An investment banker who allegedly attached a fake bomb around an Australian schoolgirl's neck in a case that made global headlines was Thursday remanded in custody for another month.

Paul Douglas Peters, 50, was charged with extortion and kidnapping after his dramatic arrest and extradition from the United States in September.

He is accused of breaking into the family home of Sydney teenager Madeleine Pulver on August 3 and strapping the device around her neck, with the schoolgirl enduring a horrifying 10-hour ordeal.

In Sydney's Central Local Court Thursday, bail was formally refused and Peters will remain in jail until he is next slated to appear on December 15.