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題名 狀態相依跳躍風險與美式選擇權評價：黃金期貨市場之實證研究
State-dependent jump risks and American option pricing: an empirical study of the gold futures market
作者 連育民
Lian, Yu Min
貢獻者 廖四郎
Liao, Szu Lang
連育民
Lian, Yu Min
關鍵詞 美式黃金期貨選擇權
狀態轉換跳躍擴散過程
Merton測度
Esscher轉換
最小平方蒙地卡羅法
American gold futures option
Regime-switching jump-diffusion process
Merton measure
Esscher transform
Least-squares Monte Carlo method
日期 2013
上傳時間 4-Jun-2014 14:41:45 (UTC+8)
摘要 本文實證探討黃金期貨報酬率的特性並在標的黃金期貨價格遵循狀態轉換跳躍擴散過程時實現美式選擇權之評價。在這樣的動態過程下，跳躍事件被一個複合普瓦松過程與對數常態跳躍振幅所描述，以及狀態轉換到達強度是由一個其狀態代表經濟狀態的隱藏馬可夫鏈所捕捉。考量不同的跳躍風險假設，我們使用Merton測度與Esscher轉換推導出在一個不完全市場設定下的風險中立黃金期貨價格動態過程。為了達到所需的精確度，最小平方蒙地卡羅法被用來近似美式黃金期貨選擇權的價值。基於實際市場資料，我們提供實證與數值結果來說明這個動態模型的優點。
This dissertation empirically investigates the characteristics of gold futures returns and achieves the valuation of American-style options when the underlying gold futures price follows a regime-switching jump-diffusion process. Under such dynamics, the jump events are described as a compound Poisson process with a log-normal jump amplitude, and the regime-switching arrival intensity is captured by a hidden Markov chain whose states represent the economic states. Considering the different jump risk assumptions, we use the Merton measure and Esscher transform to derive risk-neutral gold futures price dynamics under an incomplete market setting. To achieve a desired accuracy level, the least-squares Monte Carlo method is used to approximate the values of American gold futures options. Our empirical and numerical results based on actual market data are provided to illustrate the advantages of this dynamic model.
參考文獻 Amin, K. I., 1993. Jump diffusion option valuation in discrete time. The Journal of Finance 48, 1833–1863.
Ball, C. A., Torous, W. N., 1983. A simplified jump process for common stock returns. Journal of Financial and Quantitative Analysis 18, 53–65.
Ball, C. A., Torous, W. N., Tschoegl, A. E., 1985. An empirical investigation of the EOE gold options market. Journal of Banking and Finance 9, 101–113.
Baur, D. G., Lucey, B. M., 2010. Is gold a hedge or a safe haven? An analysis of stocks, bonds and gold. Financial Review 45, 217–229.
Baur, D. G., McDermott, T. K., 2010. Is gold a safe haven? International evidence. Journal of Banking and Finance 34, 1886–1898.
Beckers, S., 1981. A note on estimating the parameters of the diffusion jump model of stock returns. Journal of Financial and Quantitative Analysis 16, 127–140.
Beckers, S., 1984. On the efficiency of the gold options market. Journal of Banking and Finance 8, 459–470.
Boyle, P., Broadie, M., Glasserman, P., 1997. Monte Carlo methods for security pricing. Journal of Economic Dynamics and Control 21, 1267–1321.
Brennan, M., Schwartz, E., 1977. The valuation of American put options. Journal of Finance 32, 449–462.
Capie, F., Mills, T. C., Wood, G., 2005. Gold as a hedge against the dollar. Journal of International Financial Markets, Institutions and Money 15, 343–352.
Carr, P., Geman, H., Madan, D., Yor, M., 2002. The fine structure of asset returns: an empirical investigation. Journal of Business 75, 305–332.
Chan, W. H., Maheu, J. M., 2002. Conditional jump dynamics in stock market returns. Journal of Business & Economic Statistics 20, 377–389.
Chang, C., Fuh, C. D., Lin, S. K., 2013. A tale of two regimes: theory and empirical evidence for a Markov-modulated jump diffusion model of equity returns and derivative pricing implications. Journal of Banking and Finance 37, 3204–3217.
Cox, J. C., Ross, S. A., Rubinstein, M., 1979. Option pricing: a simplified approach. Journal of Financial Economics 7, 229–263.
Duan, J. C., Ritchken, P., Sun, Z., 2006. Approximating GARCH-jump models, jump-diffusion processes, and option pricing. Mathematical Finance 16, 21–52.
Elliott, R. J., Chan, L., Siu, T. K., 2005. Option pricing and Esscher transform under regime switching. Annals of Finance 1, 423–432.
Elliott, R. J., Osakwe, C.-J. U., 2006. Option pricing for pure jump processes with Markov switching compensators. Finance and Stochastics 10, 250–275.
Elliott, R. J., Siu, T. K., Chan, L., Lau, J. W., 2007. Pricing options under a generalized Markov-modulated jump-diffusion model. Stochastic Analysis and Applications 25, 821–843.
Elliott, R. J., Siu, T. K., 2011. A risk-based approach for pricing American options under a generalized Markov regime-switching model. Quantitative Finance 11, 1633–1646.
Eraker, B., Johannes, M., Polson, N., 2003. The impact of jumps in volatility and returns. Journal of Finance 58, 1269–1300.
Eraker, B., 2004. Do stock market and volatility jump? Reconciling evidence from spot and option prices. Journal of Finance 59, 1367–1404.
Gerber, H. U., Shiu, E. S. W., 1994. Option pricing by Esscher transforms (with discussions). Transactions of Society of Actuaries 46, 99–191.
Gerber, H. U., Shiu, E. S. W., 1996. Actuarial bridges to dynamic hedging and option pricing. Insurance: Mathematics and Economics 18, 183–218.
Hull, J., White, A., 1990. Valuing derivative securities using the explicit finite difference method. Journal of Financial and Quantitative Analysis 25, 87–100.
Khalaf, L., Saphores, J.-D., Bilodeau, J.-F., 2003. Simulation-based exact jump tests in models with conditional heteroskedasticity. Journal of Economic Dynamics and Control 28, 531–553.
Kou, S. G., 2002. A jump-diffusion model for option pricing. Management Science 48, 1086–1101.
Lange, K., 1995a. A gradient algorithm locally equivalent to the EM algorithm. Journal of the Royal Statistical Society 57, 425–437.
Lange, K., 1995b. A quasi-Newton acceleration of the EM algorithm. Statistica Sinica 5, 1–18.
Last, G., Brandt, A., 1995. Marked point processes on the real line: the dynamic approach. Springer-Verlag, New York.
Longstaff, F. A., Schwartz, E. S., 2001. Valuing American options by simulation: a simple least-squares approach. Review of Financial Studies 14, 113–147.
Maheu, J. M., McCurdy, T. H., 2004. News arrival, jump dynamics and volatility components for individual stock returns. Journal of Finance 59, 755–793.
McCown, J. R., Zimmerman, J. R., 2006. Is gold a zero-beta asset? Analysis of the investment potential of precious metals. Unpublished working paper, Oklahoma City University. Available from http://ssrn.com/abstract=920496.
McCown, J. R., Zimmerman, J. R., 2007. Analysis of the investment potential and inflation-hedging ability of precious metals. Unpublished working paper, Oklahoma City University. Available from http://ssrn.com/abstract=1002966.
Meng, X. L., Rubin, D. B., 1991. Using EM to obtain asymptotic variance-covariance matrices: the SEM algorithm. Journal of the American Statistical Association 86, 899–909.
Merton, R. C., 1976. Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics 3, 125–144.
Ogden, J. P., Tucker, A. L., Vines, T. W., 1990. Arbitraging American gold spot and futures options. Financial Review 25, 577–592.
Reboredo, J. C., 2013. Is gold a safe haven or a hedge for the US dollar? Implications for risk management. Journal of Banking and Finance 37, 2665–2676.
Zagaglia, P., Marzo, M., 2013. Gold and the U.S. dollar: tales from the turmoil. Quantitative Finance 13, 571–582.
描述 博士
國立政治大學
金融研究所
95352506
102
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0095352506
資料類型 thesis
dc.contributor.advisor 廖四郎zh_TW
dc.contributor.advisor Liao, Szu Langen_US
dc.contributor.author (Authors) 連育民zh_TW
dc.contributor.author (Authors) Lian, Yu Minen_US
dc.creator (作者) 連育民zh_TW
dc.creator (作者) Lian, Yu Minen_US
dc.date (日期) 2013en_US
dc.date.accessioned 4-Jun-2014 14:41:45 (UTC+8)-
dc.date.available 4-Jun-2014 14:41:45 (UTC+8)-
dc.date.issued (上傳時間) 4-Jun-2014 14:41:45 (UTC+8)-
dc.identifier (Other Identifiers) G0095352506en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/66468-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 金融研究所zh_TW
dc.description (描述) 95352506zh_TW
dc.description (描述) 102zh_TW
dc.description.abstract (摘要) 本文實證探討黃金期貨報酬率的特性並在標的黃金期貨價格遵循狀態轉換跳躍擴散過程時實現美式選擇權之評價。在這樣的動態過程下，跳躍事件被一個複合普瓦松過程與對數常態跳躍振幅所描述，以及狀態轉換到達強度是由一個其狀態代表經濟狀態的隱藏馬可夫鏈所捕捉。考量不同的跳躍風險假設，我們使用Merton測度與Esscher轉換推導出在一個不完全市場設定下的風險中立黃金期貨價格動態過程。為了達到所需的精確度，最小平方蒙地卡羅法被用來近似美式黃金期貨選擇權的價值。基於實際市場資料，我們提供實證與數值結果來說明這個動態模型的優點。zh_TW
dc.description.abstract (摘要) This dissertation empirically investigates the characteristics of gold futures returns and achieves the valuation of American-style options when the underlying gold futures price follows a regime-switching jump-diffusion process. Under such dynamics, the jump events are described as a compound Poisson process with a log-normal jump amplitude, and the regime-switching arrival intensity is captured by a hidden Markov chain whose states represent the economic states. Considering the different jump risk assumptions, we use the Merton measure and Esscher transform to derive risk-neutral gold futures price dynamics under an incomplete market setting. To achieve a desired accuracy level, the least-squares Monte Carlo method is used to approximate the values of American gold futures options. Our empirical and numerical results based on actual market data are provided to illustrate the advantages of this dynamic model.en_US
dc.description.tableofcontents 中文摘要 I
Abstract II
Acknowledgements III
Contents IV
List of Tables VI
List of Figures VII
1. Introduction 1
2. Model Framework and Pricing Method 9
2.1 Markov-modulated Poisson process 9
2.2 Gold futures price modeling 11
2.3 Least-squares Monte Carlo approach 12
3. Valuation of American Gold Futures Options in a Markov Regime-Switching Jump-Diffusion Economy 15
3.1 Merton measure for the Markov regime-switching jump-diffusion process 16
3.2 Esscher transform for the Markov regime-switching jump-diffusion process 18
3.3 Valuing American gold futures options 22
4. Empirical Analyses and Numerical Illustrations 24
4.1 Empirical results 24
4.2 Pricing performance 34
5. Conclusions and Future Extensions 37
References 39
Appendix A: Distributional properties of RSJM under 44
Appendix B: Solving the Esscher parameters 47
Appendix C: Distributional properties of RSJM under 49		zh_TW
dc.format.extent 538588 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0095352506en_US
dc.subject (關鍵詞) 美式黃金期貨選擇權zh_TW
dc.subject (關鍵詞) 狀態轉換跳躍擴散過程zh_TW
dc.subject (關鍵詞) Merton測度zh_TW
dc.subject (關鍵詞) Esscher轉換zh_TW
dc.subject (關鍵詞) 最小平方蒙地卡羅法zh_TW
dc.subject (關鍵詞) American gold futures optionen_US
dc.subject (關鍵詞) Regime-switching jump-diffusion processen_US
dc.subject (關鍵詞) Merton measureen_US
dc.subject (關鍵詞) Esscher transformen_US
dc.subject (關鍵詞) Least-squares Monte Carlo methoden_US
dc.title (題名) 狀態相依跳躍風險與美式選擇權評價：黃金期貨市場之實證研究zh_TW
dc.title (題名) State-dependent jump risks and American option pricing: an empirical study of the gold futures marketen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Amin, K. I., 1993. Jump diffusion option valuation in discrete time. The Journal of Finance 48, 1833–1863.
Ball, C. A., Torous, W. N., 1983. A simplified jump process for common stock returns. Journal of Financial and Quantitative Analysis 18, 53–65.
Ball, C. A., Torous, W. N., Tschoegl, A. E., 1985. An empirical investigation of the EOE gold options market. Journal of Banking and Finance 9, 101–113.
Baur, D. G., Lucey, B. M., 2010. Is gold a hedge or a safe haven? An analysis of stocks, bonds and gold. Financial Review 45, 217–229.
Baur, D. G., McDermott, T. K., 2010. Is gold a safe haven? International evidence. Journal of Banking and Finance 34, 1886–1898.
Beckers, S., 1981. A note on estimating the parameters of the diffusion jump model of stock returns. Journal of Financial and Quantitative Analysis 16, 127–140.
Beckers, S., 1984. On the efficiency of the gold options market. Journal of Banking and Finance 8, 459–470.
Boyle, P., Broadie, M., Glasserman, P., 1997. Monte Carlo methods for security pricing. Journal of Economic Dynamics and Control 21, 1267–1321.
Brennan, M., Schwartz, E., 1977. The valuation of American put options. Journal of Finance 32, 449–462.
Capie, F., Mills, T. C., Wood, G., 2005. Gold as a hedge against the dollar. Journal of International Financial Markets, Institutions and Money 15, 343–352.
Carr, P., Geman, H., Madan, D., Yor, M., 2002. The fine structure of asset returns: an empirical investigation. Journal of Business 75, 305–332.
Chan, W. H., Maheu, J. M., 2002. Conditional jump dynamics in stock market returns. Journal of Business & Economic Statistics 20, 377–389.
Chang, C., Fuh, C. D., Lin, S. K., 2013. A tale of two regimes: theory and empirical evidence for a Markov-modulated jump diffusion model of equity returns and derivative pricing implications. Journal of Banking and Finance 37, 3204–3217.
Cox, J. C., Ross, S. A., Rubinstein, M., 1979. Option pricing: a simplified approach. Journal of Financial Economics 7, 229–263.
Duan, J. C., Ritchken, P., Sun, Z., 2006. Approximating GARCH-jump models, jump-diffusion processes, and option pricing. Mathematical Finance 16, 21–52.
Elliott, R. J., Chan, L., Siu, T. K., 2005. Option pricing and Esscher transform under regime switching. Annals of Finance 1, 423–432.
Elliott, R. J., Osakwe, C.-J. U., 2006. Option pricing for pure jump processes with Markov switching compensators. Finance and Stochastics 10, 250–275.
Elliott, R. J., Siu, T. K., Chan, L., Lau, J. W., 2007. Pricing options under a generalized Markov-modulated jump-diffusion model. Stochastic Analysis and Applications 25, 821–843.
Elliott, R. J., Siu, T. K., 2011. A risk-based approach for pricing American options under a generalized Markov regime-switching model. Quantitative Finance 11, 1633–1646.
Eraker, B., Johannes, M., Polson, N., 2003. The impact of jumps in volatility and returns. Journal of Finance 58, 1269–1300.
Eraker, B., 2004. Do stock market and volatility jump? Reconciling evidence from spot and option prices. Journal of Finance 59, 1367–1404.
Gerber, H. U., Shiu, E. S. W., 1994. Option pricing by Esscher transforms (with discussions). Transactions of Society of Actuaries 46, 99–191.
Gerber, H. U., Shiu, E. S. W., 1996. Actuarial bridges to dynamic hedging and option pricing. Insurance: Mathematics and Economics 18, 183–218.
Hull, J., White, A., 1990. Valuing derivative securities using the explicit finite difference method. Journal of Financial and Quantitative Analysis 25, 87–100.
Khalaf, L., Saphores, J.-D., Bilodeau, J.-F., 2003. Simulation-based exact jump tests in models with conditional heteroskedasticity. Journal of Economic Dynamics and Control 28, 531–553.
Kou, S. G., 2002. A jump-diffusion model for option pricing. Management Science 48, 1086–1101.
Lange, K., 1995a. A gradient algorithm locally equivalent to the EM algorithm. Journal of the Royal Statistical Society 57, 425–437.
Lange, K., 1995b. A quasi-Newton acceleration of the EM algorithm. Statistica Sinica 5, 1–18.
Last, G., Brandt, A., 1995. Marked point processes on the real line: the dynamic approach. Springer-Verlag, New York.
Longstaff, F. A., Schwartz, E. S., 2001. Valuing American options by simulation: a simple least-squares approach. Review of Financial Studies 14, 113–147.
Maheu, J. M., McCurdy, T. H., 2004. News arrival, jump dynamics and volatility components for individual stock returns. Journal of Finance 59, 755–793.
McCown, J. R., Zimmerman, J. R., 2006. Is gold a zero-beta asset? Analysis of the investment potential of precious metals. Unpublished working paper, Oklahoma City University. Available from http://ssrn.com/abstract=920496.
McCown, J. R., Zimmerman, J. R., 2007. Analysis of the investment potential and inflation-hedging ability of precious metals. Unpublished working paper, Oklahoma City University. Available from http://ssrn.com/abstract=1002966.
Meng, X. L., Rubin, D. B., 1991. Using EM to obtain asymptotic variance-covariance matrices: the SEM algorithm. Journal of the American Statistical Association 86, 899–909.
Merton, R. C., 1976. Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics 3, 125–144.
Ogden, J. P., Tucker, A. L., Vines, T. W., 1990. Arbitraging American gold spot and futures options. Financial Review 25, 577–592.
Reboredo, J. C., 2013. Is gold a safe haven or a hedge for the US dollar? Implications for risk management. Journal of Banking and Finance 37, 2665–2676.
Zagaglia, P., Marzo, M., 2013. Gold and the U.S. dollar: tales from the turmoil. Quantitative Finance 13, 571–582.		zh_TW