Journal of Risk

Risk.net

On correlating Lévy processes

Ernst Eberlein, Dilip B. Madan

ASBTRACT

In this paper, a relatively simple approach to correlating unit period returns of Lévy processes is developed.We write the Lévy process as a time changed Brownian motion and correlate the Brownian motions. It is shown that sample correlations understate the required correlation between the Brownian motions and we show how to correct for this. Pairwise tests illustrate the adequacy of the model and the significant improvement offered over the Gaussian alternative. We therefore advocate that the correlated time change model is a simple basic alternative to dependence modeling. From the perspective of explaining portfolio returns in higher dimensions we find adequacy for long-short portfolios. The long-only portfolios appear to require a more complex modeling of dependency. We leave these questions for future research.

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to Risk.net? View our subscription options

If you already have an account, please sign in here.

You need to sign in to use this feature. If you don’t have a Risk.net account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here: