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題名 加密貨幣風險管理： Lévy過程與時變波動率的應用
Cryptocurrency Risk Management Using Lévy Processes and Time-Varying Volatility
作者 吳海棠
Wu, Hai-Tang
貢獻者 岳夢蘭
Yueh, Meng-Lan
吳海棠
Wu, Hai-Tang
關鍵詞 加密貨幣
最大概似估計
風險值
平均風險值
Cryptocurrency
Quasi maximum likelihood estimation
Value-at-risk
Average value-at-risk
日期 2024
上傳時間 1-Jul-2024 12:38:36 (UTC+8)
摘要 加密貨幣已經成為金融領域的一股革命性力量，通過其去中心化的架構和區塊鏈技術重塑了傳統金融。儘管引起了廣泛的關注，但由於其固有的波動性和缺乏內在價值資訊，加密貨幣在風險管理和估值方面面臨著獨特的挑戰。本文提出了一種新穎的方法，採用Lévy-GJR-GARCH模型來分析三種主要加密貨幣——比特幣、以太幣和瑞波幣的風險。 通過資料分析，我們觀察到加密貨幣報酬的不同特徵，包括波動率聚類、偏態和超額峰度，偏離了正態分佈的假設。利用Lévy-GJR-GARCH模型，將Lévy過程與GJR-GARCH模型結合起來，我們能夠準確捕捉這些實證現象。我們的研究結果強調了將非正態分佈特徵（如無限跳躍過程）納入模型中以有效地建模加密貨幣回報和波動性的重要性。 此外，通過採用兩步擬最大概似估計方法，我們證明了無限跳躍模型在評估尾部風險和極端損失方面優於標準和有限跳躍模型。對我們的模型預測前一天的風險值（VaR）和平均風險價值（AVaR）的回溯測試結果表明，在市場波動較大的情況下，具有無限跳躍的模型提供了更為保守的風險估計。 本研究通過為投資者、機構和監管機構提供強大的工具，推動了加密貨幣市場風險管理策略的進展。通過準確捕捉加密貨幣回報的動態，並結合創新的分佈框架，我們的研究增強了對市場行為的理解，並促進了更為明智的決策，在應對加密貨幣投資的複雜性時提供了更多資訊。
Cryptocurrencies have emerged as a transformative force in the financial landscape, reshaping traditional finance with their decentralized architecture and blockchain technology. Despite garnering significant attention, they present unique challenges in risk modeling and valuation due to their inherent volatility and lack of intrinsic value information. This paper proposes a novel approach by employing the Lévy-GJR-GARCH model to analyze the risk of three major cryptocurrencies—Bitcoin, Ethereum, and Ripple. Through extensive data analysis, we observe distinct features in cryptocurrency returns, including volatility clustering, skewness, and excess kurtosis, deviating from the assumptions of normal distributions. Leveraging the Lévy-GJR-GARCH model, which integrates flexible Lévy processes with GJR-GARCH for time-varying volatility, we accurately capture these empirical phenomena. Our findings underscore the importance of incorporating non-normal distributional characteristics, such as infinite jump processes, to effectively model cryptocurrency returns and volatility. Furthermore, employing a two-step quasi-maximum likelihood estimation method, we demonstrate the superiority of infinite jump models over standard and finite activity models in assessing tail risks and extreme losses. Backtesting our models for one-day-ahead forecasts of Value-at-Risk (VaR) and Average Value-at-Risk (AVaR) reveals that models with infinite jumps provide more conservative risk estimates, particularly during volatile market conditions. This research contributes to advancing risk management strategies in cryptocurrency markets by providing robust tools for investors, institutions, and regulators. By accurately capturing the dynamics of cryptocurrency returns and incorporating innovative distributional frameworks, our study enhances understanding of market behaviors and facilitates more informed decision-making in navigating the complexities of cryptocurrency investments.
參考文獻 Alexander, C., & Sheedy, E. (2008). Developing a stress testing framework based on market risk models. Journal of Banking & Finance, 32(10), 2220-2236. Alexander, C., Choi, J., Park, H., & Sohn, S. (2020). BitMEX bitcoin derivatives: Price discovery, informational efficiency, and hedging effectiveness. Journal of Futures Markets, 40(1), 23-43. Alexander, C., Deng, J., Feng, J., & Wan, H. (2022). Net buying pressure and the information in bitcoin option trades. Journal of Financial Markets, 100764. Bariviera, A. F. (2021). One model is not enough: Heterogeneity in cryptocurrencies’ multifractal profiles. Finance Research Letters, 39, 101649. Barndorff-Nielsen, O. E. (1997). Processes of normal inverse Gaussian type. Finance and stochastics, 2(1), 41-68. Berkowitz, J. (2001). Testing density forecasts, with applications to risk management. Journal of Business & Economic Statistics, 19(4), 465-474. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307-327. Borri, N. (2019). Conditional tail-risk in cryptocurrency markets. Journal of Empirical Finance, 50, 1-19. Borri, N., & Shakhnov, K. (2022). The cross-section of cryptocurrency returns. The Review of Asset Pricing Studies, 12(3), 667-705. Christoffersen, P. F. (1998). Evaluating interval forecasts. International Economic Review, 841-862. Chu, J., Chan, S., Nadarajah, S., & Osterrieder, J. (2017). GARCH modelling of cryptocurrencies. Journal of Risk and Financial Management, 10(4), 17. Engle, R. F., & Ng, V. K. (1993). Measuring and testing the impact of news on volatility. The Journal of Finance, 48(5), 1749-1778. Entrop, O., Frijns, B., & Seruset, M. (2020). The determinants of price discovery on bitcoin markets. Journal of Futures Markets, 40(5), 816-837. Gkillas, K., & Katsiampa, P. (2018). An application of extreme value theory to cryptocurrencies. Economics Letters, 164, 109-111. Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The Journal of Finance, 48(5), 1779-1801. Hafner, C. M. (2020). Testing for bubbles in cryptocurrencies with time-varying volatility. Journal of Financial Econometrics, 18(2), 233-249. Hansen, P. R., Kim, C., & Kimbrough, W. (2021). Periodicity in Cryptocurrency Volatility and Liquidity. arXiv preprint arXiv:2109.12142. Hoang, L. T., & Baur, D. G. (2020). Forecasting bitcoin volatility: Evidence from the options market. Journal of Futures Markets, 40(10), 1584-1602. Hou, A. J., Wang, W., Chen, C. Y., & Härdle, W. K. (2020). Pricing cryptocurrency options. Journal of Financial Econometrics, 18(2), 250-279. Huang, J. Z., Ni, J., & Xu, L. (2022). Leverage effect in cryptocurrency markets. Pacific-Basin Finance Journal, 73, 101773. Kim, Y. S., Rachev, S. T., Bianchi, M. L., Mitov, I., & Fabozzi, F. J. (2011). Time series analysis for financial market meltdowns. Journal of Banking & Finance, 35(8), 1879-1891. Klein, T., Thu, H. P., & Walther, T. (2018). Bitcoin is not the New Gold–A comparison of volatility, correlation, and portfolio performance. International Review of Financial Analysis, 59, 105-116. Kou, S. G. (2002). A jump-diffusion model for option pricing. Management Science, 48(8), 1086-1101. Li, H., Wells, M. T., & Yu, C. L. (2008). A Bayesian analysis of return dynamics with Lévy jumps. The Review of Financial Studies, 21(5), 2345-2378. Li, Z., Reppen, A. M., & Sircar, R. (2024). A mean field games model for cryptocurrency mining. Management Science, 70(4), 2188-2208. Liu, Y., & Tsyvinski, A. (2021). Risks and returns of cryptocurrency. The Review of Financial Studies, 34(6), 2689-2727. Liu, Y., Tsyvinski, A., & Wu, X. (2022). Common risk factors in cryptocurrency. The Journal of Finance, 77(2), 1133-1177. Madan, D. B., & Seneta, E. (1990). The variance gamma (VG) model for share market returns. Journal of Business, 511-524. Madan, D. B., Carr, P. P., & Chang, E. C. (1998). The variance gamma process and option pricing. Review of Finance, 2(1), 79-105. Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3(1-2), 125-144. Osterrieder, J., & Lorenz, J. (2017). A statistical risk assessment of Bitcoin and its extreme tail behavior. Annals of Financial Economics, 12(01), 1750003. Phillip, A., Chan, J. S., & Peiris, S. (2018). A new look at cryptocurrencies. Economics Letters, 163, 6-9. Rachev, S. T., Kim, Y. S., Bianchi, M. L., & Fabozzi, F. J. (2011). Financial models with Lévy processes and volatility clustering. John Wiley & Sons. Rosiński, J. (2007). Tempering stable processes. Stochastic processes and their applications, 117(6), 677-707. Scaillet,O., Treccani, A., & Trevisan, C. (2020). High-frequency jump analysis of the bitcoin market. Journal of Financial Econometrics, 18(2), 209-232. Vidal-Tomás, D. (2021). An investigation of cryptocurrency data: The market that never sleeps. Quantitative Finance, 21(12), 2007-2024. Zhang, W., Wang, P., Li, X., & Shen, D. (2018). Some stylized facts of the cryptocurrency market. Applied Economics, 50(55), 5950-5965.
描述 博士
國立政治大學
財務管理學系
108357502
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0108357502
資料類型 thesis
dc.contributor.advisor 岳夢蘭zh_TW
dc.contributor.advisor Yueh, Meng-Lanen_US
dc.contributor.author (Authors) 吳海棠zh_TW
dc.contributor.author (Authors) Wu, Hai-Tangen_US
dc.creator (作者) 吳海棠zh_TW
dc.creator (作者) Wu, Hai-Tangen_US
dc.date (日期) 2024en_US
dc.date.accessioned 1-Jul-2024 12:38:36 (UTC+8)-
dc.date.available 1-Jul-2024 12:38:36 (UTC+8)-
dc.date.issued (上傳時間) 1-Jul-2024 12:38:36 (UTC+8)-
dc.identifier (Other Identifiers) G0108357502en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/152061-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 財務管理學系zh_TW
dc.description (描述) 108357502zh_TW
dc.description.abstract (摘要) 加密貨幣已經成為金融領域的一股革命性力量，通過其去中心化的架構和區塊鏈技術重塑了傳統金融。儘管引起了廣泛的關注，但由於其固有的波動性和缺乏內在價值資訊，加密貨幣在風險管理和估值方面面臨著獨特的挑戰。本文提出了一種新穎的方法，採用Lévy-GJR-GARCH模型來分析三種主要加密貨幣——比特幣、以太幣和瑞波幣的風險。 通過資料分析，我們觀察到加密貨幣報酬的不同特徵，包括波動率聚類、偏態和超額峰度，偏離了正態分佈的假設。利用Lévy-GJR-GARCH模型，將Lévy過程與GJR-GARCH模型結合起來，我們能夠準確捕捉這些實證現象。我們的研究結果強調了將非正態分佈特徵（如無限跳躍過程）納入模型中以有效地建模加密貨幣回報和波動性的重要性。 此外，通過採用兩步擬最大概似估計方法，我們證明了無限跳躍模型在評估尾部風險和極端損失方面優於標準和有限跳躍模型。對我們的模型預測前一天的風險值（VaR）和平均風險價值（AVaR）的回溯測試結果表明，在市場波動較大的情況下，具有無限跳躍的模型提供了更為保守的風險估計。 本研究通過為投資者、機構和監管機構提供強大的工具，推動了加密貨幣市場風險管理策略的進展。通過準確捕捉加密貨幣回報的動態，並結合創新的分佈框架，我們的研究增強了對市場行為的理解，並促進了更為明智的決策，在應對加密貨幣投資的複雜性時提供了更多資訊。zh_TW
dc.description.abstract (摘要) Cryptocurrencies have emerged as a transformative force in the financial landscape, reshaping traditional finance with their decentralized architecture and blockchain technology. Despite garnering significant attention, they present unique challenges in risk modeling and valuation due to their inherent volatility and lack of intrinsic value information. This paper proposes a novel approach by employing the Lévy-GJR-GARCH model to analyze the risk of three major cryptocurrencies—Bitcoin, Ethereum, and Ripple. Through extensive data analysis, we observe distinct features in cryptocurrency returns, including volatility clustering, skewness, and excess kurtosis, deviating from the assumptions of normal distributions. Leveraging the Lévy-GJR-GARCH model, which integrates flexible Lévy processes with GJR-GARCH for time-varying volatility, we accurately capture these empirical phenomena. Our findings underscore the importance of incorporating non-normal distributional characteristics, such as infinite jump processes, to effectively model cryptocurrency returns and volatility. Furthermore, employing a two-step quasi-maximum likelihood estimation method, we demonstrate the superiority of infinite jump models over standard and finite activity models in assessing tail risks and extreme losses. Backtesting our models for one-day-ahead forecasts of Value-at-Risk (VaR) and Average Value-at-Risk (AVaR) reveals that models with infinite jumps provide more conservative risk estimates, particularly during volatile market conditions. This research contributes to advancing risk management strategies in cryptocurrency markets by providing robust tools for investors, institutions, and regulators. By accurately capturing the dynamics of cryptocurrency returns and incorporating innovative distributional frameworks, our study enhances understanding of market behaviors and facilitates more informed decision-making in navigating the complexities of cryptocurrency investments.en_US
dc.description.tableofcontents 1. Introduction 7 2. Methodology 12 2.1 VaR and AVaR 13 2.2 GJR-GARCH Model 15 2.3 Lévy-Khinchine formula 16 2.4 Return innovation with Lévy distributions 17 2.5 Parameter Estimation with Quasi Maximum Likelihood Estimation 20 2.6 Backtesting measurements 22 2.6.1 Christoffersen likelihood ratio test 23 2.6.2 Berkowitz likelihood ratio test 24 3. Empirical results 25 3.1 Data and Preliminary Analysis 25 3.2 Parameter estimation 27 3.2.1 Estimated parameters in GJR-GARCH 28 3.2.2 Innovation 30 3.2.3 Fitting performance 32 4. VaR performance 35 5. Conclusion 39 References 41zh_TW
dc.format.extent 3476139 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0108357502en_US
dc.subject (關鍵詞) 加密貨幣zh_TW
dc.subject (關鍵詞) 最大概似估計zh_TW
dc.subject (關鍵詞) 風險值zh_TW
dc.subject (關鍵詞) 平均風險值zh_TW
dc.subject (關鍵詞) Cryptocurrencyen_US
dc.subject (關鍵詞) Quasi maximum likelihood estimationen_US
dc.subject (關鍵詞) Value-at-risken_US
dc.subject (關鍵詞) Average value-at-risken_US
dc.title (題名) 加密貨幣風險管理： Lévy過程與時變波動率的應用zh_TW
dc.title (題名) Cryptocurrency Risk Management Using Lévy Processes and Time-Varying Volatilityen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Alexander, C., & Sheedy, E. (2008). Developing a stress testing framework based on market risk models. Journal of Banking & Finance, 32(10), 2220-2236. Alexander, C., Choi, J., Park, H., & Sohn, S. (2020). BitMEX bitcoin derivatives: Price discovery, informational efficiency, and hedging effectiveness. Journal of Futures Markets, 40(1), 23-43. Alexander, C., Deng, J., Feng, J., & Wan, H. (2022). Net buying pressure and the information in bitcoin option trades. Journal of Financial Markets, 100764. Bariviera, A. F. (2021). One model is not enough: Heterogeneity in cryptocurrencies’ multifractal profiles. Finance Research Letters, 39, 101649. Barndorff-Nielsen, O. E. (1997). Processes of normal inverse Gaussian type. Finance and stochastics, 2(1), 41-68. Berkowitz, J. (2001). Testing density forecasts, with applications to risk management. Journal of Business & Economic Statistics, 19(4), 465-474. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307-327. Borri, N. (2019). Conditional tail-risk in cryptocurrency markets. Journal of Empirical Finance, 50, 1-19. Borri, N., & Shakhnov, K. (2022). The cross-section of cryptocurrency returns. The Review of Asset Pricing Studies, 12(3), 667-705. Christoffersen, P. F. (1998). Evaluating interval forecasts. International Economic Review, 841-862. Chu, J., Chan, S., Nadarajah, S., & Osterrieder, J. (2017). GARCH modelling of cryptocurrencies. Journal of Risk and Financial Management, 10(4), 17. Engle, R. F., & Ng, V. K. (1993). Measuring and testing the impact of news on volatility. The Journal of Finance, 48(5), 1749-1778. Entrop, O., Frijns, B., & Seruset, M. (2020). The determinants of price discovery on bitcoin markets. Journal of Futures Markets, 40(5), 816-837. Gkillas, K., & Katsiampa, P. (2018). An application of extreme value theory to cryptocurrencies. Economics Letters, 164, 109-111. Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The Journal of Finance, 48(5), 1779-1801. Hafner, C. M. (2020). Testing for bubbles in cryptocurrencies with time-varying volatility. Journal of Financial Econometrics, 18(2), 233-249. Hansen, P. R., Kim, C., & Kimbrough, W. (2021). Periodicity in Cryptocurrency Volatility and Liquidity. arXiv preprint arXiv:2109.12142. Hoang, L. T., & Baur, D. G. (2020). Forecasting bitcoin volatility: Evidence from the options market. Journal of Futures Markets, 40(10), 1584-1602. Hou, A. J., Wang, W., Chen, C. Y., & Härdle, W. K. (2020). Pricing cryptocurrency options. Journal of Financial Econometrics, 18(2), 250-279. Huang, J. Z., Ni, J., & Xu, L. (2022). Leverage effect in cryptocurrency markets. Pacific-Basin Finance Journal, 73, 101773. Kim, Y. S., Rachev, S. T., Bianchi, M. L., Mitov, I., & Fabozzi, F. J. (2011). Time series analysis for financial market meltdowns. Journal of Banking & Finance, 35(8), 1879-1891. Klein, T., Thu, H. P., & Walther, T. (2018). Bitcoin is not the New Gold–A comparison of volatility, correlation, and portfolio performance. International Review of Financial Analysis, 59, 105-116. Kou, S. G. (2002). A jump-diffusion model for option pricing. Management Science, 48(8), 1086-1101. Li, H., Wells, M. T., & Yu, C. L. (2008). A Bayesian analysis of return dynamics with Lévy jumps. The Review of Financial Studies, 21(5), 2345-2378. Li, Z., Reppen, A. M., & Sircar, R. (2024). A mean field games model for cryptocurrency mining. Management Science, 70(4), 2188-2208. Liu, Y., & Tsyvinski, A. (2021). Risks and returns of cryptocurrency. The Review of Financial Studies, 34(6), 2689-2727. Liu, Y., Tsyvinski, A., & Wu, X. (2022). Common risk factors in cryptocurrency. The Journal of Finance, 77(2), 1133-1177. Madan, D. B., & Seneta, E. (1990). The variance gamma (VG) model for share market returns. Journal of Business, 511-524. Madan, D. B., Carr, P. P., & Chang, E. C. (1998). The variance gamma process and option pricing. Review of Finance, 2(1), 79-105. Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3(1-2), 125-144. Osterrieder, J., & Lorenz, J. (2017). A statistical risk assessment of Bitcoin and its extreme tail behavior. Annals of Financial Economics, 12(01), 1750003. Phillip, A., Chan, J. S., & Peiris, S. (2018). A new look at cryptocurrencies. Economics Letters, 163, 6-9. Rachev, S. T., Kim, Y. S., Bianchi, M. L., & Fabozzi, F. J. (2011). Financial models with Lévy processes and volatility clustering. John Wiley & Sons. Rosiński, J. (2007). Tempering stable processes. Stochastic processes and their applications, 117(6), 677-707. Scaillet,O., Treccani, A., & Trevisan, C. (2020). High-frequency jump analysis of the bitcoin market. Journal of Financial Econometrics, 18(2), 209-232. Vidal-Tomás, D. (2021). An investigation of cryptocurrency data: The market that never sleeps. Quantitative Finance, 21(12), 2007-2024. Zhang, W., Wang, P., Li, X., & Shen, D. (2018). Some stylized facts of the cryptocurrency market. Applied Economics, 50(55), 5950-5965.zh_TW