Before you can save a copy of what you stream online, you must enable the "SAVE TO HARD DISK" option in your Stream Settings configuration. So, click on the Settings Tab and click on the gear icon beside "STREAM SETTINGS":
And check "SAVE TO HARD DISK":
Once this is enabled, what you stream will be recorded to your hard disk.
Please take note that the recorded stream will be a duplicate of what you sent to the streaming service, which means that if you experience any bandwidth problems, this will also be reflected in the recording.
And please also note that you cannot start a separate recording while you are already streaming and vice versa. Doing so will cancel your last recording and start a new one.