The Collaborative International Dictionary of English v.0.48:

Hyperbolize \Hy*per"bo*lize\, v. i. [imp. & p. p.
   Hyperbolized; p. pr. & vb. n. Hyperbolizing.] [Cf. F.
   hyperboliser.]
   To speak or write with exaggeration. --Bp. Montagu.
   [1913 Webster]