Suppose that a European call option to buy a share for $$100\mathrm{.}00$ costs $$5\mathrm{.}00$ and is held until

maturity. Under what circumstances will the holder of the option make a profit? Under

what circumstances will the option be exercised? Draw a diagram illustrating how the profit

from a long position in the option depends on the stock price at maturity of the option.

Suppose that a European put option to sell a share for $$60$ costs $$8$ and is held until

maturity. Under what circumstances will the seller of the option $($the party with the short

position$)$ make a profit? Under what circumstances will the option be exercised? Draw a

diagram illustrating how the profit from a short position in the option depends on the

stock price at maturity of the option.

Describe the terminal value of the following portfolio: a newly entered$-$into long forward

contract on an asset and a long position in a European put option on the asset with the

same maturity as the forward contract and a strike price that is equal to the forward price

of the asset at the time the portfolio is set up$.$ Show that the European put option has the

same value as a European call option with the same strike price and maturity.

A trader buys a call option with a strike price of $$45$ and a put option with a strike price

of $$40.$ Both options have the same maturity. The call costs $$3$ and the put costs $$4.$ Draw

a diagram showing the variation of the trader$$s profit with the asset price.