On arbitrarily slow convergence rates for strong numerical approximations of Cox-Ingersoll-Ross processes and squared Bessel processes. (English) Zbl 1425.91401
The Cox-Ingersoll-Ross (CIR) processes are known to be used extensively today in modeling the pricing of financial derivatives. Generally, discretization methods (such as Milstein-type) are characterized by slow convergence. In the article, the authors reveals that each such discretization method achieves at most a strong convergence order of \(\frac{\delta}{2}\), where \(0 <\delta < 2\) is the dimension of the squared Bessel process associated to the considered (CIR) process. The reader can be found a refined lower bound for strong \(L^{1}\)-distances between the constructed squared Bessel processes and lower error bounds for (CIR) processes and squared Bessel processes in the general case. The investigations are of interest to researchers of this topic.
Reviewer: Nikolay Kyurkchiev (Plovdiv)
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 91G30 | Interest rates, asset pricing, etc. (stochastic models) |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
Cox-Ingersoll-Ross process; squared Bessel process; strong (pathwise) approximation; lower error bound; optimal approximationReferences:
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