An exotic European derivative on a stock showcases the following payoff structure at maturity in $2$ years:

$250-$ ST if ST $<=120$

ST if $120<$ ST $<=180$

$170$ if ST $>180$

where ST signifies the stock price at maturity. The stock's current price is $$150,$ and its volatility is $20\%.$

No dividends are expected, and the risk$-$free rate is $3\%.$

A$.$ Using a spreadsheet software, plot this payoff and compare it with a basic stock investment for the

range $[$$$0,$ $$250]$ with intervals of $$10.$

B$.$ Price this derivative employing a $5-$step binomial tree. Illustrate deltas at each node.

C$.$ Ponder on the possibility of replicating this payoff using standard options and other securities