I’m guessing that credit risk for European-style options is less than or equal to that of American-style options because the counterparties in European-style option contracts have a defined expiration date on which the contract can be exercised. The counterparty in an European-style option contract can plan to have cash or securities available to make the option contract whole if the contract is exercised on the expiration date. In American-style option contracts, the option can be exercised at any time up to the expiration date. This gives the holder of the option the flexibility to determine the option’s exercise date. As such, the counterparty to the option contract may or may not have the liqudity required to meet the delivery requirements for the American-style option contract if it is exercised prior to expiration date. This would make the credit risk of an American-style option contract at least equal to, if not greater than, the credit risk of an European-style option contract.