$$ Analyze the following option trading strategies and show a maximum gain, maximum loss, and stock prices to have break$-$even using profit$-$loss graphs and cash flow $($profit$-$loss$)$ tables based on the following quotations, which may or may not be in equilibrium in the short term. The quotation date is in June, and the remaining maturity of August, September, and October options are two months, three months, and four months, respectively. The underlying asset $($stock$)$ price is $$33$ on June $1$st$.$ The risk$-$free interest rate is $6\%$ per annum.

o Please take into account the time value of money.

o Please show different possible stock prices at maturity to draw a meaningful diagram.

Strike Call Put

Price Aug. Sep. Oct. Aug. Sep. Oct.

$321\mathrm{.}201\mathrm{.}602\mathrm{.}200\mathrm{.}100\mathrm{.}500\mathrm{.}90$

$330\mathrm{.}501\mathrm{.}011\mathrm{.}600\mathrm{.}200\mathrm{.}901\mathrm{.}30$

$340\mathrm{.}200\mathrm{.}601\mathrm{.}201\mathrm{.}101\mathrm{.}401\mathrm{.}80$

$1.$ A Protective Put position with a stock and a put option with an October $$33$ strike.

$2.$ A Covered Call position with a short position in a call option with an October $$33$ strike.