While the employer is required to provide a form ES800 which is a separation notice, it is often omitted. If the employee files for unemployment, the Department of Labor will request information on why you were terminated.
You can still file a demand for arbitration with the Financial Industry Regulatory Authority (FINRA). This may be a case of unsuitability. A margin account is borrowing against your investments. You might argue that your investments did not meet your needs given the amount you were borrowing. Get a second opinion from a local lawyer.