My name is ***** ***** I will be assisting you with your question.
I have fielded many complaints like yours about binary options brokers here on this website. Unfortunately it is only legal here in the US to trade with a brokerage company subject to regulatory oversight by the US Commodity Futures Trading Commission. That is, they must be traded on a U.S. Commodity Futures Trading Commission exchange. If they are unregulated by the CFTC and/or if they are out of the country and not regulated by a European regulatory authority either, these traders are ouside of the reach of the law, make their own rules and literally anything goes.
We hear horror stories of unauthorized tradings, wildly expensive fees to withdraw earnings that only lead to more fees, and credit card fraud. Then, when you go to look for them to exercise legal remedies, you frequently find that you don't even know where they are or that they don't respond any more to your emails and aren't anywhere at all.
You did not give the name of the binary brokerage you were dealing with, so I do not know whether it is regulated either here or anywhere else. If it is regulated by the CFTC, that is who you would contact, and, yes, you could sue them.
If they are located out of the US and they are regulated by a foreign regulatory authority, you would contact that regulatory authority for your remedy.
If the company not regulated by any other authority either you would have to sue them out of the country, if you can find out where they really are, that is.
You could also report the unregulated brokerage to the CFTC, the FBI's Internet Crime Complaint Center at IC3
.gov, and the Federal Trade Commission