Convexity preserving jump-diffusion models for option pricing

We investigate which jump-diffusion models are convexity preserving. The study of convexity preserving models is motivated bymonotonicity results for such models in the volatility and in the jump parameters.We give a necessary condition for convexity to be preserved in several-dimensional jump-diffusion models. This necessary condition is then used to show that, within a large class of possible models, the only convexity preserving models are the ones with linear coefficients. © 2006 Elsevier Inc. All rights reserved