Old English hopian "have the theological virtue of Hope; hope for (salvation, mercy), trust in (God's word)," also "to have trust, have confidence; assume confidently or trust" (that something is or will be so), a word of unknown origin. Not the usual Germanic term for this, but in use in North Sea Germanic languages (cognates: Old Frisian hopia, Middle Low German, Middle Dutch, Dutch hopen; Middle High German hoffen "to hope," which is borrowed from Low German).
From early 13c. as "to wish for" (something), "desire." Related: Hoped; hoping. To hope against hope (1610s) "hold to hope in the absence of any justification for hope" echoes Romans iv.18:
Who against hope, beleeued in hope, that hee might become the father of many nations: according to that which was spoken, So shall thy seede bee. [King James Version, 1611]
The Wycliffite Bible (c. 1384) has this as "Abraham agens hope bileuede that he schulde be maad fadir of manye folkis."
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