TAIL RISK MONOTONICITY IN GARCH(1,1) MODELS

Paul Glasserman, Dan Pirjol () and Qi Wu ()
Additional contact information
Paul Glasserman: Columbia Business School, Columbia University, 1114 Kravis Hall, New York, NY 10027, USA
Dan Pirjol: School of Business, Stevens Institute of Technology, Hoboken, NJ 07030, USA
Qi Wu: School of Data Science, City University of Hong Kong, Kowloon, Hong Kong

International Journal of Theoretical and Applied Finance (IJTAF), 2024, vol. 27, issue 03n04, 1-33

Abstract: The stationary distribution of a GARCH(1,1) process has a power law decay, under broadly applicable conditions. We study the change in the exponent of the tail decay under temporal aggregation of parameters, with the distribution of innovations held fixed. This comparison is motivated by the fact that GARCH models are often fit to the same time series at different frequencies. The resulting models are not strictly compatible so we seek more limited properties we call forecast consistency and tail consistency. Forecast consistency is satisfied through a parameter transformation. Tail consistency leads us to derive conditions under which the tail exponent increases under temporal aggregation, and these conditions cover most relevant combinations of parameters and innovation distributions. But we also prove the existence of counterexamples near the boundary of the admissible parameter region where monotonicity fails. These counterexamples include normally distributed innovations.

Keywords: GARCH; stochastic orders; tail asymptotics; temporal aggregation; Pareto tail (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219024923500292
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:27:y:2024:i:03n04:n:s0219024923500292

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219024923500292

Access Statistics for this article

International Journal of Theoretical and Applied Finance (IJTAF) is currently edited by L P Hughston

More articles in International Journal of Theoretical and Applied Finance (IJTAF) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().