Open AccessSome Further Results on the Tempered Multistable Approach
Author(s) -
Olivier Le Courtois
Publication year - 2018
Publication title -
asia-pacific financial markets
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.175
H-Index - 22
eISSN - 1573-6946
pISSN - 1387-2834
DOI - 10.1007/s10690-018-9240-y
Subject(s) - representation (politics) , property (philosophy) , series (stratigraphy) , function (biology) , value (mathematics) , computer science , term (time) , field (mathematics) , mathematics , physics , machine learning , pure mathematics , paleontology , philosophy , epistemology , quantum mechanics , evolutionary biology , politics , political science , law , biology
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.