A stock sells for $$135.$ At the end of the current period, you expect the stock to be either $$150$ or $$120.$ A call option with X$=130$ exists on the stock.

The relevant interest rate is $12\%.$

$1.$ Find and interpret the hedge ratio.

$2.$ Using the hedge ratio, set up a perfectly hedged portfolio. Also, show that this portfolio is perfectly hedged.

$3.$ Find the price of the call using the hedge$-$ratio method.

$4.$ Find the price of the call using a replicating$-$portfolio method.