On the analysis of Ait-Sahalia-type model for rough volatility modelling

DOI10.1007/s10959-023-01269-2OpenAlexW4380537531MaRDI QIDQ6204804

Xuerong Mao, Frank Norbert Proske, Emmanuel Coffie

Publication date: 2 April 2024

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10959-023-01269-2

zbMATH Keywords

fractional Brownian motionMalliavin calculusstrong solutionhigher momentsrough volatility

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30)

Cites Work

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• Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model
• A singular stochastic differential equation driven by fractional Brownian motion
• Stochastic analysis of the fractional Brownian motion
• Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than 1/2
• Bismut-Elworthy-Li formula, singular SDEs, fractional Brownian motion, Malliavin calculus, stochastic flows, stochastic volatility
• Truncated EM numerical method for generalised Ait-Sahalia-type interest rate model with delay
• \(n\)-covariation, generalized Dirichlet processes and calculus with respect to finite cubic variation processes.
• The Malliavin Calculus and Related Topics
• Volatility is rough
• Conditional Distributions of Processes Related to Fractional Brownian Motion
• Stochastic differential equations driven by fractional Brownian motion with locally Lipschitz drift and their implicit Euler approximation
• Estimation of the Hurst index of the solutions of fractional SDE with locally Lipschitz drift
• Stochastic Calculus for Fractional Brownian Motion and Applications

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