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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/95492


    Title: Edgeworth 級數在選擇權定價之應用及實證研究
    Option pricing using Edgeworth series with empirical study
    Authors: 黃國倫
    Huang, kuo lun
    Contributors: 翁久幸
    Weng,chiu hsing
    黃國倫
    Huang,kuo lun
    Keywords: 微笑曲線
    錯價
    Edgeworth展開式
    volatility smile
    misprice
    Edgeworth expansion
    Date: 2010
    Issue Date: 2016-05-09 16:23:42 (UTC+8)
    Abstract: 被廣泛應用在選擇權定價的Black-Scholes 模型[3] 時常在深價內與深價外
    的選擇權價格有錯價的現象，也就是理論價格估計實際市場價格的偏差。藉由
    Black-Scholes 評價公式所反推出的隱含波動度往往不像我們所期待的在不同履約價格具有一致性，這種現象被稱為波動度的微笑曲線。在這份論文裡，我們參考Jarrow and Rudd [13] 提出的方法，將Edgeworth展開式套用在Black-Scholes模型作延伸應用，進而推導出偏態峰態修正後的的評價公式，再利用台指選擇權的市場資料作實證分析並與Filho and Rosenfeld [1] 的研究作比較。我們發現從台指選擇權的實證結果得到非常態分配的隱含偏態和隱含峰態。此外，理論價格的估計偏誤比例顯著的被新的模型改善且隱含波動度的微笑曲線也變的較為平坦，這個方法提供我們一個有效的方法，利用標的資產的偏態峰態得到該資產的近似分配。
    The Black-Scholes [3] option pricing model widely applied in option contracts frequently misprices deep-in-the-money and deep-out-of-the-money options. The implied volatilities computed by the Black-Scholes formula are not identical on each strike price as we expect. This phenomenon is called the volatility smile or skew. In this thesis, we derived a skewness- and kurtosis-adjusted option pricing model using an Edgeworth expansion constructed by Jarrow and Rudd [13] to an investigation of TAIEX option prices and compare the results with those in Filho and Rosenfeld [1]. We found that non-normal skewness and kurtosis are implied by TAIEX option returns. Moreover, the magnitude of price deviations were signicantly corrected and the volatility skew is
    attened. This approach provides an useful way to derive an approximate distribution of a underlying security with its skewness and kurtosis.
    Reference: [1] R. G. Balieiro Filho and R. Rosenfeld. Testing option pricing with Edgeworth expansion. Physica A, 344:484{490, 2004.
    [2] F. Black. Fact and fantasy in the use of options. Financial Analysts Journal, 31:36-72, 1975.
    [3] F. Black and M. Scholes. The pricing of options and corporate liabilities. Journal of Political Economy, 81:637{659, 1973.
    [4] L. Borland. Option pricing formulas based on a non-gaussian stock price model. Physical Review Letters, 89(9), 2002.
    [5] C. J. Corrado and T. Su. Implied volatility skews and stock index skewness and kurtosis in S&P 500 index returns implied by option prices. Journal of Financial Research, XIX(2):175{192, 1996.
    [6] C. J. Corrado and T. Su. S&P 500 index option tests of Jarrow and Rudd`s approximate option valuation formula. Journal of Futures Markets, 16(6):611{629, 1996.
    [7] C. J. Corrado and T. Su. Implied volatility skews and stock index skewness and kurtosis in S&P 500 index returns implied by option prices. The Journal of Derivatives, Summer:8{19, 1997.
    [8] P. Hall. The Bootstrap and Eedgeworth Expansion. New York: Springer-Verlagew York: Springer-Verlag, 1992.39
    [9] S. L. Heston. A closed form solution for options with stochastic volatility with application to bond and currency options. Review of Financial Studies, 6:327{344,1993.
    [10] J. Hull and A. White. The pricing of options on assets with stochastic volatilities. The Journal of Finance, 42:281{300, 1987.
    [11] J. C. Hull. Options, Futures, And Other Derivative Securities. Prentice-Hall, 1993.
    [12] D. Jackson. Fourier Series And Orthogonal Polynomials. Mathematical Association of America, 1941.
    [13] R. Jarrow and A. Rudd. Approximate option valuation for arbitrary stochastic processes. Journal of Financial Economics, 10:347{369, 1982.
    [14] J. D. MacBeth and J. D. Emannel. Further results on the contrast elasticity of variance call option pricing model. The Journal of Financial and Quantitative Analysis,
    19(4):533{554, 1982.
    [15] J. D. MacBeth and L. J. Merville. An empirical examination of the black-scholes call option pricing model. Journal of Finance, 34:1173{1186, 1979.
    [16] R. C. Merton. The theory of rational option pricing. Bell Journal of Economics and Management Science, 4:141{183, 1973.
    [17] S. Natenberg. Option Volatility & Pricing : Advanced Trading Strategies and Techniques. Irwin Professional Pub., 2 edition, 1994.
    [18] M. Rubinstein. Alternative paths to portfolio insurance. Financial Analysts Journal,
    41(4):42{52, 1985.
    [19] M. Rubinstein. Implied binomial trees. Journal of Finance, 49(3):771{818, 1994.
    Description: 碩士
    國立政治大學
    統計學系
    97354011
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0097354011
    Data Type: thesis
    Appears in Collections:[Department of Statistics] Theses

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