It is permissible for the one who prayes tahajud to hold the Quran in any way it is suitable for him.

My parents pray Tahajjud every night, sometimes together and at times, separately. When they pray individually, they each read while holding the kitaab. To my understanding, one can recite from the kitaab only during a voluntary prayer. Is this correct? And when holding a kitaab, does one hold the Quran directly in front of them or cross arms and hold it?