QUESTION $4[30$ MARKS$]$

$($a$)$ Show and explain

$($i$)$ the pay$-$off profile for the put holder.

$($ii$)$ the pay$-$off profile for the call writer.

b$)$ Discuss using an example, how the Black Scholes Options Pricing Model operates.

$($c$)$ Write short notes on the following:

$($i$)$ Security Market Line $($SML$)$

$($ii$)$ Portfolio Diversification.