Time-consistency of risk measures with GARCH volatilities and their estimation

Claudia Kl\"uppelberg and Jianing Zhang

Papers from arXiv.org

Abstract: In this paper we study time-consistent risk measures for returns that are given by a GARCH(1,1) model. We present a construction of risk measures based on their static counterparts that overcomes the lack of time-consistency. We then study in detail our construction for the risk measures Value-at-Risk (VaR) and Average Value-at-Risk (AVaR). While in the VaR case we can derive an analytical formula for its time-consistent counterpart, in the AVaR case we derive lower and upper bounds to its time-consistent version. Furthermore, we incorporate techniques from Extreme Value Theory (EVT) to allow for a more tail-geared statistical analysis of the corresponding risk measures. We conclude with an application of our results to a data set of stock prices.

Date: 2015-04, Revised 2016-02
New Economics Papers: this item is included in nep-ets and nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1504.04774

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