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Aims. The present study was conducted to determine the optical extinction curve for Cerro Paranal under typical clear-sky observing conditions, with the purpose of providing the community with a function to be used to correct the observed spectra, with an accuracy of 0.01 mag airmass(-1). Additionally, this work was meant to analyze the variability of the various components, to derive the main atmospheric parameters, and to set a term of reference for future studies, especially in view of the construction of the Extremely Large Telescope on the nearby Cerro Armazones. Methods. The extinction curve of Paranal was obtained through low-resolution spectroscopy of 8 spectrophotometric standard stars observed with FORS1 mounted at the 8.2 m Very Large Telescope, covering a spectral range 3300-8000 angstrom. A total of 600 spectra were collected on more than 40 nights distributed over six months, from October 2008 to March 2009. The average extinction curve was derived using a global fit algorithm, which allowed us to simultaneously combine all the available data. The main atmospheric parameters were retrieved using the LBLRTM radiative transfer code, which was also utilised to study the impact of variability of the main molecular bands of O-2, O-3, and H2O, and to estimate their column densities. Results. In general, the extinction curve of Paranal appears to conform to those derived for other astronomical sites in the Atacama desert, like La Silla and Cerro Tololo. However, a systematic deficit with respect to the extinction curve derived for Cerro Tololo before the El Chichon eruption is detected below 4000 angstrom. We attribute this downturn to a non standard aerosol composition, probably revealing the presence of volcanic pollutants above the Atacama desert. An analysis of all spectroscopic extinction curves obtained since 1974 shows that the aerosol composition has been evolving during the last 35 years. The persistence of traces of non meteorologic haze suggests the effect of volcanic eruptions, like those of El Chichon and Pinatubo, lasts several decades. The usage of the standard CTIO and La Silla extinction curves implemented in IRAF and MIDAS produce systematic over/under-estimates of the absolute flux.