Statistical aspects of some recent financial models
by
Ross Maller
University of Western Australia
Coauthors: Claudia Klueppelberg (Munich University of Technology), Alex Szimayer (Caesar Research Centre, Bonn), Mark Van De Vyver (UWA)

I'll outline some large-sample theory for testing hypotheses on a couple of ßtochastic volatility" models which are currently of great interest in Finance. The first (class of) models, the "(Generalised) Autoregressive Conditional Heteroscedasticity" models, has been well studied in a discrete time setting, but I'll present a new continuous time version of it, using a Levy process in place of the usual innovations. The second type is the Ornstein-Uhlenbeck processes, a kind of continuous time version of autoregressive series. I'll set up a parameterised version driven by a Levy process. In both instances I'll develop hypothesis tests which have some interesting and unusual statistical features: the ünit-root" (random walk) aspect appears, as well as a parameter which "disappears under the null".

Date received: January 23, 2002