This article provides an iterative fitting algorithm to generate maximum likelihood estimates under the Cox regression model and employs non‐Gaussian distributions—the jump diffusion (JD), variance gamma (VG), and normal inverse Gaussian (NIG) distributions—to model the error terms of the Renshaw and Haberman (2006) (RH) model. In terms of mean absolute percentage error, the RH model with non‐Gaussian innovations provides better mortality projections, using 1900–2009 mortality data from England and Wales, France, and Italy. Finally, the lower hedge costs of longevity swaps according to the RH model with non‐Gaussian innovations are not only based on the lower swap curves implied by the best prediction model, but also in terms of the fatter tails of the unexpected losses it generates.