A method for reducing filtrate loss of oil based drilling fluids comprising the following steps: a) preparing by emulsion polymerization an aqueous dispersion containing: i) from 20% to 60% by weight of a copolymer comprising from 60% to 90% by weight of styrene and/or vinyltoluene monomers, from 7 to 40% by weight of 2-ethylhexyl acrylate monomers and from 0.01 to 3% of polyfunctional unsaturated monomers; ii) from 40 to 80% by weight of water; iii) from 0.1% to 5% by weight of at least one surfactant; b) providing an oil based drilling fluid containing the aqueous dispersion obtained from step a), or its copolymer in powder form; c) injecting and circulating the drilling fluid in the borehole.