Fractional Levy Model with Time-Varying Volatility in High-Frequency Trading Market

• Activity Number: 112
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Risk Analysis
• Author(s): Young Shin Aaron Kim*+ and James Glimm and Svetlozar T. Rachev
• Companies: Stony Brook University and Stony Brook University and Stony Brook University
• Keywords: Fractional Levy Process ; Long range dependence ; Risk Assessment ; Value At Risk ; Average Value at Risk ; Portfolio Optimization

Abstract

Young Shin Aaron Kim (College of Business, Stony Brook University)

James Glimm (Department of Applied Mathematics & Statistics, Stony Brook University)

Svetlozar T. Rachev (College of Business, Stony Brook University; Department of Applied Mathematics & Statistics, Stony Brook University)

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