$5.$ A stock is priced at $$30/$share$.$ The interest rate is $7\%/$year$.$ A three$-$month European call option with a strike price of $$35$ has a Black$-$Scholes price of $$0\mathrm{.}28.$a$.$ What is the value of a European put with the same underlying asset, same strike price and same time to expiration? b$.$ The delta of the call is $\mathrm{.}1515.$ How would you make a synthetic call $($i$.$e$.,$ how many shares and how many dollars in T$-$bills$)?$ c$.$ What is the delta of an otherwise identical put? How would you make a synthetic put? d$.$ If a trader sold $100$ calls, what share position would he$/$she need to take to be delta neutral?