$1.$ For each of the following cases, calculate

$($i$)$ the cashflow paid or received today on entering the position,

$($ii$)$ the gross payoff at expiry, and

$($iii$)$ the net payoff from your option trading

All options are European style and cover $100$ shares in the underlying asset.

a$)$ You enter a long call option with a strike price of $$6$ and premium of $$2\mathrm{.}30.$ At expiry, the share price is $$7\mathrm{.}80.$

b$)$ You enter a long call option with a strike price of $$9$ and premium of $$0\mathrm{.}80.$ At expiry, the share price is $$7\mathrm{.}90.$

c$)$ You enter a short call option with an exercise price of $$5$ and premium of $$0\mathrm{.}70.$ The share price at expiry is $$5\mathrm{.}40.$

d$)$ You enter a short call option with an exercise price of $$5$ and premium of $$0\mathrm{.}70.$ The share price at expiry is $$4\mathrm{.}90.$

e$)$ You buy a long$-$put option with a strike price of $$10$ for a premium of $$1\mathrm{.}20.$ At expiry, the share price is $$8\mathrm{.}50.$

f$)$ You write $($i$.$e$.,$ short$)$ a put option with strike price $$7$ for a premium of $$0\mathrm{.}60.$ At expiry, the share price is $$5.$