All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is not an obligation to recite loudly Al-Faatihah or any other chapter during the optional night prayer. A person has the choice either to recite loudly or silently in the optional night prayer. Indeed, the Prophet used to recite sometimes loudly and sometimes secretly.
'Aa'ishah was asked whether the Prophet used to recite loudly or secretly during optional night prayer and she answered that he used to do both. So the questioner said: "All perfect praise be to Allaah who made the matter easy." [An-Nasaa'i, Abu Daawood and At-Tirmithi]
Allaah Knows best.