The role of adaptivity in a numerical method for the Cox-Ingersoll-Ross model

We demonstrate the effectiveness of an adaptive explicit Euler method for the approximate solution of the Cox-Ingersoll-Ross model. This relies on a class of path-bounded timestepping strategies which work by reducing the stepsize as solutions approach a neighbourhood of zero. The method is hybrid in the sense that a convergent backstop method is invoked if the timestep becomes too small, or to prevent solutions from overshooting zero and becoming negative. Under parameter constraints that imply Feller’s condition, we prove that such a scheme is strongly convergent, of order at least 1/2. Control of the strong error is important for multi-level Monte Carlo techniques. Under Feller’s condition we also prove that the probability of ever needing the backstop method to prevent a negative value can be made arbitrarily small. Numerically, we compare this adaptive method to fixed step implicit and explicit schemes, and a novel semi-implicit adaptive variant. We observe that the adaptive approach leads to methods that are competitive in a domain that extends beyond Feller’s condition, indicating suitability for the modelling of stochastic volatility in Heston-type asset models.

Grantor dc:publisher

University College Cork

Year dc:date.issued

2022

Author dc:creator

• Maulana, Heru

Advisor dc:contributor.advisor

• Kelly, Conall

• Cox–Ingersoll–Ross model
• Adaptive timestepping
• Explicit Euler–Maruyama method
• Strong convergence
• Positivity

Statement dc:rights

• © 2022, Heru Maulana.

Licence dc:rights.uri

• https://creativecommons.org/licenses/by-nc-nd/4.0/

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/10468/13582

OAI identifier oai:identifier

oai:cora.ucc.ie:10468/13582