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題名 好跳躍與壞跳躍風險之議題
Good Jump and Bad Jump Risk Matters作者 匡顯吉
Kuang, Xian-Ji貢獻者 林士貴<br>張興華
Lin, Shih-Kuei<br>Chang, Hsing-Hua
匡顯吉
Kuang, Xian-Ji關鍵詞 變異數風險溢酬
好跳躍與壞跳躍
選擇權評價
橫斷面迴歸
時間序列分析
Variance risk premium
Good jump and bad jump
Option pricing
Cross-sectional regression
Time series analysis日期 2023 上傳時間 1-Dec-2023 13:48:52 (UTC+8) 摘要 在資產定價領域中，理解資產預期報酬與波動性關係是重要議題。在本文中，我們擴展基於 affine GARCH 框架非對稱雙指數跳躍-擴散模型，在 affine GARCH 設定下提出創新模型，該模型使用兩個指數分佈來描述好與壞的跳躍。此外，我們為此模型配置推導出選擇權定價之封閉形式解。我們研究發現，將跳躍成分納入變異數過程可以提高模型估計性能，其中壞跳躍成分貢獻遠大於其好的對應部分。在我們實證分析中，通過模型估計，我們推斷出由這些好與壞跳躍產生之變異數風險溢價。通過橫斷面迴歸，我們確定了這兩種變異數風險溢價都作為已定價風險因子。時間序列分析進一步確認，壞跳躍方差風險溢價在預測報酬方面佔主導地位。
The understanding of the relationship between an asset’s expected return and its volatility is pivotal in asset pricing. In this paper, we extend the asymmetric double exponential jump-diffusion model grounded in the affine generalized autoregressive conditional heteroskedastic (GARCH) framework. We propose a model within the affine GARCH setting that uses two exponential distributions to separately model good and bad jumps. Furthermore, we deduce a closed-form solution for option pricing within this model structure. Our results suggest that the integration of jump components into the variance process significantly bolsters model estimation performance—the bad jump component markedly outstrips its good counterpart in contribution. In our empirical evaluation, we discern the variance risk premiums attributable to these good and bad jumps through model estimation. A cross-sectional regression reveals that both variance risk premiums serve as priced risk factors. Moreover, a time-series examination underscores the prevailing role of the bad jump variance risk premium in forecasting returns.參考文獻 Bakshi, G., Cao, C., and Chen, Z. (1997). Empirical performance of alternative option pricing models. The Journal of Finance, 52, 2003-2049. Bates, D. S. (1991). The crash of ’87: was it expected? The evidence from options markets. The Journal of Finance, 46(3), 1009-1044. Bates, D. S. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options. Review of Financial Studies, 9, 69-107. Bégin, J. F., Dorion, C., and Gauthier, G. (2020). Idiosyncratic jump risk matters: Evidence from equity returns and options. The Review of Financial Studies, 33, 155-211. Bekaert, G., Engstrom, E., and Ermolov, A. (2015). Bad environments, good environments: A non-Gaussian asymmetric volatility model. Journal of Econometrics, 186(1), 258-275. Black, F., Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Po- litical Economy, 81, 637-654. Bollerslev, T., Tauchen, G., and Zhou, H. (2009). Expected stock returns and variance risk premia. Review of Financial Studies, 22, 4463-4492. Brennan, M. (1979). The pricing of contingent claims in discrete time models. The Journal of Finance, 34, 53-68. Carr, P., and L. Wu. (2007). Stochastic skew in currency options. Journal of Financial Economics, 86, 213-247. Chang, H. L., Chang, Y. C., Cheng, H. W., Peng, P. H., and Tseng, K. (2019). Jump variance risk: Evidence from option valuation and stock returns. Journal of Futures Markets, 39, 890-915. Christoffersen, P., Heston, S., and Jacobs, K. (2013). Capturing option anomalies with a variance dependent pricing kernel. The Review of Financial Studies, 26, 1963-2006. Christoffersen, P., Jacobs, K., and Ornthanalai, C. (2012). Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options. Journal of Financial Economics, 106, 447–472. Chernov, M., and Ghysels, E. (2000). A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation. Journal of Financial Economics, 56, 407-458. Duan, J. C. (1995). The GARCH option pricing model. Mathematical Finance, 5, 13-32. Duffie, D., Pan, J., and Singleton, K. (2000). Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 68, 1343-1376. Durham, G., J. Geweke, and P. Ghosh. (2015). A comment on Christoffersen, Jacobs, and Ornthanalai (2012),“Dynamic jump intensities and risk premiums: Evidence from S&P 500 returns and options”. Journal of Financial Economics, 115, 210–214. Eraker, B. (2004). Do stock prices and volatility jump? Reconciling evidence from spot and option prices. Journal of Finance, 59, 1367-1404. Eraker, B., Johannes, M.S., and Polson, N. (2003). The impact of jumps in volatility and returns. Journal of Finance, 58, 1269-1300. Feunou, B., Jahan-Parvar, M. R., and Tédongap, R. (2013). Modeling market downside volatility. Review of Finance, 17(1), 443-481. Giglio, S., and Xiu, D. (2021). Asset pricing with omitted factors. Journal of Political Economy, 129(7), 1947-1990. Harvey, C. R., and Siddique, A. (2000). Conditional skewness in asset pricing tests. The Journal of Finance, 55(3), 1263-1295. Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 6, 327-343. Heston, S. L., and Nandi, S. (2000). A closed-form GARCH option valuation model. Review of Financial Studies, 13, 585–625. Hull, J., and White, A. (1987). The pricing of options on assets with stochastic volatilities. Journal of Finance, 42, 281-300. Kilic, M., and Shaliastovich, I. (2019). Good and bad variance premia and expected returns. Management Science, 65, 2522-2544. Kou, S. G. (2002). A jump diffusion model for option pricing. Management Science, 48, 1086–1101. Kou, S. G., and Wang, H. (2004). Option pricing under a double exponential jump diffusion model. Management Science, 50, 1178–1192. Kou, S., Yu, C., and Zhong, H. (2017). Jumps in equity index returns before and during the recent financial crisis: A Bayesian analysis. Management Science, 63, 988-1010. Li, J., and Zinna, G. (2018). The variance risk premium: Components, term structures, and stock return predictability. Journal of Business and Economic Statistics, 36(3), 411-425. Malik, S., and Pitt, M. K. (2011). Particle filters for continuous likelihood evaluation and maximisation. Journal of Econometrics, 165, 190-209. Merton, Robert C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3, 125-144. Newey, W. K., and McFadden, D. (1994). Chapter 36 large sample estimation and hypothesis testing. In Handbook of Econometrics, 2111-2245. Elsevier. Newey, W. K., and West, K. D. (1994). Automatic lag selection in covariance matrix estimation. The Review of Economic Studies, 61(4), 631-653. Ornthanalai, C. (2014). Lévy jump risk: Evidence from options and returns. Journal of Financial Economics, 112, 69-90. Rubinstein, M. (1976). The valuation of uncertain income streams and the pricing of options. The Bell Journal of Economics, 7, 407–425. Trolle, A., and E. Schwartz. (2009). Unspanned stochastic volatility and the pricing of com- modity derivatives. Review of Financial Studies, 22, 4423–4461. Yang, X. (2018). Good jump, bad jump, and option valuation. Journal of Futures Markets, 38, 1097-1125. 描述 博士
國立政治大學
金融學系
108352502資料來源 http://thesis.lib.nccu.edu.tw/record/#G0108352502 資料類型 thesis dc.contributor.advisor 林士貴<br>張興華 zh_TW dc.contributor.advisor Lin, Shih-Kuei<br>Chang, Hsing-Hua en_US dc.contributor.author (Authors) 匡顯吉 zh_TW dc.contributor.author (Authors) Kuang, Xian-Ji en_US dc.creator (作者) 匡顯吉 zh_TW dc.creator (作者) Kuang, Xian-Ji en_US dc.date (日期) 2023 en_US dc.date.accessioned 1-Dec-2023 13:48:52 (UTC+8) - dc.date.available 1-Dec-2023 13:48:52 (UTC+8) - dc.date.issued (上傳時間) 1-Dec-2023 13:48:52 (UTC+8) - dc.identifier (Other Identifiers) G0108352502 en_US dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/148533 - dc.description (描述) 博士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 金融學系 zh_TW dc.description (描述) 108352502 zh_TW dc.description.abstract (摘要) 在資產定價領域中，理解資產預期報酬與波動性關係是重要議題。在本文中，我們擴展基於 affine GARCH 框架非對稱雙指數跳躍-擴散模型，在 affine GARCH 設定下提出創新模型，該模型使用兩個指數分佈來描述好與壞的跳躍。此外，我們為此模型配置推導出選擇權定價之封閉形式解。我們研究發現，將跳躍成分納入變異數過程可以提高模型估計性能，其中壞跳躍成分貢獻遠大於其好的對應部分。在我們實證分析中，通過模型估計，我們推斷出由這些好與壞跳躍產生之變異數風險溢價。通過橫斷面迴歸，我們確定了這兩種變異數風險溢價都作為已定價風險因子。時間序列分析進一步確認，壞跳躍方差風險溢價在預測報酬方面佔主導地位。 zh_TW dc.description.abstract (摘要) The understanding of the relationship between an asset’s expected return and its volatility is pivotal in asset pricing. In this paper, we extend the asymmetric double exponential jump-diffusion model grounded in the affine generalized autoregressive conditional heteroskedastic (GARCH) framework. We propose a model within the affine GARCH setting that uses two exponential distributions to separately model good and bad jumps. Furthermore, we deduce a closed-form solution for option pricing within this model structure. Our results suggest that the integration of jump components into the variance process significantly bolsters model estimation performance—the bad jump component markedly outstrips its good counterpart in contribution. In our empirical evaluation, we discern the variance risk premiums attributable to these good and bad jumps through model estimation. A cross-sectional regression reveals that both variance risk premiums serve as priced risk factors. Moreover, a time-series examination underscores the prevailing role of the bad jump variance risk premium in forecasting returns. en_US dc.description.tableofcontents 1 Introduction 1 2 Literature Review 8 2.1 Jump risks on asset pricing 8 2.2 Background of option valuation 10 3 GARCH model with good and bad jump dynamics 14 3.1 The asset return process and variance dynamic process 14 3.2 Conditional higher moments of return process 16 3.3 The pricing kernel 16 3.4 The risk-neutral measure and option valuation 18 3.5 Good and bad jump variance risk premium 21 4 Data and model estimation 23 4.1 Data 23 4.2 Model estimation 23 4.2.1 Joint MLE 23 4.2.2 Particle filter algorithm 26 4.2.3 Model performance 26 5 Empirical results 34 6 Conclusion 38 Bibliography 39 Appendices 43 zh_TW dc.format.extent 1534212 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0108352502 en_US dc.subject (關鍵詞) 變異數風險溢酬 zh_TW dc.subject (關鍵詞) 好跳躍與壞跳躍 zh_TW dc.subject (關鍵詞) 選擇權評價 zh_TW dc.subject (關鍵詞) 橫斷面迴歸 zh_TW dc.subject (關鍵詞) 時間序列分析 zh_TW dc.subject (關鍵詞) Variance risk premium en_US dc.subject (關鍵詞) Good jump and bad jump en_US dc.subject (關鍵詞) Option pricing en_US dc.subject (關鍵詞) Cross-sectional regression en_US dc.subject (關鍵詞) Time series analysis en_US dc.title (題名) 好跳躍與壞跳躍風險之議題 zh_TW dc.title (題名) Good Jump and Bad Jump Risk Matters en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Bakshi, G., Cao, C., and Chen, Z. (1997). Empirical performance of alternative option pricing models. The Journal of Finance, 52, 2003-2049. Bates, D. S. (1991). The crash of ’87: was it expected? The evidence from options markets. The Journal of Finance, 46(3), 1009-1044. Bates, D. S. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche Mark options. Review of Financial Studies, 9, 69-107. Bégin, J. F., Dorion, C., and Gauthier, G. (2020). Idiosyncratic jump risk matters: Evidence from equity returns and options. The Review of Financial Studies, 33, 155-211. Bekaert, G., Engstrom, E., and Ermolov, A. (2015). Bad environments, good environments: A non-Gaussian asymmetric volatility model. Journal of Econometrics, 186(1), 258-275. Black, F., Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Po- litical Economy, 81, 637-654. Bollerslev, T., Tauchen, G., and Zhou, H. (2009). Expected stock returns and variance risk premia. Review of Financial Studies, 22, 4463-4492. Brennan, M. (1979). The pricing of contingent claims in discrete time models. The Journal of Finance, 34, 53-68. Carr, P., and L. Wu. (2007). Stochastic skew in currency options. Journal of Financial Economics, 86, 213-247. Chang, H. L., Chang, Y. C., Cheng, H. W., Peng, P. H., and Tseng, K. (2019). Jump variance risk: Evidence from option valuation and stock returns. Journal of Futures Markets, 39, 890-915. Christoffersen, P., Heston, S., and Jacobs, K. (2013). Capturing option anomalies with a variance dependent pricing kernel. The Review of Financial Studies, 26, 1963-2006. Christoffersen, P., Jacobs, K., and Ornthanalai, C. (2012). Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options. Journal of Financial Economics, 106, 447–472. Chernov, M., and Ghysels, E. (2000). A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation. Journal of Financial Economics, 56, 407-458. Duan, J. C. (1995). The GARCH option pricing model. Mathematical Finance, 5, 13-32. Duffie, D., Pan, J., and Singleton, K. (2000). Transform analysis and asset pricing for affine jump-diffusions. Econometrica, 68, 1343-1376. Durham, G., J. Geweke, and P. Ghosh. (2015). A comment on Christoffersen, Jacobs, and Ornthanalai (2012),“Dynamic jump intensities and risk premiums: Evidence from S&P 500 returns and options”. Journal of Financial Economics, 115, 210–214. Eraker, B. (2004). Do stock prices and volatility jump? Reconciling evidence from spot and option prices. Journal of Finance, 59, 1367-1404. Eraker, B., Johannes, M.S., and Polson, N. (2003). The impact of jumps in volatility and returns. Journal of Finance, 58, 1269-1300. Feunou, B., Jahan-Parvar, M. R., and Tédongap, R. (2013). Modeling market downside volatility. Review of Finance, 17(1), 443-481. Giglio, S., and Xiu, D. (2021). Asset pricing with omitted factors. Journal of Political Economy, 129(7), 1947-1990. Harvey, C. R., and Siddique, A. (2000). Conditional skewness in asset pricing tests. The Journal of Finance, 55(3), 1263-1295. Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 6, 327-343. Heston, S. L., and Nandi, S. (2000). A closed-form GARCH option valuation model. Review of Financial Studies, 13, 585–625. Hull, J., and White, A. (1987). The pricing of options on assets with stochastic volatilities. Journal of Finance, 42, 281-300. Kilic, M., and Shaliastovich, I. (2019). Good and bad variance premia and expected returns. Management Science, 65, 2522-2544. Kou, S. G. (2002). A jump diffusion model for option pricing. Management Science, 48, 1086–1101. Kou, S. G., and Wang, H. (2004). Option pricing under a double exponential jump diffusion model. Management Science, 50, 1178–1192. Kou, S., Yu, C., and Zhong, H. (2017). Jumps in equity index returns before and during the recent financial crisis: A Bayesian analysis. Management Science, 63, 988-1010. Li, J., and Zinna, G. (2018). The variance risk premium: Components, term structures, and stock return predictability. Journal of Business and Economic Statistics, 36(3), 411-425. Malik, S., and Pitt, M. K. (2011). Particle filters for continuous likelihood evaluation and maximisation. Journal of Econometrics, 165, 190-209. Merton, Robert C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3, 125-144. Newey, W. K., and McFadden, D. (1994). Chapter 36 large sample estimation and hypothesis testing. In Handbook of Econometrics, 2111-2245. Elsevier. Newey, W. K., and West, K. D. (1994). Automatic lag selection in covariance matrix estimation. The Review of Economic Studies, 61(4), 631-653. Ornthanalai, C. (2014). Lévy jump risk: Evidence from options and returns. Journal of Financial Economics, 112, 69-90. Rubinstein, M. (1976). The valuation of uncertain income streams and the pricing of options. The Bell Journal of Economics, 7, 407–425. Trolle, A., and E. Schwartz. (2009). Unspanned stochastic volatility and the pricing of com- modity derivatives. Review of Financial Studies, 22, 4423–4461. Yang, X. (2018). Good jump, bad jump, and option valuation. Journal of Futures Markets, 38, 1097-1125. zh_TW
