It is well known that volatility smirks and heavy-tailed asset return distributions are two violations of the Black-Scholes model. This paper investigates the role of jump size distribution played in explaining these two abnormalities. We consider a jump-diffusion model with Laplace jump size distribution, in comparison to the conventional normal distribution. In addition, our analysis is built upon a pure exchange economy, in which the representative agent’s risk preference shows a fanning characteristic. We find that, when a fanning effect is present, Laplace model produces a more remarkable leptokurtic pattern of the risk-neutral distribution implied by options, as well as generating more pronounced volatility smirks than the normal model.