Due $29$ September $2023$

Problem $1\mathrm{.}1$

Assume that the spot price of gold is $$2,032$ per ounce $($as of $24-$Jan$-2024).$ Suppose that the market quotes a forward contract on gold with delivery in $1$ year at $$2,100.$ The risk$-$free interest rate is $r=5\mathrm{.}0\%.$

i$)$ Is there an arbitrage opportunity? If yes, describe the steps required to realize the arbitrage. Neglect the storage cost.

ii$)$ Consider now the case when the forward price is $$2,200.$ Is there an arbitrage opportunity? If yes, describe the steps required to realize the arbitrage.