An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process
From MaRDI portal
Publication:5345939
DOI10.1098/rspa.2011.0505zbMath1364.65013OpenAlexW2115906242MaRDI QIDQ5345939
Steffen Dereich, Andreas Neuenkirch, Lukasz Szpruch
Publication date: 7 June 2017
Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1098/rspa.2011.0505
Numerical methods (including Monte Carlo methods) (91G60) Numerical solutions to stochastic differential and integral equations (65C30)
Related Items (64)
Convergence rates of large-time sensitivities with the Hansen-Scheinkman decomposition ⋮ Analysis of non-negativity and convergence of solution of the balanced implicit method for the delay Cox-Ingersoll-Ross model ⋮ The role of adaptivity in a numerical method for the Cox-Ingersoll-Ross model ⋮ Functional limit theorems for additive and multiplicative schemes in the Cox-Ingersoll-Ross model ⋮ Strong Convergence Rates for Euler Approximations to a Class of Stochastic Path-Dependent Volatility Models ⋮ Approximating explicitly the mean-reverting CEV process ⋮ Generalized Ait-Sahalia-type interest rate model with Poisson jumps and convergence of the numerical approximation ⋮ A note on strong approximation of SDEs with smooth coefficients that have at most linearly growing derivatives ⋮ On non-polynomial lower error bounds for adaptive strong approximation of SDEs ⋮ The truncated Euler-Maruyama method for CIR model driven by fractional Brownian motion ⋮ Dirichlet Forms and Finite Element Methods for the SABR Model ⋮ Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients ⋮ Convergence of the deep BSDE method for FBSDEs with non-Lipschitz coefficients ⋮ Instantaneous turbulent kinetic energy modelling based on Lagrangian stochastic approach in CFD and application to wind energy ⋮ Weak Convergence Rate of a Time-Discrete Scheme for the Heston Stochastic Volatility Model ⋮ On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients ⋮ Strong convergence rates for Cox-Ingersoll-Ross processes -- full parameter range ⋮ Extinction-time for stochastic population models ⋮ An application of the Malliavin calculus for calculating the precise and approximate prices of options with stochastic volatility ⋮ An Explicit Euler Scheme with Strong Rate of Convergence for Financial SDEs with Non-Lipschitz Coefficients ⋮ Two methods of estimation of the drift parameters of the Cox–Ingersoll–Ross process: Continuous observations ⋮ An adaptive splitting method for the Cox-Ingersoll-Ross process ⋮ Multiple-delay stochastic McKean-Vlasov equations with Hölder diffusion coefficients and their numerical schemes ⋮ Semi-implicit Euler-Maruyama approximation for noncolliding particle systems ⋮ The modified truncated Euler-Maruyama method for stochastic differential equations with concave diffusion coefficients ⋮ Multilevel Monte Carlo simulation for the Heston stochastic volatility model ⋮ Drift-implicit Euler scheme for sandwiched processes driven by Hölder noises ⋮ Multilevel Monte Carlo using approximate distributions of the CIR process ⋮ Strong approximation of Bessel processes ⋮ Strong convergence rate of implicit Euler scheme to a CIR model with delay ⋮ Mean-reverting schemes for solving the CIR model ⋮ Positivity-preserving truncated Euler-Maruyama method for generalised Ait-Sahalia-type interest model ⋮ High Order Splitting Methods for SDEs Satisfying a Commutativity Condition ⋮ Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations ⋮ Construction of a Third-Order K-Scheme and Its Application to Financial Models ⋮ On arbitrarily slow convergence rates for strong numerical approximations of Cox-Ingersoll-Ross processes and squared Bessel processes ⋮ On the weak convergence rate of an exponential Euler scheme for SDEs governed by coefficients with superlinear growth ⋮ Unnamed Item ⋮ On sub-polynomial lower error bounds for quadrature of SDEs with bounded smooth coefficients ⋮ Tamed Euler-Maruyama approximation for stochastic differential equations with locally Hölder continuous diffusion coefficients ⋮ Convergence of an Euler Scheme for a Hybrid Stochastic-Local Volatility Model with Stochastic Rates in Foreign Exchange Markets ⋮ Lower error bounds for strong approximation of scalar SDEs with non-Lipschitzian coefficients ⋮ A transformed jump-adapted backward Euler method for jump-extended CIR and CEV models ⋮ The truncated Milstein method for stochastic differential equations with commutative noise ⋮ On a positivity preserving numerical scheme for jump-extended CIR process: the alpha-stable case ⋮ Uniform approximation of the Cox-Ingersoll-Ross process ⋮ Convergence and non-negativity preserving of the solution of balanced method for the delay CIR model with jump ⋮ Exponential integrability properties of Euler discretization schemes for the Cox-Ingersoll-Ross process ⋮ Positivity preserving logarithmic Euler-Maruyama type scheme for stochastic differential equations ⋮ Strong convergence and asymptotic stability of explicit numerical schemes for nonlinear stochastic differential equations ⋮ First order strong approximations of scalar SDEs defined in a domain ⋮ Convergence and stability of modified partially truncated Euler-Maruyama method for nonlinear stochastic differential equations with Hölder continuous diffusion coefficient ⋮ Optimal strong convergence rate of a backward Euler type scheme for the Cox-Ingersoll-Ross model driven by fractional Brownian motion ⋮ The log-asset dynamic with Euler-Maruyama scheme under Wishart processes ⋮ Least-squares estimation for the subcritical Heston model based on continuous-time observations ⋮ CHI-SQUARE SIMULATION OF THE CIR PROCESS AND THE HESTON MODEL ⋮ Stochastic differential equations driven by fractional Brownian motion with locally Lipschitz drift and their implicit Euler approximation ⋮ Dynamics and approximation of positive solution of the stochastic SIS model affected by air pollutants ⋮ Strong and weak convergence rates of logarithmic transformed truncated EM methods for SDEs with positive solutions ⋮ Loss of regularity for Kolmogorov equations ⋮ How to handle negative interest rates in a CIR framework ⋮ Semi-implicit Euler-Maruyama scheme for polynomial diffusions on the unit ball ⋮ Verhulst versus CIR ⋮ Study on split-step Rosenbrock type method for stiff stochastic differential systems
Cites Work
- Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model
- A note on Euler approximations for SDEs with Hölder continuous diffusion coefficients
- A note on Euler's approximations
- The optimal uniform approximation of systems of stochastic differential equations
- Exact simulation of diffusions
- A Theory of the Term Structure of Interest Rates
- On the discretization schemes for the CIR (and Bessel squared) processes
- Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes
- Multilevel Monte Carlo Path Simulation
- Exact and Computationally Efficient Likelihood-Based Estimation for Discretely Observed Diffusion Processes (with Discussion)
- Fast strong approximation Monte Carlo schemes for stochastic volatility models
- Boundary Preserving Semianalytic Numerical Algorithms for Stochastic Differential Equations
- High order discretization schemes for the CIR process: Application to affine term structure and Heston models
- Convergence of discretized stochastic (interest rate) processes with stochastic drift term
- Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
- A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
- Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence
This page was built for publication: An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process