A more complete view of a magnetosphere of a close orbit giant exoplanet, so called “Hot
Jupiter”, based on the Paraboloid Magnetospheric Model (PMM), is proposed. The key element
of the considered model consists in taking into account the effects of an expanding upper
atmosphere of a Hot Jupiter heated and ionized by the stellar XUV radiation. As a result,
an extended magnetodisk is built around the planet. The magnetic field produced by
magnetodisk ring currents, dominates above the contribution of intrinsic magnetic dipole
of a Hot Jupiter and finally determines the size and shape of the whole magnetosphere.