TY - GEN A1 - Bayer, Christian A1 - Friz, Peter A1 - Loeffen, Ronnie T1 - Semi-closed form cubature and applications to Financial diffusion models N2 - Cubature methods, a powerful alternative to Monte Carlo due to Kusuoka [Adv. Math. Econ. 6, 69–83, 2004] and Lyons–Victoir [Proc. R. Soc. Lond. Ser. A 460, 169–198, 2004], involve the solution to numerous auxiliary ordinary differential equations. With focus on the Ninomiya-Victoir algorithm [Appl. Math. Fin. 15, 107–121, 2008], which corresponds to a concrete level 5 cubature method, we study some parametric diffusion models motivated from financial applications, and exhibit structural conditions under which all involved ODEs can be solved explicitly and efficiently. We then enlarge the class of models for which this technique applies, by introducing a (model-dependent) variation of the Ninomiya-Victoir method. Our method remains easy to implement; numerical examples illustrate the savings in computation time. KW - Ninomiya–Victoir method KW - cubature method KW - Monte Carlo simulation Y1 - 2012 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1156 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-11564 ER -