Research article Special Issues

Volatility estimation using a rational GARCH model

  • 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.

    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

    Related Papers:

  • 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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    [1] Alderweireld T, Nuyts J (2004) Detailed empirical study of the term structure of interest rates. Emergence of power laws and scaling laws. Physica A 331: 602–616.
    [2] Andersen TG, Bollerslev T (1998) Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. Int Econ Rev 39: 885–905. doi: 10.2307/2527343
    [3] Aasi M (2006) Comparison of MCMC methods for estimating GARCH models. J Japan Stat Society 36: 199–212. doi: 10.14490/jjss.36.199
    [4] Barndorff-Nielsen OE, Shephard N (2001) Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics. J Roy Stat Soc B 63: 167–241. doi: 10.1111/1467-9868.00282
    [5] Bollerslev T (1986) Generalized Autoregressive Conditional Heteroskedasticity. J Econometrics 31: 307–327. doi: 10.1016/0304-4076(86)90063-1
    [6] Chen TT, Takaishi T (2013) Empirical study of the GARCH model with rational errors. JPCS 454: 9714–9722.
    [7] Clark MA (2006) The rational hybrid Monte Carlo algorithm. POS 75: 453–456.
    [8] Clark MA, Kennedy AD (2006) Accelerating dynamical-fermion computations using the Rational Hybrid Monte Carlo algorithm with multiple pseudofermion fields. Phys Rev lett 98: 051601.
    [9] Engle RF (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50: 987–1007. doi: 10.2307/1912773
    [10] Glosten LR, Jagannathan R, Runkle DE (1993) On the relation between the expected value and the volatility of the nominal excess return on stocks. J Financ 48: 1779–1801. doi: 10.1111/j.1540-6261.1993.tb05128.x
    [11] Hansen PR, Lunde A (2005) A forecast comparison of volatility models: does anything beat a GARCH(1, 1)? J appl Econom 20: 873–889. doi: 10.1002/jae.800
    [12] Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57: 97–109. doi: 10.1093/biomet/57.1.97
    [13] Metropolis N, Rosenbluth AW, Rosenbluth MN, et al. (1953) Equation of state calculations by fast computing machines. J Chem phys 21: 1087–1092. doi: 10.1063/1.1699114
    [14] Mitsui H,Watanabe T (2003) Bayesian analysis of GARCH option pricing models. J Japan Statist Soc (Japanese Issue) 33: 307–324.
    [15] Nelson DB (1991) Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59: 347–370. doi: 10.2307/2938260
    [16] Nuyts J, Platten I (2001) Phenomenology of the term structure of interest rates with Padé Approximants. Physica A 299: 528–546. doi: 10.1016/S0378-4371(01)00320-X
    [17] Patton AJ (2011) Volatility forecast comparison using imperfect volatility proxies. J Econom 160: 246–256. doi: 10.1016/j.jeconom.2010.03.034
    [18] Sentana E (1995) Quadratic ARCH models. Rev Econ Stud 62: 639–661. doi: 10.2307/2298081
    [19] Spiegelhalter DJ, Best NG, Carlin BP, et al. (2002) Bayesian measures of model complexity and fit. J Roy Stat Soc B 64: 583–639. doi: 10.1111/1467-9868.00353
    [20] de Forcrand P, Takaishi T (1997) Fast fermion Monte Carlo. Nucl Phys B - Proc Sup 53: 968–970. doi: 10.1016/S0920-5632(96)00829-8
    [21] Takaishi T, de Forcrand P (2001a) Odd-flavor simulations by Hybrid Monte Carlo. Non-Perturbative Methods and Lattice QCD, World Scientific 112–120.
    [22] Takaishi T, de Forcrand P (2001b) Simulation of nf= 3 QCD by Hybrid Monte Carlo. Nucl Phys B-Proc Sup 94: 818–822.
    [23] Takaishi T, de Forcrand P (2001c) Simulations of Odd Flavors QCD by Hybrid Monte Carlo. Int Symposium Quantum Chromodynamics Color Confinement, CONFINEMENT 2000, World Scientific 383–387.
    [24] Takaishi T, de Forcrand P (2002) Odd-flavor Hybrid Monte Carlo Algorithm for Lattice QCD. Int J Mod Phys C 13: 343–365. doi: 10.1142/S0129183102003152
    [25] Takaishi T (2009a) An Adaptive Markov Chain Monte Carlo Method for GARCH Model. Lecture Notes Inst Computer Sciences, Social Inform Telecommun Engineering. Complex Sciences 5: 1424–1434.
    [26] Takaishi T (2009b) Bayesian Estimation of GARCH Model with an Adaptive Proposal Density. New Advances Intell Decis Technol, Stud Comput Intell 199: 635–643.
    [27] Takaishi T (2009c) Bayesian Inference on QGARCH Model Using the Adaptive Construction Scheme. Proc 8th IEEE/ACIS Int Conf Computer Inf Science 525–529.
    [28] Takaishi T (2010) Bayesian inference with an adaptive proposal density for GARCH models. JPCS 221: 012011.
    [29] Takaishi T (2017) Rational GARCH model: An empirical test for stock returns. Physica A 473: 451–460. doi: 10.1016/j.physa.2017.01.011
    [30] Takaishi T, Chen TT (2012) Bayesian Inference of the GARCH model with Rational Errors. Int Proc Econ Dev Res 29: 303–307.

    © 2018 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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