English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  Items with full text/Total items : 93889/124336 (76%)
Visitors : 28949409      Online Users : 528
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
  • Adv. Search
    HomeLoginUploadHelpAboutAdminister Goto mobile version
    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/36657
    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/36657

    Title: Empirical Performance and Asset Pricing in Markov Jump Diffusion Models
    Authors: 林士貴
    Lin, Shih-Kuei
    Contributors: 傅承德

    Fuh, Cheng-Der
    Weng, Chiu-Hsing

    Lin, Shih-Kuei
    Keywords: 均衡分析
    Equilibrium analysis
    European call option
    Laplace inverse transform
    Long memory
    Markov jump diffusion model
    Markov modulated Poisson process
    Numerical inversion method
    Switch jump diffusion model
    Volatility clustering
    Volatility smile
    Date: 2003
    Issue Date: 2009-09-18 19:08:37 (UTC+8)
    Abstract: 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.
    Reference: 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,
    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.
    Description: 博士
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0088354503
    Data Type: thesis
    Appears in Collections:[統計學系] 學位論文

    Files in This Item:

    File SizeFormat

    All items in 政大典藏 are protected by copyright, with all rights reserved.

    社群 sharing

    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - Feedback