Suppose we know $S=8,x=8,r=12\%,T=\frac{8}{12},=18\%,$ and $=12\%.$ We have a short position in call options on $1,000$ shares of stock. Assume each stock option contract is for one share of stock. Based on this information, please answer:

a$),$ What is the delta of our portfolio? $\{\}$

b$),$ Assuming the hedging instrument is stock, we need to $\{\}($i$.$e$.,$ long, short$)\{\}$ shares of stock to execute an appropriate delta hedge.

c$),$ Assuming the hedging instrument is put option, we need to $\{\}($i$.$e$.,$ long, short$)\{\}$ put options to execute an appropriate delta hedge.