Abstract
The ability of θ-Milstein methods with
References
[1] A. Alfonsi, On the discretization schemes for the CIR (and Bessel squared) processes, Monte Carlo Methods Appl. 11 (2005), no. 4, 355–384. 10.1163/156939605777438569Suche in Google Scholar
[2] M. Bossy and H. Olivero, Strong convergence of the symmetrized Milstein scheme for some CEV-like SDEs, Bernoulli 24 (2018), no. 3, 1995–2042. 10.3150/16-BEJ918Suche in Google Scholar
[3] J. C. Cox, J. E. Ingersoll, Jr. and S. A. Ross, A theory of the term structure of interest rates, Econometrica 53 (1985), no. 2, 385–407. 10.2307/1911242Suche in Google Scholar
[4] S. Dereich, A. Neuenkirch and L. Szpruch, An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 468 (2012), no. 2140, 1105–1115. 10.1098/rspa.2011.0505Suche in Google Scholar
[5] I. I. Gikhman, A short remark on Feller’s square root condition, preprint (2011), https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1756450. 10.2139/ssrn.1756450Suche in Google Scholar
[6] M. Hefter and A. Herzwurm, Optimal strong approximation of the one-dimensional squared Bessel process, Commun. Math. Sci. 15 (2017), no. 8, 2121–2141. 10.4310/CMS.2017.v15.n8.a2Suche in Google Scholar
[7] M. Hefter and A. Herzwurm, Strong convergence rates for Cox–Ingersoll–Ross processes—full parameter range, J. Math. Anal. Appl. 459 (2018), no. 2, 1079–1101. 10.1016/j.jmaa.2017.10.076Suche in Google Scholar
[8] D. J. Higham, A-stability and stochastic mean-square stability, BIT 40 (2000), no. 2, 404–409. 10.1023/A:1022355410570Suche in Google Scholar
[9] D. J. Higham and X. Mao, Convergence of Monte Carlo simulations involving the mean-reverting square root process, J. Comput. Finance 8 (2005), no. 3, 35–61. 10.21314/JCF.2005.136Suche in Google Scholar
[10] C. Kahl, M. Günther and T. Rossberg, Structure preserving stochastic integration schemes in interest rate derivative modeling, Appl. Numer. Math. 58 (2008), no. 3, 284–295. 10.1016/j.apnum.2006.11.013Suche in Google Scholar
[11] K. Kladívko, Maximum likelihood estimation of the Cox–Ingersoll–Ross process: The Matlab implementation, Tech. Comput. Prag. 7 (2007), no. 8, 1–8. Suche in Google Scholar
[12] P. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, Heidelberg, 1992. 10.1007/978-3-662-12616-5Suche in Google Scholar
[13] S. Llamazares-Elias and A. Tocino, Mean-reverting schemes for solving the CIR model, J. Comput. Appl. Math. 434 (2023), Article ID 115354. 10.1016/j.cam.2023.115354Suche in Google Scholar
[14] R. Lord, R. Koekkoek and D. Van Dijk, A comparison of biased simulation schemes for stochastic volatility models, Quant. Finance 10 (2010), no. 2, 177–194. 10.1080/14697680802392496Suche in Google Scholar
[15] X. Mao, Stochastic Differential Equations and Applications, Woodhead Publishing, Amsterdam, 2007. 10.1533/9780857099402Suche in Google Scholar
[16] G. N. Milstein, Numerical Integration of Stochastic Differential Equations, Math. Appl. 313, Kluwer Academic, Dordrecht, 1995. 10.1007/978-94-015-8455-5Suche in Google Scholar
[17] B. Øksendal, Stochastic Differential Equations, Universitext, Springer, Berlin, 2003. 10.1007/978-3-642-14394-6Suche in Google Scholar
[18] C. Scalone, Positivity preserving stochastic θ-methods for selected SDEs, Appl. Numer. Math. 172 (2022), 351–358. 10.1016/j.apnum.2021.10.017Suche in Google Scholar
[19] S. E. Shreve, Stochastic Calculus for Finance. II, Springer Finance, Springer, New York, 2004. 10.1007/978-1-4757-4296-1Suche in Google Scholar
[20] T. Yamada and S. Watanabe, On the uniqueness of solutions of stochastic differential equations, J. Math. Kyoto Univ. 11 (1971), 155–167. 10.1215/kjm/1250523691Suche in Google Scholar
© 2025 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Impact of psychrometry on the aerosol distribution pattern in human lungs
- Bayesian inference of traffic intensity in M/M/1 queue under symmetric and asymmetric loss functions
- On the variance of Schatten p-norm estimation with Gaussian sketching matrices
- A meshfree Random Walk on Boundary algorithm with iterative refinement
- Combining randomized and deterministic iterative algorithms for high accuracy solution of large linear systems and boundary integral equations
- Preservation of structural properties of the CIR model by θ-Milstein schemes
Artikel in diesem Heft
- Frontmatter
- Impact of psychrometry on the aerosol distribution pattern in human lungs
- Bayesian inference of traffic intensity in M/M/1 queue under symmetric and asymmetric loss functions
- On the variance of Schatten p-norm estimation with Gaussian sketching matrices
- A meshfree Random Walk on Boundary algorithm with iterative refinement
- Combining randomized and deterministic iterative algorithms for high accuracy solution of large linear systems and boundary integral equations
- Preservation of structural properties of the CIR model by θ-Milstein schemes