Analytic Moments for GARCH Processes

Carol Alexander, Emese Lazar and Silvia Stanescu
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Silvia Stanescu: Kent Business School, University of Kent

ICMA Centre Discussion Papers in Finance from Henley Business School, University of Reading

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.

Keywords: Approximate predictive distributions; conditional and unconditional moments; GARCH; kurtosis; skewness; simulation (search for similar items in EconPapers)
JEL-codes: C53 (search for similar items in EconPapers)
Date: 2010-11, Revised 2011-04
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Related works:
Working Paper: Analytic Moments for GARCH Processes (2018)
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