The World Trade Network (WTN) is a network of exchange flows among countries whose topological and statistical properties are a valuable source of information. Degree and strength (weighted degree) are key magnitudes to understand its structure and generative mechanisms. In this work, we describe a stochastic model that yields synthetic networks that closely mimic the properties of annual empirical data. The model combines two popular mechanisms of network generation: preferential attachment and multiplicative process. Agreement between empirical and synthetic networks is checked using the available series from 1962 to 2017.