Put,$$180,$$$12\mathrm{.}3,],[$TSLA March $200$ Put,$$200,$$$14\mathrm{.}9,]]$

$1.$Describe what your best strategy is $($Hint: think of a strategy we learned in class$).$

$2.$Calculate your returns when JNJ price rises to $$175.$

$3.$ What is the break$-$even prices of this strategy?