Volatility estimation and crash risk forecasting using unified GARCH models: Empirical evidence from the Russian invasion of Ukraine

Chikashi Tsuji; Chikashi Tsuji

doi:10.3934/QFE.2026018

Quantitative Finance and Economics

2026, Volume 10, Issue 3: 438-480. doi: 10.3934/QFE.2026018

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Research article

Volatility estimation and crash risk forecasting using unified GARCH models: Empirical evidence from the Russian invasion of Ukraine

Chikashi Tsuji ^,

Graduate School of Economics, Chuo University, Tokyo, Japan

Received: 22 December 2025 Revised: 12 February 2026 Accepted: 01 April 2026 Published: 15 July 2026
JEL Codes: G10, G15, G32

Given the significant impact on economies and financial markets, this study aims to effectively estimate stock return volatilities related to the Russian invasion of Ukraine on February 24, 2022. To achieve this, we developed fully unified generalized autoregressive conditional heteroscedasticity (GARCH) models based on behavioral finance theories that incorporate asymmetry, skewed distribution errors, and structural breaks. Using daily samples from July 2020 to March 2025, which include the impact of the Russian invasion, we first revealed that our fully unified GARCH models are effective in estimating Russian stock market index return volatilities, demonstrating the efficacy of our model unification approach. Additionally, using two other sets of daily 1,000 samples up until one week before or four weeks before the Russian invasion, we found that both one week and four weeks before the invasion, our fully unified GARCH models more effectively predicted the soaring Russian stock market volatilities affected by the Russian invasion. This shows the ability of our fully unified GARCH models to predict crash risk in the Russian stock market, which is one of the most novel pieces of evidence from our work. Furthermore, for the Russian stock index, the volatility estimates from our fully unified GARCH models have shown predictive power for the volatilities of non-fully unified models, while those from non-fully unified models do not predict the volatilities of the fully unified models. This finding also demonstrates the novelty of our work. Moreover, we provided numerous valuable interpretations, implications, and innovative perspectives for future research and practice of quantitative finance and economics. Furthermore, we emphasize that, in addition to extending GARCH models, this paper offers: (i) insight into the link between models, theory, and real-world data; (ii) perspectives on the relationship between information, human psychology, and structural breaks; and (iii) valuable broader implications of the impacts of Russia's invasion of Ukraine. These novel insights are crucial and will inspire future research across multiple disciplines.
- adaptive markets hypothesis,
- artificial intelligence,
- crash risk,
- efficient market hypothesis,
- GARCH,
- skew-GED error,
- skew-t error,
- Russian invasion of Ukraine,
- structural break,
- volatility
Citation: Chikashi Tsuji. Volatility estimation and crash risk forecasting using unified GARCH models: Empirical evidence from the Russian invasion of Ukraine[J]. Quantitative Finance and Economics, 2026, 10(3): 438-480. doi: 10.3934/QFE.2026018

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Abstract

Given the significant impact on economies and financial markets, this study aims to effectively estimate stock return volatilities related to the Russian invasion of Ukraine on February 24, 2022. To achieve this, we developed fully unified generalized autoregressive conditional heteroscedasticity (GARCH) models based on behavioral finance theories that incorporate asymmetry, skewed distribution errors, and structural breaks. Using daily samples from July 2020 to March 2025, which include the impact of the Russian invasion, we first revealed that our fully unified GARCH models are effective in estimating Russian stock market index return volatilities, demonstrating the efficacy of our model unification approach. Additionally, using two other sets of daily 1,000 samples up until one week before or four weeks before the Russian invasion, we found that both one week and four weeks before the invasion, our fully unified GARCH models more effectively predicted the soaring Russian stock market volatilities affected by the Russian invasion. This shows the ability of our fully unified GARCH models to predict crash risk in the Russian stock market, which is one of the most novel pieces of evidence from our work. Furthermore, for the Russian stock index, the volatility estimates from our fully unified GARCH models have shown predictive power for the volatilities of non-fully unified models, while those from non-fully unified models do not predict the volatilities of the fully unified models. This finding also demonstrates the novelty of our work. Moreover, we provided numerous valuable interpretations, implications, and innovative perspectives for future research and practice of quantitative finance and economics. Furthermore, we emphasize that, in addition to extending GARCH models, this paper offers: (i) insight into the link between models, theory, and real-world data; (ii) perspectives on the relationship between information, human psychology, and structural breaks; and (iii) valuable broader implications of the impacts of Russia's invasion of Ukraine. These novel insights are crucial and will inspire future research across multiple disciplines.

References

[1]	Abakah EJA, Gil-Alana LA, Madigu G, Romero-Rojo F (2020) Volatility persistence in cryptocurrency markets under structural breaks. Int Rev Econ Financ 69: 680–691. https://doi.org/10.1016/j.iref.2020.06.035 doi: 10.1016/j.iref.2020.06.035
[2]	Ahmed S, Alshater MM, Ammari AE, Hammami H (2022) Artificial intelligence and machine learning in finance: A bibliometric review. Res Int Bus Financ 61: 101646. https://doi.org/10.1016/j.ribaf.2022.101646 doi: 10.1016/j.ribaf.2022.101646
[3]	Ahmed S, Hasan MM, Kamal MR (2023) Russia–Ukraine crisis: The effects on the European stock market. Eur Financ Manag 29: 1078–1118. https://doi.org/10.1111/eufm.12386 doi: 10.1111/eufm.12386
[4]	Alam MK, Tabash MI, Billah M, Kumar S, Anagreh S (2022) The impacts of the Russia–Ukraine invasion on global markets and commodities: A dynamic connectedness among G7 and BRIC markets. J Risk Financial Manag 15: 352. https://doi.org/10.3390/jrfm15080352 doi: 10.3390/jrfm15080352
[5]	Ardia D, Bluteaua K, Rüede M (2019) Regime changes in Bitcoin GARCH volatility dynamics. Financ Res Lett 29: 266–271. https://doi.org/10.1016/j.frl.2018.08.009 doi: 10.1016/j.frl.2018.08.009
[6]	Assaf R, Gupta D, Kumar R (2023) The price of war: Effect of the Russia–Ukraine war on the global financial market. J Econ Asymmetries 28: e00328. https://doi.org/10.1016/j.jeca.2023.e00328 doi: 10.1016/j.jeca.2023.e00328
[7]	Awartani BMA, Corradi V (2005) Predicting the volatility of the S & P-500 stock index via GARCH models: The role of asymmetries. Int J Forecasting 21: 167–183. https://doi.org/10.1016/j.ijforecast.2004.08.003 doi: 10.1016/j.ijforecast.2004.08.003
[8]	Aziz G, Sarwar S (2023) Revisit the role of governance indicators to achieve sustainable economic growth of Saudi Arabia – pre and post implementation of 2030 Vision. Struct Change Econ Dyn 66: 213–227. https://doi.org/10.1016/j.strueco.2023.04.008 doi: 10.1016/j.strueco.2023.04.008
[9]	Aziz G, Waheed R, Sarwar S, Khan MS (2023) The significance of governance indicators to achieve carbon neutrality: A new insight of life expectancy. Sustainability 15: 766. https://doi.org/10.3390/su15010766 doi: 10.3390/su15010766
[10]	Bekaert G, Wu G (2000) Asymmetric volatility and risk in equity markets. Rev Financ Stud 13: 1–42. https://doi.org/10.1093/rfs/13.1.1 doi: 10.1093/rfs/13.1.1
[11]	Benartzi S, Thaler RH (1995) Myopic loss aversion and the equity premium puzzle. Q J Econ 110: 73–92. https://doi.org/10.2307/2118511 doi: 10.2307/2118511
[12]	Beraich M, Amzile K, Laamire J, Zirari O, Fadali MA (2022) Volatility spillover effects of the US, European and Chinese financial markets in the context of the Russia–Ukraine conflict. Int J Financ Stud 10: 95. https://doi.org/10.3390/ijfs10040095 doi: 10.3390/ijfs10040095
[13]	Berkelaar AB, Kouwenberg R, Post T (2004) Optimal portfolio choice under loss aversion. Rev Econ Stat 86: 973–987. https://doi.org/10.1162/0034653043125167 doi: 10.1162/0034653043125167
[14]	Black F (1976) Studies of stock price volatility changes. Proceeding of the American Statistical Association, Business and Economic Statistics Section 177–181.
[15]	Blavatskyy PR (2011) Loss aversion. Econ Theory 46: 127–148. http://dx.doi.org/10.2139/ssrn.1151722 doi: 10.2139/ssrn.1151722
[16]	Bollerslev T (1986) Generalized autoregressive conditional heteroskedasticity. J Econometrics 31: 307–327. https://doi.org/10.1016/0304-4076(86)90063-1 doi: 10.1016/0304-4076(86)90063-1
[17]	Boubaker S, Goodell JW, Pandey DK, Kumari V (2022) Heterogeneous impacts of wars on global equity markets: Evidence from the invasion of Ukraine. Financ Res Lett 48: 102934. https://doi.org/10.1016/j.frl.2022.102934 doi: 10.1016/j.frl.2022.102934
[18]	Boungou W, Yatié A (2022) The impact of the Ukraine–Russia war on world stock market returns. Econ Lett 215: 110516. https://doi.org/10.1016/j.econlet.2022.110516 doi: 10.1016/j.econlet.2022.110516
[19]	Cable News Network (2022) Here's what we know about how Russia's invasion of Ukraine unfolded. February 24, 2022. https://edition.cnn.com/2022/02/24/europe/ukraine-russia-attack-timeline-intl (accessed on 18 November 2025)
[20]	Campbell JY, Hentschel L (1992) No news is good news: An asymmetric model of changing volatility in stock returns. J Financ Econ 31: 281–318. https://doi.org/10.1016/0304-405X(92)90037-X doi: 10.1016/0304-405X(92)90037-X
[21]	Chaklader B, Gupta BB, Panigrahi PK (2023) Analyzing the progress of FINTECH-companies and their integration with new technologies for innovation and entrepreneurship. J Bus Res 161: 113847. https://doi.org/10.1016/j.jbusres.2023.113847 doi: 10.1016/j.jbusres.2023.113847
[22]	Chowdhury MAF, Hassan MK, Abdullah M, Hossain MM (2025) Geopolitical risk transmission dynamics to commodity, stock, and energy markets. Quant Finance Econ 9: 76–99. https://doi.org/10.3934/QFE.2025003 doi: 10.3934/QFE.2025003
[23]	Christie AA (1982) The stochastic behavior of common stock variances: Value, leverage and interest rate effects. J Financ Econ 10: 407–432. https://doi.org/10.1016/0304-405X(82)90018-6 doi: 10.1016/0304-405X(82)90018-6
[24]	Das BC, Hasan F, Sutradhar SR, Shafique S (2023) Ukraine–Russia conflict and stock markets reactions in Europe. Glob J Flex Syst Manag 24: 395–407. https://doi.org/10.1007/s40171-023-00345-0 doi: 10.1007/s40171-023-00345-0
[25]	Dirican C (2015) The impacts of robotics, artificial intelligence on business and economics. Procedia - Soc Behav Sci 195: 564–573. https://doi.org/10.1016/j.sbspro.2015.06.134 doi: 10.1016/j.sbspro.2015.06.134
[26]	Engle RF, Ng VK (1993) Measuring and testing the impact of news on volatility. J Financ 48: 1749–1778. https://doi.org/10.1111/j.1540-6261.1993.tb05127.x doi: 10.1111/j.1540-6261.1993.tb05127.x
[27]	Fama EF (1970) Efficient capital markets: A review of theory and empirical work. J Financ 25: 383–417. https://doi.org/10.2307/2325486 doi: 10.2307/2325486
[28]	Federle J, Meier A, Müller GJ, Sehn V (2026) Proximity to war: The stock market response to the Russian invasion of Ukraine. J Money Credit Bank forthcoming. https://doi.org/10.1111/jmcb.13226
[29]	Fethi MD, Pasiouras F (2010) Assessing bank efficiency and performance with operational research and artificial intelligence techniques: A survey. Eur J Oper Res 204: 189–198. https://doi.org/10.1016/j.ejor.2009.08.003 doi: 10.1016/j.ejor.2009.08.003
[30]	Financial Times (2022) IMF cuts global growth forecast to 3.6% as Ukraine war hits neighbours hard. https://www.ft.com/content/0a006298-6c41-461d-98db-34e6d291dc87 (accessed on 18 November 2025).
[31]	French KR, Schwert GW, Stambaugh RF (1987) Expected stock returns and volatility. J Financ Econ 19: 3–29. https://doi.org/10.1016/0304-405X(87)90026-2 doi: 10.1016/0304-405X(87)90026-2
[32]	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. https://doi.org/10.1111/j.1540-6261.1993.tb05128.x doi: 10.1111/j.1540-6261.1993.tb05128.x
[33]	Hansen BE (1994) Autoregressive conditional density estimation. Int Econ Rev 35: 705–730. https://doi.org/10.2307/2527081 doi: 10.2307/2527081
[34]	Hasan F, Al‑Okaily M, Choudhury T, Kayani U (2024) A comparative analysis between FinTech and traditional stock markets: Using Russia and Ukraine war data. Electron Commer Res 24: 629–654. https://doi.org/10.1007/s10660-023-09734-0 doi: 10.1007/s10660-023-09734-0
[35]	Höhler J, Harmens I, Lansink AO (2026) The impact of the Russia–Ukraine war on stock prices, profits and perceptions in the food supply chain. Agribusiness forthcoming. https://doi.org/10.1002/agr.21964
[36]	Inclán C, Tiao GC (1994) Use of cumulative sums of squares for retrospective detection of changes of variance. J Am Stat Assoc 89: 913–923. https://doi.org/10.1080/01621459.1994.10476824 doi: 10.1080/01621459.1994.10476824
[37]	Izzeldin M, Muradoğlu YG, Pappas V, Petropoulou A, Sivaprasad S (2023) The impact of the Russian–Ukrainian war on global financial markets. Int Rev Financ Anal 87: 102598. https://doi.org/10.1016/j.irfa.2023.102598 doi: 10.1016/j.irfa.2023.102598
[38]	Kahneman D, Knetsch JL, Thaler RH (1986) Fairness as a constraint on profit seeking: Entitlements in the market. Am Econ Rev 76: 728–741. https://www.jstor.org/stable/1806070
[39]	Kahneman D, Knetsch JL, Thaler RH (1991) Anomalies: The endowment effect, loss aversion, and status quo bias. J Econ Perspect 5: 193–206. https://doi.org/10.1257/jep.5.1.193 doi: 10.1257/jep.5.1.193
[40]	Kakhkharov J, Onur I, Yalcin E, Zhu R (2024) Global evidence on the Russia–Ukraine conflict and energy stock returns. Int Rev Econ Financ 93: 413–435. https://doi.org/10.1016/j.iref.2024.03.063 doi: 10.1016/j.iref.2024.03.063
[41]	Kumari V, Kumar G, Pandey DK (2023) Are the European Union stock markets vulnerable to the Russia–Ukraine war? J Behav Exp Financ 37: 100793. https://doi.org/10.1016/j.jbef.2023.100793 doi: 10.1016/j.jbef.2023.100793
[42]	Lo AW (2004) The adaptive markets hypothesis: Market efficiency from an evolutionary perspective. J Portfolio Manage 30: 15–29. https://doi.org/10.3905/jpm.2004.442611 doi: 10.3905/jpm.2004.442611
[43]	Lo AW (2012) Adaptive markets and the new world order. Financ Anal J 68: 18–29. http://dx.doi.org/10.2139/ssrn.1977721 doi: 10.2139/ssrn.1977721
[44]	Luan Y, Ye S, Li Y, Jia L, Yue XG (2022) Revisiting natural resources volatility via TGARCH and EGARCH. Resour Policy 78: 102896. https://doi.org/10.1016/j.resourpol.2022.102896 doi: 10.1016/j.resourpol.2022.102896
[45]	Malik F (2022) Volatility spillover among sector equity returns under structural breaks. Rev Quant Financ Account 58: 1063–1080. https://doi.org/10.1007/s11156-021-01018-8 doi: 10.1007/s11156-021-01018-8
[46]	Manelli A, Pace R, Leone M (2024) Russia–Ukraine conflict, commodities and stock market: A quantile VAR analysis. J Risk Financial Manag 17: 29. https://doi.org/10.3390/jrfm17010029 doi: 10.3390/jrfm17010029
[47]	Mensi W, Al-Yahyaee KH, Kang SH (2019) Structural breaks and double long memory of cryptocurrency prices: A comparative analysis from Bitcoin and Ethereum. Financ Res Lett 29: 222–230. https://doi.org/10.1016/j.frl.2018.07.011 doi: 10.1016/j.frl.2018.07.011
[48]	Nelson DB (1991) Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59: 347–370. https://doi.org/10.2307/2938260 doi: 10.2307/2938260
[49]	Nerlinger M, Utz S (2022) The impact of the Russia–Ukraine conflict on energy firms: A capital market perspective. Financ Res Lett 50: 103243. https://doi.org/10.1016/j.frl.2022.103243 doi: 10.1016/j.frl.2022.103243
[50]	Newey WK, West KD (1987) A simple, positive semi-definite, hetoroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55: 703–708. https://doi.org/10.2307/1913610 doi: 10.2307/1913610
[51]	Pestova A, Mamonov M, Ongena S (2022) The price of war: Macroeconomic effects of the 2022 sanctions on Russia. Centre for Economic Policy Research 71–78. https://cepr.org/voxeu/columns/price-war-macroeconomic-effects-2022-sanctions-russia (accessed on 18 November 2025).
[52]	Ross GJ (2013) Modelling financial volatility in the presence of abrupt changes. Physica A 392: 350–360. https://doi.org/10.1016/j.physa.2012.08.015 doi: 10.1016/j.physa.2012.08.015
[53]	Ross SA (1989) Information and volatility: The no-arbitrage martingale approach to timing and resolution irrelevancy. J Financ 44: 1–17. https://doi.org/10.2307/2328272 doi: 10.2307/2328272
[54]	Silva TC, Wilhelm PVB, Tabak BM (2023) Trade matters except to war neighbors: The international stock market reaction to 2022 Russia's invasion of Ukraine. Res Int Bus Financ 65: 101935. https://doi.org/10.1016/j.ribaf.2023.101935 doi: 10.1016/j.ribaf.2023.101935
[55]	Theodossiou P (2015) Skewed generalized error distribution of financial assets and option pricing. Multinatl Financ J 19: 223–266. hhttp://dx.doi.org/10.2139/ssrn.219679 doi: 10.2139/ssrn.219679
[56]	Tsuji C (2016) Does the fear gauge predict downside risk more accurately than econometric models? Evidence from the US stock market. Cogent Econ Financ 4: 1220711. https://doi.org/10.1080/23322039.2016.1220711 doi: 10.1080/23322039.2016.1220711
[57]	Tsuji C (2018) Return transmission and asymmetric volatility spillovers between oil futures and oil equities: New DCC-MEGARCH analyses. Econ Model 74: 167–185. https://doi.org/10.1016/j.econmod.2018.05.007 doi: 10.1016/j.econmod.2018.05.007
[58]	Tsuji C (2020) Correlation and spillover effects between the US and international banking sectors: New evidence and implications for risk management. Int Rev Financ Anal 70: 101392. https://doi.org/10.1016/j.irfa.2019.101392 doi: 10.1016/j.irfa.2019.101392
[59]	Tsuji C (2024) The historical transition of return transmission, volatility spillovers, and dynamic conditional correlations: A fresh perspective and new evidence from the US, UK, and Japanese stock markets. Quant Finance Econ 8: 410–436. https://doi.org/10.3934/QFE.2024016 doi: 10.3934/QFE.2024016
[60]	Tversky A, Kahneman D (1991) Loss aversion in riskless choice: A reference-dependent model. Q J Econ 106: 1039–1061. https://doi.org/10.2307/2937956 doi: 10.2307/2937956
[61]	Umar Z, Polat O, Choi SY, Teplova T (2022) The impact of the Russia–Ukraine conflict on the connectedness of financial markets. Financ Res Lett 48: 102976. https://doi.org/10.1016/j.frl.2022.102976 doi: 10.1016/j.frl.2022.102976
[62]	Wang P, Moore T (2009) Sudden changes in volatility: The case of five central European stock markets. J Int Financ Mark Inst & Money 19: 33–46. https://doi.org/10.1016/j.intfin.2007.08.006 doi: 10.1016/j.intfin.2007.08.006
[63]	Whaley RE (2000) The investor fear gauge. J Portfolio Manage 26: 12–17. https://doi.org/10.3905/jpm.2000.319728 doi: 10.3905/jpm.2000.319728
[64]	Whaley RE (2009) Understanding the VIX. J Portfolio Manage 35: 98–105. https://doi.org/10.3905/JPM.2009.35.3.098 doi: 10.3905/JPM.2009.35.3.098
[65]	World Bank (2022) Developing economies must act now to dampen the shocks from the Ukraine conflict. Worldbank.org. https://blogs.worldbank.org/en/voices/developing-economies-must-act-now-dampen-shocks-ukraine-conflict (accessed on 18 November 2025).
[66]	Wu G (2001) The determinants of asymmetric volatility. Rev Financ Stud 14: 837–859. https://doi.org/10.1093/rfs/14.3.837 doi: 10.1093/rfs/14.3.837
[67]	Yousaf I, Patel R, Yarovaya L (2022) The reaction of G20+ stock markets to the Russia–Ukraine conflict "black-swan" event: Evidence from event study approach. J Behav Exp Financ 35: 100723. https://doi.org/10.1016/j.jbef.2022.100723 doi: 10.1016/j.jbef.2022.100723
[68]	Zakoian JM (1994) Threshold heteroskedastic models. J Econ Dyn Control 18: 931–995. https://doi.org/10.1016/0165-1889(94)90039-6 doi: 10.1016/0165-1889(94)90039-6

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