$1$ A UK firm is planning to construct a plant in China for building

Quantum computers. The overall investment costs $20$ million Chi$-$

nese Yuan and is paid in full at delivery in one year from now. The

current exchange rate is $S_0=0\mathrm{.}12(0\mathrm{.}12$ units of British sterling

per Yuan$).$ The one$-$year risk$-$free annual interest rate $($continuously

compounded$)$ is $R_{uk}=4\mathrm{.}5\%$ and $R_{ch}=3\mathrm{.}5\%.$ With this informa$-$

tion, answer the following questions:

$($i$)$ Compute how many British pounds the firm needs to set aside

today in order to meet the cost of the project without incurring

currency $($exchange rate$)$ risk at the completion of the plant in

one year from now. Explain how this can be achieved using the

forward currency market.

$($ii$)$ Explain two different risk$-$free investment alternatives that would

allow the UK firm to obtain $20$ million of Chinese Yuan at deliv$-$

ery of the project in one year from now $($Note that one of these

strategies may have been used in $($i$)$ above$).$

$($iii$)$ The firm has noted that the forward contract on Chinese cur$-$

rency with $1$ year delivery is $0\mathrm{.}11.$ Derive an arbitrage strategy

that allows the firm to finance the project entirely with zero cost

and without bearing any risk.

$($N$.$B$.$ All interest rates are continuously compounded.$)$