First and second moment reversion for a discretized square root process with jumps

DOI10.1080/10236190802705719zbMath1188.91241OpenAlexW2056414623MaRDI QIDQ5305973

Desmond J. Higham, Graeme D. Chalmers

Publication date: 24 March 2010

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236190802705719

zbMATH Keywords

stabilitystochastic differential equationMonte Carlovarianceinterest ratevolatilityimplicitItô Lemma

Mathematics Subject Classification ID

Numerical methods (including Monte Carlo methods) (91G60) Monte Carlo methods (65C05) Applications of stochastic analysis (to PDEs, etc.) (60H30) Financial applications of other theories (91G80) Interest rates, asset pricing, etc. (stochastic models) (91G30)

Related Items (8)

Convergence of Numerical Approximation for Jump Models Involving Delay and Mean-Reverting Square Root Process ⋮ A long term analysis of stochastic theta methods for mean reverting linear process with jumps ⋮ Numerical conservation issues for jump Pearson diffusions ⋮ Strong Convergence Analysis of Split-Step θ-Scheme for Nonlinear Stochastic Differential Equations with Jumps ⋮ A transformed jump-adapted backward Euler method for jump-extended CIR and CEV models ⋮ Positivity and convergence of the balanced implicit method for the nonlinear jump-extended CIR model ⋮ Positivity preserving stochastic \(\theta\)-methods for selected SDEs ⋮ CHI-SQUARE SIMULATION OF THE CIR PROCESS AND THE HESTON MODEL

Cites Work

• Numerical methods for nonlinear stochastic differential equations with jumps
• A Theory of the Term Structure of Interest Rates
• On the discretization schemes for the CIR (and Bessel squared) processes
• Financial Modelling with Jump Processes
• Exponential Mean-Square Stability of Numerical Solutions to Stochastic Differential Equations
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
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