It is demonstrated numerically that the supercontinuum generation and third-harmonic generation that accompany optical filamentation in nonlinear dispersive bulk media can be described as first-order scattering processes akin to the first Born approximation. In particular, for an incident ultrashort pulse the angularly resolved spectrum of the transmitted pulse is shown to be accurately determined using first-order scattering of the incident field from the nonlinearly modified refractive index due to the optical filament. Thus, although an optical filament is a highly nonlinear object, the accompanying supercontinuum generation and third-harmonic generation are driven parametrically by the filament and have negligible back action upon it.