Cubature on Wiener Space: Pathwise Convergence

Journal Article · Mon Apr 15 00:00:00 EDT 2013 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-012-9187-8· OSTI ID:22156411

Bayer, Christian

Cubature on Wiener space (Lyons and Victoir in Proc. R. Soc. Lond. A 460(2041):169-198, 2004) provides a powerful alternative to Monte Carlo simulation for the integration of certain functionals on Wiener space. More specifically, and in the language of mathematical finance, cubature allows for fast computation of European option prices in generic diffusion models.We give a random walk interpretation of cubature and similar (e.g. the Ninomiya-Victoir) weak approximation schemes. By using rough path analysis, we are able to establish weak convergence for general path-dependent option prices.

• OSTI ID: 22156411
• Journal Information: Applied Mathematics and Optimization, Vol. 67, Issue 2; Other Information: Copyright (c) 2013 Springer Science+Business Media New York; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
COMPUTERIZED SIMULATION
CONVERGENCE
DIFFUSION
FUNCTIONALS
GRAPH THEORY
MATHEMATICAL SPACE
MONTE CARLO METHOD
PRICES
RANDOMNESS