Volatility estimation using a rational GARCH model

Tetsuya Takaishi; Tetsuya Takaishi

doi:10.3934/QFE.2018.1.127

Quantitative Finance and Economics

2018, Volume 2, Issue 1: 127-136. doi: 10.3934/QFE.2018.1.127

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Research article Special Issues

Volatility estimation using a rational GARCH model

Tetsuya Takaishi ^,

Hiroshima University of Economics, 731-0192, Gion, Asaminami-ku, Hiroshima, Japan

Received: 31 August 2017 Accepted: 27 December 2017 Published: 13 March 2018
JEL Codes: C22

The rational GARCH (RGARCH) model has been proposed as an alternative GARCH model that captures the asymmetric property of volatility. In addition to the previously proposed RGARCH model, we propose an alternative RGARCH model called the RGARCH-Exp model that is more stable when dealing with outliers. We measure the performance of the volatility estimation by a loss function calculated using realized volatility as a proxy for true volatility and compare the RGARCH-type models with other asymmetric type models such as the EGARCH and GJR models. We conduct empirical studies of six stocks on the Tokyo Stock Exchange and find that a volatility estimation using the RGARCH-type models outperforms the GARCH model and is comparable to other asymmetric GARCH models.
- asymmetric volatility,
- rational GARCH model,
- bayesian inference,
- Markov ChainMonte Carlo,
- Metropolis-Hastings algorithm,
- realized volatility,
- Padé approximants,
- student-tdistribution,
- QLIKE loss function
Citation: Tetsuya Takaishi. Volatility estimation using a rational GARCH model[J]. Quantitative Finance and Economics, 2018, 2(1): 127-136. doi: 10.3934/QFE.2018.1.127

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Abstract

The rational GARCH (RGARCH) model has been proposed as an alternative GARCH model that captures the asymmetric property of volatility. In addition to the previously proposed RGARCH model, we propose an alternative RGARCH model called the RGARCH-Exp model that is more stable when dealing with outliers. We measure the performance of the volatility estimation by a loss function calculated using realized volatility as a proxy for true volatility and compare the RGARCH-type models with other asymmetric type models such as the EGARCH and GJR models. We conduct empirical studies of six stocks on the Tokyo Stock Exchange and find that a volatility estimation using the RGARCH-type models outperforms the GARCH model and is comparable to other asymmetric GARCH models.

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