Consider a European call option that enables you to buy a share of stock at $K

at time T $,$ a European put option on the same stock with the same strike and expiration, a

zero coupon bond which pays $K at time T $.$

$($a$)$ Graph the value of the put option at expiration as a function of the stock price S $=$

S$($T $).$

$($b$)$ Supposed a broker wrote $($sold$)$ both options. Graph the value of his position at expi$-$

ration for the call option as a function of the stock price S $=$ S$($T $).$

$($c$)$ Build two portfolios that at time T give the same outcome as the graph below. You

can take any position on the market.