Picture of smart phone in human hand

World leading smartphone and mobile technology research at Strathclyde...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including by Strathclyde researchers from the Department of Computer & Information Sciences involved in researching exciting new applications for mobile and smartphone technology. But the transformative application of mobile technologies is also the focus of research within disciplines as diverse as Electronic & Electrical Engineering, Marketing, Human Resource Management and Biomedical Enginering, among others.

Explore Strathclyde's Open Access research on smartphone technology now...

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

Chalmers, Graeme and Higham, Desmond (2010) First and second moment reversion for a discretized square root process with jumps. Journal of Difference Equations and Applications, 16 (2-3). pp. 143-156. ISSN 1023-6198

Full text not available in this repository. (Request a copy from the Strathclyde author)

Abstract

Mean-reversion is an important component of many financial models. When simulations are performed with numerical methods, it is therefore desirable to reproduce this qualitative property. Here, we study a square root process with jumps that has been used to model interest rates and volatilities, and we characterize the parameter regimes under which the first and second moments revert to steady state values. We then consider a class of implicit theta methods and investigate the same moment properties for the corresponding stochastic difference equation. We find that the theta method is unconditionally stable in first and second moment for theta values below a cutoff level. This cutoff level depends on the parameters governing the mean reversion and the jumps, but is always more favourable than the value of one half that arises in the deterministic setting. In the case of high jump intensity, large jump magnitude or slow mean reversion, it is even possible for the explicit Euler-Maruyama type method from this class to be unconditionally stable. We also establish upper and lower bounds for the second moment steady state that are close to that of the continuous-time process for small step-sizes. Numerical experiments are given to illustrate the results.