Title: Bias decomposition in the value-at-risk calculation by a GARCH(1,1)

Authors: GholamReza Keshavarz Haddad; Mehrnoosh Hasanzade

Addresses: Sharif University of Technology, GSME Azadi Street, Tehran, Iran; Brandeis University, MA, USA ' Department of Economics, University of Wisconsin Milwaukee, Bolton 841, Milwaukee, WI 53211, USA

Abstract: The recent researches show that value-at-risk (VaR) estimations are biased and is calculated conservatively. Bao and Ullah (2004) proved the bias of an ARCH(1) model for VaR can be decomposed in to two parts: bias due to the returns' misspecification distributional assumption for GARCH(1,1), i.e., (Bias1) and bias due to estimation error, i.e., (Bias2). Using quasi maximum likelihood estimation method this paper intends to find an analytical framework for the two sources of bias. We generate returns from Normal and t-student distributions, then estimate the GARCH(1,1) under Normal and t-student assumptions. Our findings reveal that Bias1 equals to zero for the Normal likelihood function, but Bias2 ≠ 0. Also, Bias1 and Bias2 are not zero for the t-student likelihood function as analytically were expected, however, all the biases become modest, when the number of observations and degree of freedom gets large.

Keywords: VaR; value-at-risk; GARCH(1;1); second-order bias.

DOI: 10.1504/IJCEE.2020.10029490

International Journal of Computational Economics and Econometrics, 2020 Vol.10 No.2, pp.183 - 202

Received: 08 Feb 2017
Accepted: 22 Jan 2018

Published online: 14 May 2020 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article