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題名 Empirical Performance and Asset Pricing in Markov Jump Diffusion Models
馬可夫跳躍擴散模型的實證與資產定價
作者 林士貴
Lin, Shih-Kuei
貢獻者 傅承德<br>翁久幸
Fuh, Cheng-Der<br>Weng, Chiu-Hsing
林士貴
Lin, Shih-Kuei
關鍵詞 均衡分析
歐式選擇權
拉氏倒轉變換
長記憶
馬可夫跳躍擴散模型
馬可夫控制瓦松過程
數值倒轉方法
換跳躍擴散過程
變波動聚集
波動度微笑
Equilibrium analysis
European call option
Laplace inverse transform
Leptokurtic
Long memory
Markov jump diffusion model
Markov modulated Poisson process
Numerical inversion method
Switch jump diffusion model
Volatility clustering
Volatility smile
日期 2003
上傳時間 18-Sep-2009 19:08:37 (UTC+8)
摘要 為了改進Black-Scholes模式的實證現象，許多其他的模型被建議有leptokurtic特性以及波動度聚集的現象。然而對於其他的模型分析的處理依然是一個問題。在本論文中，我們建議使用馬可夫跳躍擴散過程，不僅能整合leptokurtic與波動度微笑特性，而且能產生波動度聚集的與長記憶的現象。然後，我們應用Lucas的一般均衡架構計算選擇權價格，提供均衡下當跳躍的大小服從一些特別的分配時則選擇權價格的解析解。特別地，考慮當跳躍的大小服從兩個情況，破產與lognormal分配。當馬可夫跳躍擴散模型的馬可夫鏈有兩個狀態時，稱為轉換跳躍擴散模型，當跳躍的大小服從lognormal分配我們得到選擇權公式。使用轉換跳躍擴散模型選擇權公式，我們給定一些參數下研究公式的數值極限分析以及敏感度分析。
To improve the empirical performance of the Black-Scholes model, many alternative models have been proposed to address the leptokurtic feature of the asset return distribution, and the effects of volatility clustering phenomenon. However,
     analytical tractability remains a problem for most of the alternative models. In this dissertation, we propose a Markov jump diffusion model, that can not only incorporate both the leptokurtic feature and volatility smile, but also present the economic features of volatility clustering and long memory.
     Next, we apply Lucas`s general equilibrium framework to evaluate option price, and to provide analytical solutions of the equilibrium price for European call options when the jump size follows some specific distributions. In particular, two cases are considered, the defaultable one and the lognormal distribution. When the underlying Markov chain of the Markov jump diffusion model has two states, the so-called switch jump diffusion model, we write an explicit analytic formula under the jump size has a lognormal distribution. Numerical approximations of the option prices as well as sensitivity analysis are also given.
參考文獻 Abate, J. and Whitt, W. (1992). Numerical inversion of
probability generating functions. Operations Research Letters.
Vol. 12, 245-251.
Andersen, L. and Andreasen, J. (2000). Volatility skews and extensions of the libor market model. Applied Mathematical Finance. Vol. 7, 1-32.
Andersen, T. (1996). Return volatility and trading volume: an
information flow interpretation of stochastic volatility. it Journal of Finance. Vol. 51, 169-204.
Attari, M. (1999). Discontinuous interest rate processes:
An equilibrium model for bond option prices. The Journal of Financial and Quantitative Analysis. Vol. 34, 293-322.
Bardorff-Nielsen, O. E. and Cox, D. R. (1989). Asymptotic Techniques for Use
in Statistics. Chapman and Hall, New York.
Bjork, T., Kabanov, Y. and Runggaldier, W. (1997). Bond market structure
in the presence of Marked point processes, Mathematical Finance. Vol. 7, 211-239.
Black, F. and Scholes, M. (1973).
The pricing of options and corporate liabilities. Journal of Political Economy.
Vol. 81, 637-654.
Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity.
Journal of Econometrics. Vol. 31, 307-327.
Bollerslev, T., Engle, R. F. and Nelson, D. B. (1994). ARCH models. Handbook of Econometrics. Vol. 4, 2959-3038.
Boyle, P., Broadie, M. and Glasserman, P. (1997). Simulation methods
for security pricing. Journal of Economic Dynamics and Control. Vol 21,
1267-1321.
Clark, P. K. (1973). Asubordinated stochastic process model with finite
variance for speculative prices. Econometrica. Vol. 41, 131-155.
Cochrane, J. H. (2001). Asset Pricing. Princeton University Press, Princeton.
Cox, J., Ingersoll, E. and Ross, S. A. (1985). A theory of the term structure
of interest rates. Econometrica. Vol. 53, 385-407.
Cox, J. and Ross, S. (1976). The valuation of options for alternative stochastic processes. Journal of Financial Economics. Vol. 3, 145-166.
Das, S. R. and Foresi, S. (1996). Exact solutions for bond and option prices
with systematic jump risk. Review Derivatives Research. Vol. 1, 7-24.
Davydov, D. and Linetsky, V. (2001). The valuation and hedging of path-dependent
options under the CEV process. Management Science. Vol. 47, 949-965.
Diebold, F. X. and Inoue, A. (2001). Long memory and regime switching.
Journal of Econometrics. Vol. 105, 131-159.
Di Masi, G. B., Kabanov, Yu, M., and Runggaldier, W. J. (1994).
Mean-variance hedging of options on stocks with Markov volatility.
Theory of Probability and Its Applications, vol 39, 173-181.
Duan, J. C. (1995). The $GARCH$ option pricing model. Mathematical Finance.
Vol. 5, 13-32.
Duffie, D. (2001). Dynamic Asset Pricing Theory. Princeton University Press, Princeton.
Duffie, D., Pan, J. and Singleton, K. (2000). Transform analysis and option
pricing for affine jump-diffusions. Econometrica. Vol. 68, 1343-1376.
Duffie, D. and Singleton, K. (1999). Modeling term structures of
defaultable bonds. Review of Financial Studies. Vol. 12, 687-720.
Elliot, R. J. and Kopp, P. E. (1999). Mathematics of Financial Markets.
Spinger, New York.
Engle, R. (1982). Autoregressive conditional heteroscedasticity
with estimates of the variance of U.K. inflation. Econometrica. Vol. 50, 987-1008.
Fuh, C. D., Hu, I. and Lin, S. K. (2002). Empirical performance and asset pricing in hidden Markov models. Communications in Statistics : Theory and Methods. Vol. 32, 2479-2514.
Geweke, J., and Porter-Hudak, S. (1983). The estimation and application of long-memory time series models. {Journal of Time Series Analysis. Vol. 4, 221-238.
Ghysels, E., Harvey, A. C. and Renault, E. (1996). Stochastic volatility.
Handbook of Statistics. Vol. 14, 119-191.
Glasserman, P. and Kou, S. G. (2003). The term structure of simple
forward rates with jump risk. Mathematical finance. Vol. 13, 383-410.
Grunewald, B. and Trautmann, S. (1996).
Option Hedging in the Presence of Jump Risk. Johannes Gutenberg-Universit\\"{at Mainz, Germany.
Hamilton, J. D. (1988). Rational-expectations econometric analysis of changes in regime: an investigation of term structure of interest rates. Journal of Economic Dynamics and Control. Vol 12, 385-423.
Hamilton, J. D (1989). A new approach to the economic analysis of nonstationary
time series and the business cycle. Econometrica. Vol. 57, 357-384.
Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press, Princeton.
Harrison, J. M. and Kreps, D. M. (1979). Mattingales and arbitrage in securities markets. Journal of Economic Theory. Vol. 20, 381-408.
Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with
applications to bond and currency options. Review of Financial Studies.
Vol. 6, 327-343.
Heston, S. L., and Nandi, S. A (2000). A closed-form $GARCH$ option valuation
Model. Review of Financial Studies. Vol. 13, 585-625.
Heyde, C. C. and Yang, Y. (1997). On defining long range dependence. Journal of
Applied probability. Vol. 34, 939-944.
Hull, J. C. (2002). Options, Futures, and Other Derivative Securities.
Prentice Hall, New Jersey.
Hull, J. C. and White, A. (1987). The pricing of options on assets with stochastic volatilities. Journal of Finance. Vol 42, 281-300.
Karatzas, I. and Shreve, S. (1998). Methods of Mathematical Finance.
Springer-Verlag, New York.
Kou, S. G. (2002). A jump diffusion model for option pricing. Management Science. Vol. 48, 1086-1101.
Last, G. and Brandt, A. (1995). Marked Point Processes on the Real Line:
The Dynamic Approach. Springer-Verlag, New York.
Lucas, R. E. (1978). Asset prices in an exchange economy. Econometrica. Vol. 46, 1429-1445.
Mandelbrot, B. (1963). The variation of certain speculative prices. Journal of Business. Vol. 36, 394-419.
Merton, R. C. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science. Vol. 4, 141-183.
Merton, R. C. (1976). Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics. Vol. 3, 125-144.
Naik, V. and Lee, M. (1990). General equilibrium pricing of options on the market portfolio with discontinuous return. Review of Financial Studies. Vol. 3, 493-521.
Robinson, P. M. (1994). Semiparametric analysis of long-memory time series.
Annals of Statistics. Vol. 22, 515-539.
Robinson, P. M. (1995), Gaussian semiparametric estimation of long range dependence. Annals of Statistics. Vol. 23, 1630-1661.
Ross, S. M. (1999). An Introduction to Mathematical Finance: Option and Other Topics. Cambridge University Press, Cambridge.
Samuelson, P. A. (1973). Mathematics of speculative price. SIAM Review. Vol. 15, 1-42.
Shephard, N. (1996). Statistical aspects of $ARCH$ and stochastic volatility.
Time Series Models in Econometrics, Finance and Other Fields. Vol. 1, 1-67.
Shiryaev, A. N. (1999). Essentials of Stochastic Finance: Facts, Models,
Theory. World Scientific, Singapore.
Stokey, N. L. and Lucas, R. E. (1989). Recursive Methods in Economic Dynamics.
Harvard University Press, Cambridge.
Stein, E. M. and Stein, C. J. (1991). Stock prices distribution with stochastic volatility, an analytic approach. Review of Financial Studies. Vol. 4, 727-752.
Taylor, S. J. (1982). Financial returns modeled by the product of two stochastic processes-a study of the daily sugar prices 1961-1975. Time Series Analysis: Theory and Practice. Vol. 1, 203-226.
Taylor, S. J. (1986). Modeling Financial Time Series. John Wiley, Chichester.
Taylor, S. J. (1994). Modelling stochastic volatility. Mathematical Finance. Vol 4, 183-204.
Wiggins, J. B. (1987). Option values under stochastic volatility:
theory and empirical estimates. Journal of Financial Economics. Vol. 19, 351-372.
描述 博士
國立政治大學
統計研究所
88354503
92
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0088354503
資料類型 thesis
dc.contributor.advisor 傅承德<br>翁久幸zh_TW
dc.contributor.advisor Fuh, Cheng-Der<br>Weng, Chiu-Hsingen_US
dc.contributor.author (Authors) 林士貴zh_TW
dc.contributor.author (Authors) Lin, Shih-Kueien_US
dc.creator (作者) 林士貴zh_TW
dc.creator (作者) Lin, Shih-Kueien_US
dc.date (日期) 2003en_US
dc.date.accessioned 18-Sep-2009 19:08:37 (UTC+8)-
dc.date.available 18-Sep-2009 19:08:37 (UTC+8)-
dc.date.issued (上傳時間) 18-Sep-2009 19:08:37 (UTC+8)-
dc.identifier (Other Identifiers) G0088354503en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/36657-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計研究所zh_TW
dc.description (描述) 88354503zh_TW
dc.description (描述) 92zh_TW
dc.description.abstract (摘要) 為了改進Black-Scholes模式的實證現象，許多其他的模型被建議有leptokurtic特性以及波動度聚集的現象。然而對於其他的模型分析的處理依然是一個問題。在本論文中，我們建議使用馬可夫跳躍擴散過程，不僅能整合leptokurtic與波動度微笑特性，而且能產生波動度聚集的與長記憶的現象。然後，我們應用Lucas的一般均衡架構計算選擇權價格，提供均衡下當跳躍的大小服從一些特別的分配時則選擇權價格的解析解。特別地，考慮當跳躍的大小服從兩個情況，破產與lognormal分配。當馬可夫跳躍擴散模型的馬可夫鏈有兩個狀態時，稱為轉換跳躍擴散模型，當跳躍的大小服從lognormal分配我們得到選擇權公式。使用轉換跳躍擴散模型選擇權公式，我們給定一些參數下研究公式的數值極限分析以及敏感度分析。zh_TW
dc.description.abstract (摘要) To improve the empirical performance of the Black-Scholes model, many alternative models have been proposed to address the leptokurtic feature of the asset return distribution, and the effects of volatility clustering phenomenon. However,
     analytical tractability remains a problem for most of the alternative models. In this dissertation, we propose a Markov jump diffusion model, that can not only incorporate both the leptokurtic feature and volatility smile, but also present the economic features of volatility clustering and long memory.
     Next, we apply Lucas`s general equilibrium framework to evaluate option price, and to provide analytical solutions of the equilibrium price for European call options when the jump size follows some specific distributions. In particular, two cases are considered, the defaultable one and the lognormal distribution. When the underlying Markov chain of the Markov jump diffusion model has two states, the so-called switch jump diffusion model, we write an explicit analytic formula under the jump size has a lognormal distribution. Numerical approximations of the option prices as well as sensitivity analysis are also given.		en_US
dc.description.tableofcontents 1. INTRODUCTION ...... 1
     1.1 The Black-Scholes model ...... 3
     1.2 The jump diffusion model ...... 5
     1.3 The Markov jump diffusion model ...... 6
     1.4 Comparison with other models ...... 9
     
     2. GENERAL FRAMEWORK OF THE MODEL ...... 14
     
     2.1 Structure and assumptions ...... 15
     2.2 Markov modulated Poisson processes ...... 21
     
     3. EMPIRICAL PERFORMANCE ...... 27
     3.1 Leptokurtic and clustering features...... 27
     3.2 Long memory phenomenon ...... 34
     
     4. OPTION PRICING: THEORY ...... 41
     4.1 General equilibrium for Markov jump diffusion models .. 44
     4.2 Option pricing ...... 49
     
     5. OPTION PRICING: NUMERICAL ANALYSIS ...... 57
     5.1 Volatility smile and surface ...... 57
     5.2 Approximation of option prices ...... 60
     5.3 Sensitivity analysis ...... 64
     
     6. CONCLUSIONS AND FUTURE RESEARCHES ...... 67
     REFERENCE ...... 69		zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0088354503en_US
dc.subject (關鍵詞) 均衡分析zh_TW
dc.subject (關鍵詞) 歐式選擇權zh_TW
dc.subject (關鍵詞) 拉氏倒轉變換zh_TW
dc.subject (關鍵詞) 長記憶zh_TW
dc.subject (關鍵詞) 馬可夫跳躍擴散模型zh_TW
dc.subject (關鍵詞) 馬可夫控制瓦松過程zh_TW
dc.subject (關鍵詞) 數值倒轉方法zh_TW
dc.subject (關鍵詞) 換跳躍擴散過程zh_TW
dc.subject (關鍵詞) 變波動聚集zh_TW
dc.subject (關鍵詞) 波動度微笑zh_TW
dc.subject (關鍵詞) Equilibrium analysisen_US
dc.subject (關鍵詞) European call optionen_US
dc.subject (關鍵詞) Laplace inverse transformen_US
dc.subject (關鍵詞) Leptokurticen_US
dc.subject (關鍵詞) Long memoryen_US
dc.subject (關鍵詞) Markov jump diffusion modelen_US
dc.subject (關鍵詞) Markov modulated Poisson processen_US
dc.subject (關鍵詞) Numerical inversion methoden_US
dc.subject (關鍵詞) Switch jump diffusion modelen_US
dc.subject (關鍵詞) Volatility clusteringen_US
dc.subject (關鍵詞) Volatility smileen_US
dc.title (題名) Empirical Performance and Asset Pricing in Markov Jump Diffusion Modelszh_TW
dc.title (題名) 馬可夫跳躍擴散模型的實證與資產定價zh_TW
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Abate, J. and Whitt, W. (1992). Numerical inversion ofzh_TW
dc.relation.reference (參考文獻) probability generating functions. Operations Research Letters.zh_TW
dc.relation.reference (參考文獻) Vol. 12, 245-251.zh_TW
dc.relation.reference (參考文獻) Andersen, L. and Andreasen, J. (2000). Volatility skews and extensions of the libor market model. Applied Mathematical Finance. Vol. 7, 1-32.zh_TW
dc.relation.reference (參考文獻) Andersen, T. (1996). Return volatility and trading volume: anzh_TW
dc.relation.reference (參考文獻) information flow interpretation of stochastic volatility. it Journal of Finance. Vol. 51, 169-204.zh_TW
dc.relation.reference (參考文獻) Attari, M. (1999). Discontinuous interest rate processes:zh_TW
dc.relation.reference (參考文獻) An equilibrium model for bond option prices. The Journal of Financial and Quantitative Analysis. Vol. 34, 293-322.zh_TW
dc.relation.reference (參考文獻) Bardorff-Nielsen, O. E. and Cox, D. R. (1989). Asymptotic Techniques for Usezh_TW
dc.relation.reference (參考文獻) in Statistics. Chapman and Hall, New York.zh_TW
dc.relation.reference (參考文獻) Bjork, T., Kabanov, Y. and Runggaldier, W. (1997). Bond market structurezh_TW
dc.relation.reference (參考文獻) in the presence of Marked point processes, Mathematical Finance. Vol. 7, 211-239.zh_TW
dc.relation.reference (參考文獻) Black, F. and Scholes, M. (1973).zh_TW
dc.relation.reference (參考文獻) The pricing of options and corporate liabilities. Journal of Political Economy.zh_TW
dc.relation.reference (參考文獻) Vol. 81, 637-654.zh_TW
dc.relation.reference (參考文獻) Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity.zh_TW
dc.relation.reference (參考文獻) Journal of Econometrics. Vol. 31, 307-327.zh_TW
dc.relation.reference (參考文獻) Bollerslev, T., Engle, R. F. and Nelson, D. B. (1994). ARCH models. Handbook of Econometrics. Vol. 4, 2959-3038.zh_TW
dc.relation.reference (參考文獻) Boyle, P., Broadie, M. and Glasserman, P. (1997). Simulation methodszh_TW
dc.relation.reference (參考文獻) for security pricing. Journal of Economic Dynamics and Control. Vol 21,zh_TW
dc.relation.reference (參考文獻) 1267-1321.zh_TW
dc.relation.reference (參考文獻) Clark, P. K. (1973). Asubordinated stochastic process model with finitezh_TW
dc.relation.reference (參考文獻) variance for speculative prices. Econometrica. Vol. 41, 131-155.zh_TW
dc.relation.reference (參考文獻) Cochrane, J. H. (2001). Asset Pricing. Princeton University Press, Princeton.zh_TW
dc.relation.reference (參考文獻) Cox, J., Ingersoll, E. and Ross, S. A. (1985). A theory of the term structurezh_TW
dc.relation.reference (參考文獻) of interest rates. Econometrica. Vol. 53, 385-407.zh_TW
dc.relation.reference (參考文獻) Cox, J. and Ross, S. (1976). The valuation of options for alternative stochastic processes. Journal of Financial Economics. Vol. 3, 145-166.zh_TW
dc.relation.reference (參考文獻) Das, S. R. and Foresi, S. (1996). Exact solutions for bond and option priceszh_TW
dc.relation.reference (參考文獻) with systematic jump risk. Review Derivatives Research. Vol. 1, 7-24.zh_TW
dc.relation.reference (參考文獻) Davydov, D. and Linetsky, V. (2001). The valuation and hedging of path-dependentzh_TW
dc.relation.reference (參考文獻) options under the CEV process. Management Science. Vol. 47, 949-965.zh_TW
dc.relation.reference (參考文獻) Diebold, F. X. and Inoue, A. (2001). Long memory and regime switching.zh_TW
dc.relation.reference (參考文獻) Journal of Econometrics. Vol. 105, 131-159.zh_TW
dc.relation.reference (參考文獻) Di Masi, G. B., Kabanov, Yu, M., and Runggaldier, W. J. (1994).zh_TW
dc.relation.reference (參考文獻) Mean-variance hedging of options on stocks with Markov volatility.zh_TW
dc.relation.reference (參考文獻) Theory of Probability and Its Applications, vol 39, 173-181.zh_TW
dc.relation.reference (參考文獻) Duan, J. C. (1995). The $GARCH$ option pricing model. Mathematical Finance.zh_TW
dc.relation.reference (參考文獻) Vol. 5, 13-32.zh_TW
dc.relation.reference (參考文獻) Duffie, D. (2001). Dynamic Asset Pricing Theory. Princeton University Press, Princeton.zh_TW
dc.relation.reference (參考文獻) Duffie, D., Pan, J. and Singleton, K. (2000). Transform analysis and optionzh_TW
dc.relation.reference (參考文獻) pricing for affine jump-diffusions. Econometrica. Vol. 68, 1343-1376.zh_TW
dc.relation.reference (參考文獻) Duffie, D. and Singleton, K. (1999). Modeling term structures ofzh_TW
dc.relation.reference (參考文獻) defaultable bonds. Review of Financial Studies. Vol. 12, 687-720.zh_TW
dc.relation.reference (參考文獻) Elliot, R. J. and Kopp, P. E. (1999). Mathematics of Financial Markets.zh_TW
dc.relation.reference (參考文獻) Spinger, New York.zh_TW
dc.relation.reference (參考文獻) Engle, R. (1982). Autoregressive conditional heteroscedasticityzh_TW
dc.relation.reference (參考文獻) with estimates of the variance of U.K. inflation. Econometrica. Vol. 50, 987-1008.zh_TW
dc.relation.reference (參考文獻) Fuh, C. D., Hu, I. and Lin, S. K. (2002). Empirical performance and asset pricing in hidden Markov models. Communications in Statistics : Theory and Methods. Vol. 32, 2479-2514.zh_TW
dc.relation.reference (參考文獻) Geweke, J., and Porter-Hudak, S. (1983). The estimation and application of long-memory time series models. {Journal of Time Series Analysis. Vol. 4, 221-238.zh_TW
dc.relation.reference (參考文獻) Ghysels, E., Harvey, A. C. and Renault, E. (1996). Stochastic volatility.zh_TW
dc.relation.reference (參考文獻) Handbook of Statistics. Vol. 14, 119-191.zh_TW
dc.relation.reference (參考文獻) Glasserman, P. and Kou, S. G. (2003). The term structure of simplezh_TW
dc.relation.reference (參考文獻) forward rates with jump risk. Mathematical finance. Vol. 13, 383-410.zh_TW
dc.relation.reference (參考文獻) Grunewald, B. and Trautmann, S. (1996).zh_TW
dc.relation.reference (參考文獻) Option Hedging in the Presence of Jump Risk. Johannes Gutenberg-Universit\\"{at Mainz, Germany.zh_TW
dc.relation.reference (參考文獻) Hamilton, J. D. (1988). Rational-expectations econometric analysis of changes in regime: an investigation of term structure of interest rates. Journal of Economic Dynamics and Control. Vol 12, 385-423.zh_TW
dc.relation.reference (參考文獻) Hamilton, J. D (1989). A new approach to the economic analysis of nonstationaryzh_TW
dc.relation.reference (參考文獻) time series and the business cycle. Econometrica. Vol. 57, 357-384.zh_TW
dc.relation.reference (參考文獻) Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press, Princeton.zh_TW
dc.relation.reference (參考文獻) Harrison, J. M. and Kreps, D. M. (1979). Mattingales and arbitrage in securities markets. Journal of Economic Theory. Vol. 20, 381-408.zh_TW
dc.relation.reference (參考文獻) Heston, S. L. (1993). A closed-form solution for options with stochastic volatility withzh_TW
dc.relation.reference (參考文獻) applications to bond and currency options. Review of Financial Studies.zh_TW
dc.relation.reference (參考文獻) Vol. 6, 327-343.zh_TW
dc.relation.reference (參考文獻) Heston, S. L., and Nandi, S. A (2000). A closed-form $GARCH$ option valuationzh_TW
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