a$)$ Draw the payoff and profit at the maturity date for a call option $C_1$ on the stock from the perspective of the buyer. Suppose that the strike price is $$40$ and that the call option costs $$8.$

b$)$ Draw the payoff and profit at the maturity date for a call option $C_2$ on the stock from the perspective of the buyer. Suppose that the strike price is $$50$ and that the call option costs $$4.$

c$)$ Draw the payoff and profit at the maturity date for a call option $C_2$ on the stock from the perspective of the seller. Suppose that the strike price is $$50$ and that the call option costs $$4.$

d$)$ Draw the payoff and profit at the maturity date for a put option $P_1$ on the stock from the perspective of the buyer. Suppose that the strike price is $$40$ and that the put option costs $$10.$

e$)$ Draw the payoff and profit at the maturity date for a put option $P_2$ on the stock from the perspective of the buyer. Suppose that the strike price is $$50$ and that the put option costs $$15.$

f$)$ Draw the payoff and profit at the maturity date for a put option $P_2$ on the stock from the perspective of the seller. Suppose that the strike price is $$50$ and that the put option costs $$15.$