學術產出-學位論文

題名 外匯選擇權的定價-馬可夫鏈蒙地卡羅法(MCMC)之績效探討
作者 任紀為
貢獻者 杜化宇
任紀為
關鍵詞 馬可夫鍵蒙地卡羅
狀態轉換波動
吉普斯抽樣
笑狀波幅
Markov-chain Monte Carlo
Regime-switching volatility
Gibbs sampling
Volatility smile
日期 2004
上傳時間 18-九月-2009 13:41:54 (UTC+8)
摘要 在真實世界中,我們可以觀察到許多財務或經濟變數(股價、匯率、利率等)有時波動幅度非常微小,呈現相對穩定的狀態(Regime);有時會由於政治因素或經濟環境的變動,突然一段期間呈現瘋狂震盪的狀態。針對這種現象,已有學者提出狀態轉換波動度模型(Regime Switching Volatility Model,簡稱RSV)來捕捉此一現象。

本篇論文選擇每年交易金額非常龐大的外匯選擇權市場,以RSV模型為基礎,採用馬可夫鏈蒙地卡羅法 ( Markov Chain Monte Carlo,簡稱MCMC ) 中的吉普斯抽樣(Gibbs Sampling)法來估計RSV模型的參數,依此預測外匯選擇權在RSV模型下的價格。我們再將此價格與Black and Scholes(BS)法及實際市場交易的價格資料作比較,最後並提出笑狀波幅與隱含波動度平面的結果。結果顯示經由RSV模型與MCMC演算法所計算出來的選擇權價格確實優於傳統的BS方法,且能有效解釋波動率期間結構 (Volatility Term Structure) 與笑狀波幅 (Volatility Smile) 的現象,確實反應且捕捉到了市場上選擇權價格所應具備的特色。
參考文獻 一、中文部分(依作者姓名筆畫排列)
杜化宇,期貨與選擇概論. John C. Hull 原著,民國八十九年,雙葉書廊。
阮建豐, ”利用混合模型估計風險值的探討” ,國立政治大學統計學研究所碩士論文,民國九十年六月。
陳松男,金融工程學.,民國九十一年,華泰書局出版。
黃大展, ”隨機波動下的二元樹狀模型之探討” ,國立政治大學財務管理研究所碩士論文,民國九十年六月。
謝盈弘, ”馬可夫鏈蒙地卡羅法在外匯選擇權定價的應用” ,國立政治大學統計學研究所碩士論文,民國九十一年六月。
二、英文部分(依作者姓氏字母排列)
Bahra, B. (1997) “Implied Risk-neutral Probability Functions From Option Prices: Theory and Application.” , Working Paper.
Bauwens, L. and Lubrano, M. (1998) “Bayesian inference on GARCH models using the Gibbs sampler.” , Econometrics Journal, Vol. 1, P23-46.
Bauwens, L. and Lubrano, M. (2002) “Bayesian option pricing using asymmetric GARCH models.” , Journal of Empirical Finance, Vol. 9, P321-342.
Bollen, N. P. B. (1998) “Valuing Options in Regime-Switching Models.” , Journal of Derivatives , Vol. 6, P38-49.
Bollen, N. P. B., Gray, S. F. and Whaley, R. E. (2000) “Regime switching in foreign exchange rates: Evidence from currency option prices.” , Journal of Econometrics, Vol.94, P239-276.
Bollen, N. P. B. and Rasiel, E. (2003) “The performance of alternative valuation models in the OTC currency options market .”Journal of International Money and Finance, Vol. 22, P33-64.
Brigo, D. and Mercurio, F. (2002) “Lognormal-mixture dynamics and calibration to market volatility smiles.”International Journal of Theoretical and Applied Finance, Vol. 5, P427-446
Broadie, M., Boyle, P. and Glasserman, P. (1997) “Monte Carlo methods for security pricing.”, Journal of Economic Dynamic and Control, Vol. 21, P1267-1321.
Campa, J. M. and Chang, P. H. (1995) “Testing the expectations hypothesis on the term structure of volatilities in foreign exchange options.” , Journal of Finance, Vol. 50, P529-547.
Chib, S. and Albert, J. H. (1993) “Bayesian Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts.”, Journal of Business and Economic Statistics , Vo1. 11, P1-15.
Chib, S. and Greenberg, E. (1996) “Markov chain monte carlo simulation methods in Econometrics.”, Econometric Theory , Vol. 12, P409-431.
Chib, S. , Nardari, F. and Shephard, N. (2002) “Markov Chain Monte Carlo Methods for Stochastic Volatility Models.”, Journal of Econometrics, Vol. 108, P 281-316..
Chriss, N. A. (1997) Black-Scholes and Bayesian_Option Pricing Models, McGraw-Hill.
Clewlow, L. and Strickland, C. (1998) Implementing Derivatives Models. Wiley.
Congdon, P. (2001) Bayesian Statistical Modeling . Wiley.
Cox, J. and Ross, S. (1976) “The Value of Options for Alternative Stochastic Process” Journal of Financial Economics, Vol. 3, P145-166.
Derosa, D. F. (1998) Currency Derivatives . Wiley .
Derosa, D. F. (2000) Option on foreign exchange. Wiley.
Duan, J.(1995) “The GARCH Option Pricing Model”, Mathematical Finance, Vol. 5, P13-32.
Duan, J.and Wei, J. (1999) “Pricing Foreign Currency and Cross-Currency Options Under GARCH”, Journal of Derivatives , Vol. 3 , P51-63.
Gemmill, C. and Apostolos, S. (2000) “How useful are Implied Distribution?Evidence from Stock Index Options.”, Journal of Derivatives, Vol. 2, P83-98.
Gesser, V. and Poncet, P. (1997) “Volatility Patterns Theory and Some Evidence From the Dollar-Mark Option Market.”, Journal of Derivatives, Vol. 7, P46-61.
Gilks, W. R., Richardson, S. and Spiegelhalter D. J. (1996) Markov Chain Monte Carlo in Practice, Chapman and Hall/CRC.
Guidolin, M. and Timmermann, A. (2003) “Option Prices under Bayesian Learning : Implied Volatility Dynamics and Predictive Densities.” , Journal of Economic Dynamics & Control, Vol. 27, P717-769.
Hamilton, J. D. (1991) “A Quasi-Bayesian Approach to Estimating Parameters for Mixtures of Normal Distributions.” , Journal of Business and Economic Statistics, Vol. l9, P23-39.
Hamilton, J. D. (1994) Time Series Analysis, Princeton.
Heston, S. and Nandi, S. (2000) “A Closed-Form GARCH Option Valuation Model. ”, Review of Financial Studies, Vol. 13, P585-625.
Heston, S. (1993) “A Closed –Form Solution for Options with Stochastic Volatility with Application to Bond and Currency Options.” , Review of Financial Studies, Vol.6, P327-343.
Hull, J. and White, A. (1987) “The pricing of options on assets with stochastic volatilities.” , Journal of Finance, Vol. 42 , P281-300.
Hull, J. C. (2003), Options, Futures and Other Derivatives, 5th ed. Prentice Hall.
Jones, C. S. (1998) “Bayesian Estimation of Continuous-Time Finance Models.” , Working Paper.
Kim, C. J. and Nelson, C. R. (1999) State-Space Models with Regime-Switching: Classical and Gibbs-Sampling Approaches with Applications, MIT Press.
Malz, A. M. (1997) “Estimating the probability distribution of the future exchange rate from option prices.” , Journal of Derivatives, Vol. 7, P244-253.
Mikkelsen P. (2001) “MCMC Based Estimation of Term Structure Models”, Working Paper.
Ripley, B. D. (1987) Stochastic Simulation . Wiley.
Ross, S. M. (1997) Simulation . Academic Press.
Rossi, P. E. , Jacquier, E. and Polson, N. G. (1994) “Bayesian analysis of stochastic volatility models.”, Journal of Business and Economic Statistics, Vol.12, P371-389.
Rubinstein, R. Y. (1981) Simulation and Monte Carlo Method. Wiley.
Shepard, N. (1993) “Fitting nonlinear time-series models with applications to stochastic variance models.” , Journal of Applied Econometrics, Vol. 8 , P135-152.
So, M. K. P., Lam, K. and Li, W. K. (1998) “A stochastic volatility model with markov switching.” , Journal of Business and Economic Statistics, Vol. 16, P244-253.
Tsay, R. S. (2002) Analysis of Financial Time Series, Wiley.
Venables, W. N. and Ripley, B. D. (2000) Modern Applied Statistics with S-Plus, Springer.
Xu, X. and Taylor, S. J. (1994a) “The Magnitude of Implied Volatility Smiles: Theory and Empirical Evidence for Exchange Rates.”, Review of Future Markets, Vol. 13, P355-380.
Xu, X. and Taylor, S. J. (1994b) “The Term Structure of Volatility Implied by Foreign Exchange Options.” , Journal of Financial and Quantitative Analysis, Vol. 29 , P57-74.
描述 碩士
國立政治大學
企業管理研究所
92355055
93
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0923550551
資料類型 thesis
dc.contributor.advisor 杜化宇zh_TW
dc.contributor.author (作者) 任紀為zh_TW
dc.creator (作者) 任紀為zh_TW
dc.date (日期) 2004en_US
dc.date.accessioned 18-九月-2009 13:41:54 (UTC+8)-
dc.date.available 18-九月-2009 13:41:54 (UTC+8)-
dc.date.issued (上傳時間) 18-九月-2009 13:41:54 (UTC+8)-
dc.identifier (其他 識別碼) G0923550551en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/35061-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 企業管理研究所zh_TW
dc.description (描述) 92355055zh_TW
dc.description (描述) 93zh_TW
dc.description.abstract (摘要) 在真實世界中,我們可以觀察到許多財務或經濟變數(股價、匯率、利率等)有時波動幅度非常微小,呈現相對穩定的狀態(Regime);有時會由於政治因素或經濟環境的變動,突然一段期間呈現瘋狂震盪的狀態。針對這種現象,已有學者提出狀態轉換波動度模型(Regime Switching Volatility Model,簡稱RSV)來捕捉此一現象。

本篇論文選擇每年交易金額非常龐大的外匯選擇權市場,以RSV模型為基礎,採用馬可夫鏈蒙地卡羅法 ( Markov Chain Monte Carlo,簡稱MCMC ) 中的吉普斯抽樣(Gibbs Sampling)法來估計RSV模型的參數,依此預測外匯選擇權在RSV模型下的價格。我們再將此價格與Black and Scholes(BS)法及實際市場交易的價格資料作比較,最後並提出笑狀波幅與隱含波動度平面的結果。結果顯示經由RSV模型與MCMC演算法所計算出來的選擇權價格確實優於傳統的BS方法,且能有效解釋波動率期間結構 (Volatility Term Structure) 與笑狀波幅 (Volatility Smile) 的現象,確實反應且捕捉到了市場上選擇權價格所應具備的特色。
zh_TW
dc.description.tableofcontents 目 錄 I
圖目錄 III
表目錄 V
表目錄 V
第一章 緒論 1
第一節 研究背景與動機 1
第二節 研究目的與問題 2
第三節 研究架構 3
4
第一節 笑狀波幅、期間結構與隱含分配 4
第二節 隨機波動率模型相關文獻 7
第三節 貝氏選擇權評價相關文獻 11
第三章 研究方法 13
第一節 資料選取 13
第二節 RSV模型建構 14
第三節 馬可夫鏈蒙地卡羅法 18
第四節 預測外匯選擇權的價格及演算法的建構 23
第四章 結果分析 28
第一節 Gibbs Sampling抽樣結果 28
第二節 外匯選擇權價格模擬結果 30
第三節 笑狀波幅與隱含波動度曲面 34
第五章 結論與後續研究建議 35
第一節 結論 35
第二節 後續研究建議 37
附錄 38
參考文獻 62
zh_TW
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dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0923550551en_US
dc.subject (關鍵詞) 馬可夫鍵蒙地卡羅zh_TW
dc.subject (關鍵詞) 狀態轉換波動zh_TW
dc.subject (關鍵詞) 吉普斯抽樣zh_TW
dc.subject (關鍵詞) 笑狀波幅zh_TW
dc.subject (關鍵詞) Markov-chain Monte Carloen_US
dc.subject (關鍵詞) Regime-switching volatilityen_US
dc.subject (關鍵詞) Gibbs samplingen_US
dc.subject (關鍵詞) Volatility smileen_US
dc.title (題名) 外匯選擇權的定價-馬可夫鏈蒙地卡羅法(MCMC)之績效探討zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 一、中文部分(依作者姓名筆畫排列)zh_TW
dc.relation.reference (參考文獻) 杜化宇,期貨與選擇概論. John C. Hull 原著,民國八十九年,雙葉書廊。zh_TW
dc.relation.reference (參考文獻) 阮建豐, ”利用混合模型估計風險值的探討” ,國立政治大學統計學研究所碩士論文,民國九十年六月。zh_TW
dc.relation.reference (參考文獻) 陳松男,金融工程學.,民國九十一年,華泰書局出版。zh_TW
dc.relation.reference (參考文獻) 黃大展, ”隨機波動下的二元樹狀模型之探討” ,國立政治大學財務管理研究所碩士論文,民國九十年六月。zh_TW
dc.relation.reference (參考文獻) 謝盈弘, ”馬可夫鏈蒙地卡羅法在外匯選擇權定價的應用” ,國立政治大學統計學研究所碩士論文,民國九十一年六月。zh_TW
dc.relation.reference (參考文獻) 二、英文部分(依作者姓氏字母排列)zh_TW
dc.relation.reference (參考文獻) Bahra, B. (1997) “Implied Risk-neutral Probability Functions From Option Prices: Theory and Application.” , Working Paper.zh_TW
dc.relation.reference (參考文獻) Bauwens, L. and Lubrano, M. (1998) “Bayesian inference on GARCH models using the Gibbs sampler.” , Econometrics Journal, Vol. 1, P23-46.zh_TW
dc.relation.reference (參考文獻) Bauwens, L. and Lubrano, M. (2002) “Bayesian option pricing using asymmetric GARCH models.” , Journal of Empirical Finance, Vol. 9, P321-342.zh_TW
dc.relation.reference (參考文獻) Bollen, N. P. B. (1998) “Valuing Options in Regime-Switching Models.” , Journal of Derivatives , Vol. 6, P38-49.zh_TW
dc.relation.reference (參考文獻) Bollen, N. P. B., Gray, S. F. and Whaley, R. E. (2000) “Regime switching in foreign exchange rates: Evidence from currency option prices.” , Journal of Econometrics, Vol.94, P239-276.zh_TW
dc.relation.reference (參考文獻) Bollen, N. P. B. and Rasiel, E. (2003) “The performance of alternative valuation models in the OTC currency options market .”Journal of International Money and Finance, Vol. 22, P33-64.zh_TW
dc.relation.reference (參考文獻) Brigo, D. and Mercurio, F. (2002) “Lognormal-mixture dynamics and calibration to market volatility smiles.”International Journal of Theoretical and Applied Finance, Vol. 5, P427-446zh_TW
dc.relation.reference (參考文獻) Broadie, M., Boyle, P. and Glasserman, P. (1997) “Monte Carlo methods for security pricing.”, Journal of Economic Dynamic and Control, Vol. 21, P1267-1321.zh_TW
dc.relation.reference (參考文獻) Campa, J. M. and Chang, P. H. (1995) “Testing the expectations hypothesis on the term structure of volatilities in foreign exchange options.” , Journal of Finance, Vol. 50, P529-547.zh_TW
dc.relation.reference (參考文獻) Chib, S. and Albert, J. H. (1993) “Bayesian Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts.”, Journal of Business and Economic Statistics , Vo1. 11, P1-15.zh_TW
dc.relation.reference (參考文獻) Chib, S. and Greenberg, E. (1996) “Markov chain monte carlo simulation methods in Econometrics.”, Econometric Theory , Vol. 12, P409-431.zh_TW
dc.relation.reference (參考文獻) Chib, S. , Nardari, F. and Shephard, N. (2002) “Markov Chain Monte Carlo Methods for Stochastic Volatility Models.”, Journal of Econometrics, Vol. 108, P 281-316..zh_TW
dc.relation.reference (參考文獻) Chriss, N. A. (1997) Black-Scholes and Bayesian_Option Pricing Models, McGraw-Hill.zh_TW
dc.relation.reference (參考文獻) Clewlow, L. and Strickland, C. (1998) Implementing Derivatives Models. Wiley.zh_TW
dc.relation.reference (參考文獻) Congdon, P. (2001) Bayesian Statistical Modeling . Wiley.zh_TW
dc.relation.reference (參考文獻) Cox, J. and Ross, S. (1976) “The Value of Options for Alternative Stochastic Process” Journal of Financial Economics, Vol. 3, P145-166.zh_TW
dc.relation.reference (參考文獻) Derosa, D. F. (1998) Currency Derivatives . Wiley .zh_TW
dc.relation.reference (參考文獻) Derosa, D. F. (2000) Option on foreign exchange. Wiley.zh_TW
dc.relation.reference (參考文獻) Duan, J.(1995) “The GARCH Option Pricing Model”, Mathematical Finance, Vol. 5, P13-32.zh_TW
dc.relation.reference (參考文獻) Duan, J.and Wei, J. (1999) “Pricing Foreign Currency and Cross-Currency Options Under GARCH”, Journal of Derivatives , Vol. 3 , P51-63.zh_TW
dc.relation.reference (參考文獻) Gemmill, C. and Apostolos, S. (2000) “How useful are Implied Distribution?Evidence from Stock Index Options.”, Journal of Derivatives, Vol. 2, P83-98.zh_TW
dc.relation.reference (參考文獻) Gesser, V. and Poncet, P. (1997) “Volatility Patterns Theory and Some Evidence From the Dollar-Mark Option Market.”, Journal of Derivatives, Vol. 7, P46-61.zh_TW
dc.relation.reference (參考文獻) Gilks, W. R., Richardson, S. and Spiegelhalter D. J. (1996) Markov Chain Monte Carlo in Practice, Chapman and Hall/CRC.zh_TW
dc.relation.reference (參考文獻) Guidolin, M. and Timmermann, A. (2003) “Option Prices under Bayesian Learning : Implied Volatility Dynamics and Predictive Densities.” , Journal of Economic Dynamics & Control, Vol. 27, P717-769.zh_TW
dc.relation.reference (參考文獻) Hamilton, J. D. (1991) “A Quasi-Bayesian Approach to Estimating Parameters for Mixtures of Normal Distributions.” , Journal of Business and Economic Statistics, Vol. l9, P23-39.zh_TW
dc.relation.reference (參考文獻) Hamilton, J. D. (1994) Time Series Analysis, Princeton.zh_TW
dc.relation.reference (參考文獻) Heston, S. and Nandi, S. (2000) “A Closed-Form GARCH Option Valuation Model. ”, Review of Financial Studies, Vol. 13, P585-625.zh_TW
dc.relation.reference (參考文獻) Heston, S. (1993) “A Closed –Form Solution for Options with Stochastic Volatility with Application to Bond and Currency Options.” , Review of Financial Studies, Vol.6, P327-343.zh_TW
dc.relation.reference (參考文獻) Hull, J. and White, A. (1987) “The pricing of options on assets with stochastic volatilities.” , Journal of Finance, Vol. 42 , P281-300.zh_TW
dc.relation.reference (參考文獻) Hull, J. C. (2003), Options, Futures and Other Derivatives, 5th ed. Prentice Hall.zh_TW
dc.relation.reference (參考文獻) Jones, C. S. (1998) “Bayesian Estimation of Continuous-Time Finance Models.” , Working Paper.zh_TW
dc.relation.reference (參考文獻) Kim, C. J. and Nelson, C. R. (1999) State-Space Models with Regime-Switching: Classical and Gibbs-Sampling Approaches with Applications, MIT Press.zh_TW
dc.relation.reference (參考文獻) Malz, A. M. (1997) “Estimating the probability distribution of the future exchange rate from option prices.” , Journal of Derivatives, Vol. 7, P244-253.zh_TW
dc.relation.reference (參考文獻) Mikkelsen P. (2001) “MCMC Based Estimation of Term Structure Models”, Working Paper.zh_TW
dc.relation.reference (參考文獻) Ripley, B. D. (1987) Stochastic Simulation . Wiley.zh_TW
dc.relation.reference (參考文獻) Ross, S. M. (1997) Simulation . Academic Press.zh_TW
dc.relation.reference (參考文獻) Rossi, P. E. , Jacquier, E. and Polson, N. G. (1994) “Bayesian analysis of stochastic volatility models.”, Journal of Business and Economic Statistics, Vol.12, P371-389.zh_TW
dc.relation.reference (參考文獻) Rubinstein, R. Y. (1981) Simulation and Monte Carlo Method. Wiley.zh_TW
dc.relation.reference (參考文獻) Shepard, N. (1993) “Fitting nonlinear time-series models with applications to stochastic variance models.” , Journal of Applied Econometrics, Vol. 8 , P135-152.zh_TW
dc.relation.reference (參考文獻) So, M. K. P., Lam, K. and Li, W. K. (1998) “A stochastic volatility model with markov switching.” , Journal of Business and Economic Statistics, Vol. 16, P244-253.zh_TW
dc.relation.reference (參考文獻) Tsay, R. S. (2002) Analysis of Financial Time Series, Wiley.zh_TW
dc.relation.reference (參考文獻) Venables, W. N. and Ripley, B. D. (2000) Modern Applied Statistics with S-Plus, Springer.zh_TW
dc.relation.reference (參考文獻) Xu, X. and Taylor, S. J. (1994a) “The Magnitude of Implied Volatility Smiles: Theory and Empirical Evidence for Exchange Rates.”, Review of Future Markets, Vol. 13, P355-380.zh_TW
dc.relation.reference (參考文獻) Xu, X. and Taylor, S. J. (1994b) “The Term Structure of Volatility Implied by Foreign Exchange Options.” , Journal of Financial and Quantitative Analysis, Vol. 29 , P57-74.zh_TW