Explain what would happen to the put option$$s current value in each of the following cases. Treat each one

as if it occurs in a vacuum. For full credit, you can either calculate a new price $($and show whether it is

above, the same, or below the old one$),$ or you can explain your answer using option Greeks.

$1.$ If the stock prices went up or down by $6\%$ instead of $+15\%/-12\%.$

$2.$ If you were considering a put option with a strike price of $$160$ instead of $$140.$

$3.$ If you started today but only had $2$ time steps instead of $3.$

$3$