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

GholamReza Keshavarz Haddad and Mehrnoosh Hasanzade

International Journal of Computational Economics and Econometrics, 2020, vol. 10, issue 2, 183-202

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. (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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