Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model

DOI10.1007/s10543-010-0288-yzbMath1230.65011OpenAlexW2152573633MaRDI QIDQ634110

Jiazhu Pan, Desmond J. Higham, Lukasz Szpruch, Xuerong Mao

Publication date: 2 August 2011

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-010-0288-y

zbMATH Keywords

Monte Carlo methodinterest ratemodel calibrationmoment boundbackward Euler-Maruyama discretization algorithmIto equation

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Monte Carlo methods (65C05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Interest rates, asset pricing, etc. (stochastic models) (91G30) Ordinary differential equations and systems with randomness (34F05) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Euler-Maruyama approximations in mean-reverting stochastic volatility model under regime-switching
• Analyzing multi-level Monte Carlo for options with non-globally Lipschitz payoff
• Short rate nonlinearities and regime switches.
• The Pathwise Convergence of Approximation Schemes for Stochastic Differential Equations
• On the discretization schemes for the CIR (and Bessel squared) processes
• Multilevel Monte Carlo Path Simulation
• ESTIMATION OF CONTINUOUS-TIME MODELS FOR STOCK RETURNS AND INTEREST RATES
• Balanced Implicit Methods for Stiff Stochastic Systems
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence