A regulator register check is the short verification that a firm is genuinely authorised for the business it is offering you. Every serious supervisor publishes a searchable register — the FCA Register, the CySEC list, ASIC Connect, BaFin's company database — showing legal name, reference number, permitted activities, approved trading names and the contact details the firm itself has filed.
Doing it properly means matching all of those, not merely finding the number. Confirm that the permissions actually cover dealing in derivatives with retail clients, that the website address and trading name you were sent appear on the entry, and that the phone number and address on the register are the ones you were given. Then make first contact through the register's details rather than the ones in the email. That last step is what separates a real authorisation from a clone quoting somebody else's reference number.
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Guide
How to Check the Way a Currency Is Managed
The regime behind a currency is published, not inferred. The four primary sources that say how a rate is governed, what each one can and cannot tell you, and how to keep the answer from going stale.