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Semi-closed form cubature and applications to Financial diffusion models
Please always quote using this URN:urn:nbn:de:0296-matheon-11564
- 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.
Author: | Christian Bayer, Peter Friz, Ronnie Loeffen |
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URN: | urn:nbn:de:0296-matheon-11564 |
Referee: | Peter Karl Friz |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2012/07/17 |
Release Date: | 2012/07/17 |
Tag: | Monte Carlo simulation; Ninomiya–Victoir method; cubature method |
Institute: | Technische Universität Berlin |
MSC-Classification: | 60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65] / 60H35 Computational methods for stochastic equations [See also 65C30] |
Preprint Number: | 972 |