Yes. The compliance team at most investment banks will prevent individuals or members of their family from trading any instrument that the firm is actively trading in without going through a "waiting period". All personal trading accounts for the employee and direct family members must be registered with the compliance team. Banks employee independent investigators to ensure their employees follow through on these requirements; violations are a fireable offense, and I have seen multiple people fired for lack of compliance.

This is to prevent insider trading, among other things. Compliance issues with individual traders can result in massive fines for their employers.