A stock is priced at $$\frac{30}{?}$ share. The interest rate is $7\frac{\%}{?}$ 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 $0\mathrm{.}1515.$ 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?

e$.$ Suppose the gamma of the call is $0\mathrm{.}0625.$ If the stock price increases by $$1,$ how

does the delta change? If the stock price increases by $$3,$ does the hedged position

make money or lose money?