Tail Risk Monotonicity Under Temporal Aggregation in GARCH(1,1) Models

26 Pages Posted: 3 Jan 2020

See all articles by Paul Glasserman

Paul Glasserman

Columbia Business School

Dan Pirjol

Stevens Institute of Technology

Qi Wu

City University of Hong Kong (CityUHK)

Date Written: December 11, 2019

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. The parameter transformation we study results from approximating a GARCH process observed at one frequency with another observed at a lower frequency. We 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 regions where monotonicity fails. These counterexamples include several standard choices for innovation distributions, including the normal case.

Keywords: GARCH, Tail Risk

JEL Classification: C22, C58

Suggested Citation

Glasserman, Paul and Pirjol, Dan and Wu, Qi, Tail Risk Monotonicity Under Temporal Aggregation in GARCH(1,1) Models (December 11, 2019). Available at SSRN: https://ssrn.com/abstract=3502425 or http://dx.doi.org/10.2139/ssrn.3502425

Paul Glasserman (Contact Author)

Columbia Business School ( email )

3022 Broadway
403 Uris Hall
New York, NY 10027
United States
212-854-4102 (Phone)
212-316-9180 (Fax)

Dan Pirjol

Stevens Institute of Technology ( email )

Hoboken, NJ 07030
United States

Qi Wu

City University of Hong Kong (CityUHK) ( email )

83 Tat Chee Avenue
Kowloon
Hong Kong

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