Semi-closed form cubature and applications to financial diffusion models

DOI10.1080/14697688.2012.752102zbMath1281.91180arXiv1009.4818OpenAlexW2000698170MaRDI QIDQ5397417

Peter K. Friz, Christian Bayer, Ronnie Loeffen

Publication date: 20 February 2014

Published in: Quantitative Finance (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.4818

zbMATH Keywords

stochastic volatilitystochastic differential equationsMonte Carlo methods

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Monte Carlo methods (65C05) Stochastic models in economics (91B70) Stochastic integrals (60H05) Numerical solutions to stochastic differential and integral equations (65C30) Numerical integration (65D30)

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A weak approximation with asymptotic expansion and multidimensional Malliavin weights ⋮ Algebraic structure of vector fields in financial diffusion models and its applications ⋮ Asymptotics Beats Monte Carlo: The Case of Correlated Local Vol Baskets ⋮ Weak approximation of SDEs for tempered distributions and applications ⋮ Cubature on Wiener space: pathwise convergence ⋮ Dirichlet Forms and Finite Element Methods for the SABR Model ⋮ Total variation bound for Milstein scheme without iterated integrals ⋮ Construction of a Third-Order K-Scheme and Its Application to Financial Models ⋮ An Arbitrary High Order Weak Approximation of SDE and Malliavin Monte Carlo: Analysis of Probability Distribution Functions ⋮ A second-order discretization with Malliavin weight and Quasi-Monte Carlo method for option pricing ⋮ On the signature and cubature of the fractional Brownian motion for \(H > \frac{1}{2}\) ⋮ The principle of not feeling the boundary for the SABR model ⋮ Efficient simulation methods for the Quasi-Gaussian term-structure model with volatility smiles: practical applications of the KLNV-scheme ⋮ Short Communication: A Gaussian Kusuoka Approximation without Solving Random ODEs

Cites Work

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• A new higher-order weak approximation scheme for stochastic differential equations and the Runge-Kutta method
• A LOW-BIAS SIMULATION SCHEME FOR THE SABR STOCHASTIC VOLATILITY MODEL
• Cubature on Wiener space
• Multidimensional Stochastic Processes as Rough Paths
• High order discretization schemes for the CIR process: Application to affine term structure and Heston models
• A comparison of biased simulation schemes for stochastic volatility models

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