On the discretization schemes for the CIR (and Bessel squared) processes
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Publication:3367271
DOI10.1515/156939605777438569zbMath1100.65007OpenAlexW2254488552MaRDI QIDQ3367271
Publication date: 24 January 2006
Published in: Monte Carlo Methods and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/156939605777438569
comparison of methodsnumerical examplesCox-Ingersoll-Ross modeldiscretization schemestochastic integro-differential equationRomberg methodSquared Bessel process
Numerical methods for integral equations (65R20) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Stochastic integral equations (60H20) Random integral equations (45R05)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model
- The law of the Euler scheme for stochastic differential equations. I: Convergence rate of the distribution function
- A Theory of the Term Structure of Interest Rates
- Second-order discretization schemes of stochastic differential systems for the computation of the invariant law
- Convergence of discretized stochastic (interest rate) processes with stochastic drift term
- Numerical Methods for Stochastic Systems Preserving Symplectic Structure
- A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options