$($Q$1$A$)$ A $2-$year dual currency bond with annual coupons $($paid in US dollars at a $5$ per cent coupon rate$)$ pays $500$ per $$1,000$ par value at maturity. The dollar$-$based yield to maturity is i$ $=3\%$; the spot exchange rate is $$1\mathrm{.}26=1\mathrm{.}00$; expected inflation over the next three years is p $ $=2\%$ in the US and p$=3\%$ in the U$.$K$.$ What is the present value of this dual$-$currency bond?

$(10$ marks$)$

$($Q$1$B$)$ Valery specialises in cross$-$rate arbitrage. He notices the following quotes:

Swiss franc$/$dollar $=$ SFr$0\mathrm{.}9000/$$

Australian dollar$/$US dollar $=$ A$$1\mathrm{.}5800/$$

Australian dollar$/$Swiss franc $=$ A$$1\mathrm{.}7500/$SFr

Ignoring transaction costs, does Valery have an arbitrage opportunity based on these quotes? If there is an arbitrage opportunity, what steps would he take to make an arbitrage profit, and how would he profit if he has $$1,000,000$ available for this purpose?

$(10$ marks$)$