Question $5$

a$)$ Consider an interest rate swap with the following features:

Maturity is $5$ years

Notional principal is $100$ million

Payments occur every $6$ months

The fixed$-$rate payer pays $9\mathrm{.}05\%$ and receives LIBOR.

The floating$-$rate payer pays LIBOR and receives $9\%.$

Requirement:

Suppose at payment date, LIBOR is $6\mathrm{.}5\%,$ what is each party's payment and receipt at that date?

$(8$ marks$)$

b$)$ If the spot price of copper is $$300$ per ounce and the one year forward rate is $$300$ per ounce, and the one year interest rate is $4\%$ per annum, explain whether an arbitrage opportunity exist. If so$,$ explain how an investor would exploit such an opportunity, and approximate his payoff

$(7$ marks$)$

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