Final answer:
The correct statements regarding stock index options are that trades are settled on the next business day and exercise settlement involves the delivery of cash.
Step-by-step explanation:
The correct statement regarding stock index options is option D) I and IV.
Statement I is true as trades are settled on the next business day. Stock index options are settled in cash on the next business day after the trade has taken place. Option contracts do not involve the actual delivery of the underlying stock.
Statement IV is also true as exercise settlement involves the delivery of cash. When an option contract is exercised, the option holder receives a cash settlement equal to the difference between the exercise price and the current value of the underlying stock index. There is no physical delivery of stock involved in exercise settlement.