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."
Compare Old Frisian and Middle Dutch hope, Danish haab, Dutch hoop, all from their respective verbs. For forlorn hope, see forlorn.
"to lose hope, be without hope," mid-14c., despeiren, from Old French despeir-, stressed stem of desperer "be dismayed, lose hope, despair," from Latin desperare "to despair, to lose all hope," from de "without" (see de-) + sperare "to hope," from spes "hope" (from PIE root *spes- "prosperity;" see speed (n.)). Related: Despaired; despairing; despairingly.
of debts, "having some likelihood of recovery," 1550s, from Latin speratus, past participle of sperare "to hope," denominative of spes "hope," from PIE *spe-is-, from root spes- "prosperity" (see speed (n.)).
late 14c., desperacioun, "hopelessness, lack or loss of hope" (especially in God's mercy), a sense now obsolete; c. 1400, "a desperate state of mind," from Old French désperacion or directly from Latin desperationem (nominative desperatio) "despair, hopelessness," noun of action from past-participle stem of desperare "to despair, to lose all hope," from de "without" (see de-) + sperare "to hope," from spes "hope" (from PIE root *spes- "prosperity;" see speed (n.)).