Some Further Results on the Tempered Multistable Approach

This article provides new results on the tempered multistable approach. After a preliminary section recalling the main definitions, we show the correspondence between a series representation and a characteristic function representation for asymmetrical field-based tempered multistable processes and for asymmetrical independent increments tempered multistable processes. We also show that both processes are semimartingales, which is a convenient property in finance. Next, we study the structure of autocorrelations that is conveyed by this approach. Finally, we provide an illustration showing the term structures of Value-at-Risk that can be obtained with this model.