Realized matrix exponential stochastic volatility model: application to market, size, and value factor realized covariance. (Japanese. English summary) Zbl 07660124
Summary: A matrix exponential multivariate asymmetric stochastic volatility model with realized covariance matrix measurement is proposed. A Bayesian inference method using Markov chain Monte Carlo is developed. A new high-frequency quasi risk factors: market, size, and value factors are calculated using the Tokyo stock market index (TOPIX) size-based sub-indices and style indices. Daily factor series and their realized covariance are calculated and used in our analysis. Proposed three risk factors account for the variation of individual stock returns, and have time-varying volatilities and correlations, and volatility asymmetry. Proposed several models are fit to the proposed risk factors, and the model comparison based on the volatility prediction is conducted. For the latent volatility prediction, the results are consistent with preceding studies about univariate realized stochastic volatility models. The asymmetric covariance structure of the three factors can be shown by the news impact curves.
MSC:
| 62-XX | Statistics |
Software:
OxReferences:
| [1] | Aït-Sahalia, Y. and Jacod, J. (2014). High-frequency Financial Econometrics, Princeton University Press. · Zbl 1298.91018 |
| [2] | Andersen, T. G. and Bollerslev, T. (1998). Answering the skeptics: Yes, standard volatility models do provide accurate forecasts, International Economic Review, 885-905. |
| [3] | Andersen, T. G., Davis, R. A., Kreiß, J. P. and Mikosch, T. V. (2009). Handbook of Financial Time Series, Springer. · Zbl 1162.91004 |
| [4] | Archakov, I. and Hansen, P. R. (2021). A new parametrization of correlation matrices, Econometrica, in press. · Zbl 1497.62193 |
| [5] | 浅井学 (2019). 「カルマン・フィルターによる Realized Stochastic Volatility モデルの疑似最尤推定について」『日本統計学会誌』48(2)，215-238． |
| [6] | Asai, M. and McAleer, M. (2009). Multivariate stochastic volatility, leverage and news impact surfaces, The Econometrics Journal, 12(2), 292-309. · Zbl 1231.91483 |
| [7] | Asai, M. and So, M. K. P. (2015). Long memory and asymmetry for matrix-exponential dynamic correlation processes, Journal of Time Series Econometrics, 7(1), 69-94. · Zbl 1499.62296 |
| [8] | Asai, M., McAleer, M. and Yu, J. (2006). Multivariate stochastic volatility: a review, Econometric Reviews, 25(2-3), 145-175. · Zbl 1107.62108 |
| [9] | Asai, M., Chang, C. L. and McAleer, M. J. (2016). Realized Matrix-Exponential Stochastic Volatility with Asymmetry, Long Memory and Spillovers, Econometric Institute Research Papers, EI2016-41. · Zbl 07491160 |
| [10] | Asai, M., Chang, C. L. and McAleer, M. (2017). Realized stochastic volatility with general asymmetry and long memory, Journal of Econometrics, 199(2), 202-212. · Zbl 1388.62245 |
| [11] | Barndorff-Nielsen, O. E. and Shephard, N. (2002). Econometric analysis of realized volatility and its use in estimating stochastic volatility models, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64(2), 253-280. · Zbl 1059.62107 |
| [12] | Barndorff-Nielsen, O. E. and Shephard, N. (2004). Econometric analysis of realized covariation: High frequency based covariance, regression, and correlation in financial economics, Econometrica, 72(3), 885-925. · Zbl 1141.91634 |
| [13] | Barndorff-Nielsen, O. E., Hansen, P. R., Lunde, A. and Shephard, N. (2011). Subsampling realised kernels, Journal of Econometrics, 160(1), 204-219. · Zbl 1441.62598 |
| [14] | Bauwens, L. and Xu, Y. (2019). DCC-HEAVY: A multivariate GARCH model based on realized variances and correlations, Université catholique de Louvain. |
| [15] | Bauwens, L., Hafner, C. M. and Laurent, S. (2012). Handbook of Volatility Models and Their Applications, John Wiley & Sons. · Zbl 1325.62003 |
| [16] | Carhart, M. M. (1997). On persistence in mutual fund performance, The Journal of Finance, 52(1), 57-82. |
| [17] | Chan, J., Koop, G., Poirier, D. J. and Tobias, J. L. (2019). Bayesian Econometric Methods, 2nd edition, Cambridge University Press. |
| [18] | Chaussé, P. and Xu, D. (2018). GMM estimation of a realized stochastic volatility model: A Monte Carlo study, Econometric Reviews, 37(7), 719-743. · Zbl 1490.62313 |
| [19] | Chib, S. (2001). Markov chain Monte Carlo methods: computation and inference, in Handbook of Econometrics, 5, 3569-3649, Elsevier. |
| [20] | Connor, G., Hagmann, M., and Linton, O. (2012). Efficient semiparametric estimation of the Fama-French model and extensions, Econometrica, 80(2), 713-754. · Zbl 1274.91485 |
| [21] | Diebold, F. X. (1988). Empirical Modeling of Exchange Rate Dynamics, Springer. · Zbl 0648.90002 |
| [22] | Diebold, F. X. and Strasser, G. (2013). On the correlation structure of microstructure noise: A financial economic approach, Review of Economic Studies, 80(4), 1304-1337. · Zbl 1405.91703 |
| [23] | Dobrev, D. and Szerszen, P. (2010). The information content of high-frequency data for estimating equity return models and forecasting risk, FRB Working Paper. |
| [24] | Doornik, J. A. (2013). Ox 7: An Object-orientated Matrix Programming Language, London: Timberlake Consultants Press. |
| [25] | Engle, R. F. and Gallo, G. M. (2006). A multiple indicators model for volatility using intra-daily data, Journal of Econometrics, 131(1-2), 3-27. · Zbl 1337.62359 |
| [26] | Engle, R. F. and Kroner, K. F. (1995). Multivariate simultaneous generalized ARCH, Econometric theory, 11(1), 122-150. |
| [27] | Engle, R. F. and Ng, V. K. (1993). Measuring and testing the impact of news on volatility, The Journal of Finance, 48(5), 1749-1778. |
| [28] | Engle, R. F. and Sheppard, K. (2001). Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH. |
| [29] | Fama, E. F. and French, K. R. (1993). Common risk factors in the returns on stocks and bonds, Journal of Financial Economics, 33(1), 3-56. · Zbl 1131.91335 |
| [30] | Fama, E. F. and French, K. R. (2015). A five-factor asset pricing model, Journal of Financial Economics, 116(1), 1-22. |
| [31] | Figueroa-López, J. E. and Mancini, C. (2019). Optimum thresholding using mean and conditional mean squared error, Journal of Econometrics, 208(1), 179-210. · Zbl 1452.62762 |
| [32] | Gorgi, P., Hansen, P. R., Janus, P. and Koopman, S.J. (2019). Realized Wishart-GARCH: A score-driven multi-asset volatility model, Journal of Financial Econometrics, 17(1), 1-32. |
| [33] | Greenberg, E. (2012). Introduction to Bayesian Econometrics, Cambridge University Press. · Zbl 1151.62102 |
| [34] | Han, Y. (2006). Asset allocation with a high dimensional latent factor stochastic volatility model, The Review of Financial Studies, 19, 237-271. |
| [35] | Hansen, P. R. and Lunde, A. (2005). A forecast comparison of volatility models: does anything beat a GARCH (1, 1)? Journal of Applied Econometrics, 20(7), 873-889. |
| [36] | Hansen, P. R., Huang, Z. O. and Shek, H. H. (2012). Realized GARCH: a joint model for returns and realized measures of volatility, Journal of Applied Econometrics, 27(6), 877-906. |
| [37] | Hansen, P. R., Lunde, A. and Voev, V. (2014). Realized beta GARCH: A multivariate GARCH model with realized measures of volatility, Journal of Applied Econometrics, 29(5), 774-799. |
| [38] | Ishihara, T. and Omori, Y. (2017). Portfolio optimization using dynamic factor and stochastic volatility: evidence on Fat-tailed errors and leverage, The Japanese Economic Review, 68, 63-94. |
| [39] | Ishihara, T., Omori, Y. and Asai, M. (2016). Matrix exponential stochastic volatility with cross leverage, Computational Statistics & Data Analysis, 100, 331-350. · Zbl 1466.62109 |
| [40] | Jarque, C. M. and Bera, A. K. (1987). Regression Residuals, International Statistical Review/Revue Internationale de Statistique, 55(2), 163-172. · Zbl 0616.62092 |
| [41] | Kawakatsu, H. (2006). Matrix exponential GARCH, Journal of Econometrics, 134(1), 95-128. · Zbl 1418.62484 |
| [42] | 小池祐太 (2017). 「実現ボラティリティとその周辺」『経営と制度』15，15-42． |
| [43] | Koopman, S. J. and Scharth, M. (2012). The analysis of stochastic volatility in the presence of daily realized measures, Journal of Financial Econometrics, 11(1), 76-115. |
| [44] | 古澄英男 (2015). 『ベイズ計算統計学』朝倉書店． |
| [45] | 久保田敬一, 竹原均 (2007). 「Fama-French ファクターモデルの有効性の再検証」『現代ファイナンス』22，3-23． |
| [46] | Kurose, Y. and Omori, Y. (2020). Multiple-block dynamic equicorrelations with realized measures, leverage and endogeneity, Econometrics and Statistics, 13, 46-68. |
| [47] | Ljung, G. M. and Box, G. E. P. (1978). On a measure of lack of fit in time series models, Biometrika, 65(2), 297-303. · Zbl 0386.62079 |
| [48] | Mancini, C. and Gobbi, F. (2012). Identifying the Brownian covariation from the co-jumps given discrete observations, Econometric Theory, 28(2), 249-273. · Zbl 1298.91167 |
| [49] | 中妻照雄 (2019). 『Pythonによるベイズ統計学入門』朝倉書店． |
| [50] | Noureldin, D., Shephard, N. and Sheppard, K. (2012). Multivariate high-frequency-based volatility (HEAVY) models, Journal of Applied Econometrics, 27(6), 907-933. |
| [51] | Omori, Y. and Watanabe, T. (2008). Block sampler and posterior mode estimation for asymmetric stochastic volatility models, Computational Statistics & Data Analysis, 52(6), 2892-2910. · Zbl 1452.62783 |
| [52] | 大森裕浩 (2001). 「マルコフ連鎖モンテカルロ法の最近の展開」『日本統計学会誌』31(3)，305-344． |
| [53] | 大森裕浩, 渡部敏明 (2013). 「Realized Stochastic Volatility モデル: マルコフ連鎖モンテカルロ法を用いたベイズ分析」『日本統計学会誌』42(2)，273-303． |
| [54] | Patton, A. J. (2011). Volatility forecast comparison using imperfect volatility proxies, Journal of Econometrics, 160(1), 246-256. · Zbl 1441.62830 |
| [55] | Patton, A. J. and Sheppard, K. (2009). Evaluating volatility and correlation forecasts, in Handbook of Financial Time Series, 801-838, Springer. · Zbl 1178.91229 |
| [56] | Raghuram, G (2017). Stationarity of the Fama-French Three Factor model factor premiums in India, Pertanika Journal of Social Sciences & Humanities, 25(3), 1097-1120. |
| [57] | Rosenberg, B. (1974). Extra-market components of covariance in security returns, Journal of Financial and Quantitative Analysis, 9(2), 263-274. |
| [58] | Ross, S. (1976). The arbitrage theory of capital asset pricing, Journal of Economic Theory, 13(3), 341-360. |
| [59] | Shephard, N. and Sheppard, K. (2010). Realising the future: forecasting with high-frequency-based volatility (HEAVY) models, Journal of Applied Econometrics, 25(2), 197-231. |
| [60] | Shirota, S., Omori, Y., Lopes, H. F. and Piao, H. (2017). Cholesky realized stochastic volatility model, Econometrics and Statistics, 3, 34-59. |
| [61] | Takahashi, M., Omori, Y. and Watanabe, T. (2009). Estimating stochastic volatility models using daily returns and realized volatility simultaneously, Computational Statistics & Data Analysis, 53(6), 2404-2426. · Zbl 1453.62212 |
| [62] | 高橋慎, 大森裕浩, 渡部敏明 (2020). 「Realized Stochastic Volatility モデル: 拡張と日本の株価指数への応用」『統計数理』68(1)，65-85． |
| [63] | 渡部敏明 (2000). 『ボラティリティ変動モデル』朝倉書店． |
| [64] | Yamauchi, Y. and Omori, Y. (2019). Multivariate stochastic volatility model with realized volatilities and pairwise realized correlations, Journal of Business & Economic Statistics, 1-17. |
| [65] | Yamauchi, Y. and Omori, Y. (2020). Dynamic factor, leverage and realized covariances in multivariate stochastic volatility, CIRJE Discussion Papers, CIRJE-F-1158. |
| [66] | Yu, J. (2005). On leverage in a stochastic volatility model, Journal of Econometrics, 127(2), 165-178. · Zbl 1335.91116 |
| [67] | Zhang, L., Mykland, P. A. and Aït-Sahalia, Y. (2005). A tale of two time scales: Determining integrated volatility with noisy high-frequency data, Journal of the American Statistical Association, 100(472), 1394-1411. · Zbl 1117.62461 |
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