In　recent　years,　the　Finite　Moment　Log　Stable(FMLS),　KoBoL　and　CGMY　models,　which　follow　a　jump　process　or　a　Lévy　process,　have　become　the　most　popular　modeling　frameworks　in　the　financial　field　because　they　can　capture　some　of　the　important　characteristics　in　the　dynamic　process　of　stock　price　changes,　such　as　large　movements　or　jumps　over　small　time　steps.　In　this　paper,　we　consider　the　numerical　simulation　of　these　three　models.　We　construct　a　discrete　implicit　numerical　scheme　with　second　order　accuracy,　and　provide　a　stability　and　convergence　analysis　of　the　numerical　scheme.　Furthermore,　a　fast　bi-conjugate　gradient　stabilized　method　(FBi-CGSTAB)　is　used　to　reduce　the　storage　space　from　O(M　2　)　to　O(M)　and　the　computational　cost　from　O(M　3　)　to　O(Mlog　M)　per　iteration,　where　M　is　the　number　of　space　grid　points.　Some　numerical　examples　are　chosen　in　order　to　demonstrate　the　accuracy　and　efficiency　of　the　proposed　method　and　technique.　Finally,　as　an　application,　we　use　the　above　numerical　technique　to　price　a　European　double-knock-out　barrier　option,　and　then　the　characteristics　of　the　three　fractional　Black-Scholes　(B-S)　models　are　analyzed　through　comparison　with　the　classical　B-S　model.　©　2016　Elsevier　Inc.