2023/05/18 by Svetlana Boyarchenko, Boyarchenko, Svetlana, Sergei Levendorskiı̌ +1
Economics, Econometrics and Finance · #42A38 #42B10 #44A10 #60-08 #65G51 #65R10 #91G20 #91G60 #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2305.10725
openalex publication_date 2023/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive several sets of sufficient conditions for applicability of the new efficient numerical realization of the inverse Z-transform. For large n, the complexity of the new scheme is dozens of times smaller than the complexity of the trapezoid rule. As applications, pricing of European options and single barrier options with discrete monitoring are considered; applications to more general options with barrier-lookback features are outlined. In the case of sectorial transition operators, hence, for symmetric Lévy models, the proof is straightforward. In the case of non-symmetric Lévy models, we construct a non-linear deformation of the dual space, which makes the transition operator sectorial, with an arbitrary small opening angle, and justify the new realization. We impose mild conditions which are satisfied for wide classes of non-symmetric Stieltjes-Lévy processes.