Question $5(20$ points$)$

Suppose that a trader writes three naked put option contracts, with each contract being on $100$ shares of underlying stock. The option price is $$3$ on each share, the time to maturity is six months, and the strike price is $$60.$

a$.$ Write out the formula and draw the graph for the trader's profit on each put option on $1$ share of stock. $(10$ marks$)$

b$.$ What is the margin requirement for the trader if the current stock price is $$58?(5$ marks$)$

c$.$ How would the answer to $($b$)$ change if the trader is buying instead of writing the options? $(5$ marks$)$