Multivariate tempered stable model with long-range dependence and time-varying volatility

Frontiers in Applied Mathematics and Statistics

Kim, Young Shin¹ 

[1] College of Business, The State University of New York at Stony Brook, Stony Brook, NY, USA

关键词: Multivariate fractional normal tempered stable process;    Long-range dependence;    Fractional Brownian motion;    fractional L´;    evy processes;    high-frequency market;    Intraday trading;    Volatility clustering;    asymmetric dependence;   

DOI  :  10.3389/fams.2015.00001

学科分类：数学（综合）

来源: Frontiers

【 摘 要 】

High-frequency financial return time series data have stylized facts such as the long-range dependence, fat-tails, asymmetric dependence, and volatility clustering. In this paper, a multivariate model which describes those stylized facts is presented. To construct the model, a multivariate ARMA-GARCH model is considered along with fractional Levy process. The fractional Levy process in this paper is defined by the stochastic integral with a tempered stable driving process. Parameters of the new model are fit to high-frequency returns for five U.S stocks. Approximated form of portfolio value-at-risk and average value-at-risk are provided and portfolio optimization is discussed under the model.

【 授权许可】

CC BY