Bias of a Value-at-Risk Estimator

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Hasanzade, Mehrnoosh | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 45947 (44)
University: Sharif University of Technology
Department: Management and Economics
Advisor(s): Keshavarz Hadad, Golamreza
Abstract:
The recent researches show that Value at Risk estimations are biased and is calculated conservatively. Bao and Olah (2004) proved that the bias of an ARCH(1) model for VaR can be formulated in to two parts: bias due to return Misspecification ( ) and bias due to estimation error ( ). Using a GARCH(1,1) and quasi maximum likelihood estimation method, this research intends to find an analytical framework for the two source of biases. 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 equals to zero for the Normal likelihood function, but . Also, and 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 are large
Keywords:
Value at Risk ; General Autoregressive Conditional Heteroskedastic (GARCH) ; Second-Order Bias

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