The june crude oil futures price is $$77\mathrm{.}50/$bbl$.$ a call on june cl struck at $$78\mathrm{.}5$ is currently selling at $$1\mathrm{.}87$ and a pit struck at $$78\mathrm{.}5$ is selling at $$1\mathrm{.}04.$ these prices are quoted as of $7$ march $2024.$ the options expire on $16$ may $2024.$ the relevant interest rate is $5\mathrm{.}3\%.$ the options are european. identify the arbitrage opportunity. indicate which option you should buy, which option you should sell and whether you should buy or sell futures contract. How much will you make?

If the options are American, is there still an arbitrage opportunity? If so$,$ indicate the transactions you should undertake $($what to buy, what to sell$).$