$a$i$)$ Consider a one$-$period binomial option pricing model. The current underlying price is $100$ and next period it will either move up to $110$ or down to

$92.$ A one$-$period European call exists with a strike price of $104.$ If the

risk$-$free rate is $2\%$ per period $($assume discrete compounding$),$ what is

the delta of this call option, how would you interpret this number and how

would you build a portfolio of the underlying and the option that is risk$-$free?

$($Assume that the underlying does not pay dividends or any other form of

income$)$ An investor is currently holding a portfolio of UK stocks with a value of

$100$ million. They are worried that the UK stock market is going to fall

and thus decide to hedge the market risk by taking a position in FTSE$-100$

futures contracts. The investor$$s portfolio has a beta to the FTSE$-100$ of

exactly $0\mathrm{.}6.$ Explain how they would choose whether to go long or short the

futures contract and how many futures to buy or sell $($you are not required

to compute the number of futures to buy or sell, just to explain how you

would compute the size of the position$).$ Having taken a futures position in

the way that you suggest, what risks are hedged and what risks remain?