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Analytic Moments for GARCH Processes

Alexander, Carol and Lazar, Emese and Stanescu, Silvia (2011) Analytic Moments for GARCH Processes. Working paper. ICMA Centre Discussion Papers in Finance, Reading 10.2139/ssrn.1702623. (doi:10.2139/ssrn.1702623) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.2139/ssrn.1702623

Abstract

Conditional returns distributions generated by a GARCH process, which are important for many problems in market risk assessment and portfolio optimization, are typically generated via simulation. This paper extends previous research on analytic moments of GARCH returns distributions in several ways: we consider a general GARCH model – the GJR specification with a generic innovation distribution; we derive analytic expressions for the first four conditional moments of the forward return, of the forward variance, of the aggregated return and of the aggregated variance – corresponding moments for some specific GARCH models largely used in practice are recovered as special cases; we derive the limits of these moments as the time horizon increases, establishing regularity conditions for the moments of aggregated returns to converge to normal moments; and we demonstrate empirically that some excellent approximate predictive distributions can be obtained from these analytic moments, thus precluding the need for time-consuming simulations.

Item Type: Monograph (Working paper)
DOI/Identification number: 10.2139/ssrn.1702623
Uncontrolled keywords: Approximate predictive distributions, conditional and unconditional moments, GARCH, kurtosis, skewness, simulation
Subjects: H Social Sciences
H Social Sciences > HG Finance
Divisions: Faculties > Social Sciences > Kent Business School > Accounting and Finance
Depositing User: Cathy Norman
Date Deposited: 07 Feb 2013 11:23 UTC
Last Modified: 29 May 2019 09:59 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/33174 (The current URI for this page, for reference purposes)
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