Extending Time-Changed Lévy Asset Models Through Multivariate Subordinators
AbstractThe traditional multivariate Lévy process constructed by subordinating a Brownian motion through a univariate subordinator presents a number of drawbacks, including the lack of independence and a limited range of dependence. In order to face these, we investigate multivariate subordination, with a common and an idiosyncratic component. We introduce generalizations of some well known univariate Lévy processes for financial applications: the multivariate compound Poisson, NIG, Variance Gamma and CGMY. In all these cases the extension is parsimonious, in that one additional parameter only is needed. We characterize first the subordinator, then the time changed processes via their Lévy measure and characteristic exponent. We further study the subordinator association, as well as the subordinated processes linear and non linear dependence. We show that the processes generated with the proposed time change can include independence and that they span the whole range of linear dependence. We provide some examples of simulated trajectories,scatter plots and both linear and non linear dependence measures. The input data for these simulations are calibrated values for major stock indices.
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Bibliographic InfoPaper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 42.
Length: 35 pages
Date of creation: 2007
Date of revision:
Lévy processes; multivariate subordinators; dependence (association; correlation); multivariate asset modelling;
Find related papers by JEL classification:
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-11-24 (All new papers)
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