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    政大典藏 > College of Commerce > Department of MIS > Theses >  Item 140.119/35262


    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/35262


    Title: Valuation of Anerican Put Options: A Comparison of Existing Methods
    Authors: 邱景暉
    Contributors: 謝明華
    Hsieh,Ming-hua
    邱景暉
    Keywords: 美式賣權
    美式選擇權
    American put option
    American option
    Date: 2003
    Issue Date: 2009-09-18 14:34:55 (UTC+8)
    Abstract: 　美式賣權已經存在很長的時間，由於沒有公式解，目前只能利用數值分析方法(numerical analysis approach)和解析近似法(analytic approximations) 來評價它。這類的評價方法在文獻中相當多，但對這些方法的完整的比較卻相當貧乏。本文整理了27種評價方法和186種在文獻中常被引用的美式賣權契約，這些契約包含了各種不同狀態(有股利、沒有股利、價內、價平、價外、短到期日、長到期日)，後續的研究者可以用這些美式賣權契約來驗證他們的方法。本文實作其中14種方法並應用於上述的186種美式賣權契約上。這14種方法包含了樹狀法、有限差分法、蒙地卡羅法與解析近似法。從這些數值的結果中，本文根據精確度與計算效率整理出各種方法的優缺點與適用的時機。
    　由本文之數值分析，我們得到下列幾點結論：1.Binomial Black and Scholes with Richardson extrapolation of Broadie and Detemple (1996)與Extrapolated Flexible Binomial Model of Tian (1999)這二種方法在這14種方法中，在速度與精確度的考量下是最好的方法；2.在精確度要求在root mean squared relative error大約1%的情形下，解析近似法是最快的方法；3.Least-Squares Simulation method of Longstaff and Schwartz (2001)在評價美式賣權方面並不是一個有效的方法。
    American put option has existed for a long time. They cannot be valued by closed-form formula and require the use of numerical analysis methods and analytic approximations. There exists a great deal of methods for pricing American put option in related literatures. But a complete comparison of these methods is lacking. From literatures, we survey 27 methods and 186 commonly cited option contracts, including options on stock with dividend, non-dividend, in-the-money, at-money and out-of-money, short maturity and long maturity. In addition, we implement 14 methods, including lattice approaches, finite difference methods, Monte Carlo simulations and analytic approximations, and apply these methods to value the 186 option contracts above. From the numerical results, we summarize the advantages and disadvantages of each method in terms of speed and accuracy: 1.The binomial Black and Scholes with Richardson extrapolation of Broadie and Detemple (1996) and the extrapolated Flexible Binomial Model of Tian (1999) are both efficient improvements over the binomial method. 2.With root mean squared relative error about 1%, the analytic approximations are faster than the numerical analysis methods. 3.The Least-Squares Simulation method of Longstaff and Schwartz (2001) is not an effective method for pricing American put options.
    Reference: 1. Abramowitz, M. and I. A. Stegun, 1970, Handbook of Mathematical Functions, Dover Publications, New York.
    2. Amin, K., and A. Khanna, 1994, Convergence of American option values from discrete- to continuous-time financial models, Mathematical Finance 4, 289-304.
    3. Brennan, M., and E. Schwartz, 1977, The valuation of American put options, Journal of Finance 32, 449-462.
    4. Breen, R., 1991, The Accelerated Binomial Option Pricing Model, Journal of Financial and Quantitative Analysis 26, 153-164.
    5. Bunch, D., and H. Johnson, 1992, A Simple and Numerically Efficient Valuation Method for American Puts Using a Modified Geske-Johnson Approach, Journal of Finance 47, 809-816.
    6. Boyle, P., M. Broadie, and P. Glasserman, 1997, Monte Carlo methods for security pricing, Journal of Economic Dynamics & Control 21, 1267-1322.
    7. Barone-Adesi, G., and R. Whaley, 1987, Efficient Analytic Approximation of American Option Values, Journal of Finance 42, 301.-320
    8. Broadie M., and D. Jerome, 1996, American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods, The Review of Financial Studies 9, 1211-1250.
    9. Cox, J. C., S. A. Ross, and M. Rubinstein, 1979, Option Pricing: A Simplified Approach, Journal of Financial Economics 7, 229-263
    10. Carr, P., R. Jarrow, and R. Myneni, 1992, Alternative characterizations of American put options, Mathematical Finance 2, 87-106.
    11. Drezner Z., 1978, Computation of the Bivariate Normal Integral, Mathematics of Computation, 32, 277-279.
    12. David S. B. and H. Johnson, 2000, The American Put Option and Its Critical Stock Price, Journal of Finance, 55, 2333-2357.
    13. Geske, R., and H. E. Johnson, 1984, The American Put Option Valued Analytically, Journal of Finance 23, 1511-1524.
    14. Hull, J. C., and A. White, 1988, The Use of the Control Variate Technique in Option Pricing, Journal of Financial and Quantitative Analysis 23, 237-251
    15. Hull, J. C., and A. White, 1990, Valuing Derivative Securities Using the Explicit Finite Difference Method, Journal of Financial and Quantitative Analysis 25, 87-100.
    16. Huang J., M. G. Subrahmanyam, and G. G. Yu, 1996, Pricing and Hedging American Options: A Recursive Integration Method, The Review of Financial Studies 9, 277-300.
    17. Hull, J. C., 2003, Options, Futures, and Other Derivative Securities, 4th edition.
    18. Ibanez A., 2003, Robust pricing of the American put option: A note on Richardson extrapolation and the early exercise premium, Management Science 49, 1210-1228
    19. Johnson, H. E., 1983, An Analytic Approximation for the American Put Price, Journal of Financial and Quantitative Analysis 18, 141-149.
    20. Kim J., 1990, The Analytic Valuation of American Options, The Review of Financial Studies 3, 547-572.
    21. Kamrad B., and P. Ritchken, 1991, Multinomial approximating models for options with k-state variables, Management Science 37, 1640-1652
    22. Longstaff F., and E. Schwartz, 2001, Valuing American Options by Simulation：A Simple Least-Squares Approach, The Review of Financial Studies 14, 113-147
    23. Leisen, and P. J. Dietmar, 1998, Pricing the American put option: A detailed convergence analysis for binomial models, Journal of Economic Dynamics & Control 22, 1419-1435.
    24. Leisen, and P. J. Dietmar, 1999, The random-time binomial model, Journal of Economic Dynamics & Control 23, 1355-1386.
    25. Moreno M., and J. F. Navas., 2003, On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives, Review of Derivatives Research 6, 107-128
    26. Nengjiu J., and R. Zhong, 1999, An approximate formula for pricing American options, Journal of Derivatives 7, 31-41.
    27. Parkinson M., 1977, Option Pricing – The American Put, The Journal of Business 50, 21-36.
    28. Pantazopoulos K. N., E. N. Houstis, and S. Kortesis, 1998, Front-Tracking Finite Difference Methods for the Valuation of American Options, Computational Economics 12, 255-273.
    29. Rogers L. C. G., 2002, Monte Carlo valuation of American options, Mathematical Finance 12, 271-286.
    30. Stephen E., 1996, A note on modified lattice approaches to option pricing, Journal of Futures Markets 16, 585-594.
    31. Sullivan M, 2000, Valuing American put options using Gaussian quadrature, The Review of Financial Studies 13, 75-94.
    32. Trigeorgis, L., 1991, A Log-Transformed Binomial Numerical Analysis Method for Valuing Complex Multi-Option Investments, Journal of Financial and Quantitative Analysis 26, 309-326
    33. Tian, Y., 1999, A flexible binomial option pricing model, The Journal of Futures Markets 19, 817-843.
    Description: 碩士
    國立政治大學
    資訊管理研究所
    91356036
    92
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0913560361
    Data Type: thesis
    Appears in Collections:[Department of MIS] Theses

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