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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/99312


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    题名: GARCH-Lévy匯率選擇權評價模型 與實證分析
    Pricing Model and Empirical Analysis of Currency Option under GARCH-Lévy processes
    作者: 朱苡榕
    Zhu, Yi Rong
    贡献者: 林士貴
    蔡紋琦
    Lin, Shih Kuei
    Tsai, Wen Chi
    朱苡榕
    Zhu, Yi Rong
    关键词: 匯率選擇權評價
    GARCH
    Lévy過程
    跳躍風險
    波動聚集
    Currency option pricing formula
    GARCH
    Lévy-process
    Jump risk
    Volatility clustering
    日期: 2016
    上传时间: 2016-07-20 16:52:24 (UTC+8)
    摘要: 本研究利用GARCH動態過程的優點捕捉匯率報酬率之異質變異與波動度叢聚性質，並以GARCH動態過程為基礎，考慮跳躍風險服從Lévy過程，再利用特徵函數與快速傅立葉轉換方法推導出GARCH-Lévy動態過程下的歐式匯率選擇權解析解。以日圓兌換美元(JPY/USD)之歐式匯率選擇權為實證資料，比較基準GARCH選擇權評價模型與GARCH-Lévy選擇權評價模型對市場真實價格的配適效果與預測能力。實證結果顯示，考慮跳躍風險為無限活躍之Lévy過程，即GARCH-VG與GARCH-NIG匯率選擇權評價模型，不論是樣本內的評價誤差或是在樣本外的避險誤差皆勝於考慮跳躍風險為有限活躍Lévy過程的GARCH-MJ匯率選擇權評價模型。整體而言，本研究發現進行匯率選擇權之評價時，GARCH-NIG匯率選擇權評價模型有較小的樣本內及樣本外評價誤差。
    In this thesis, we make use of GARCH dynamic to capture volatility clustering and heteroskedasticity in exchange rate. We consider a jump risk which follows Lévy process based on GARCH model. Furthermore, we use characteristic function and fast fourier transform to derive the currency option pricing formula under GARCH-Lévy process. We collect the JPY/USD exchange rate data for our empirical analysis and then compare the goodness of fit and prediction performance between GARCH benchmark and GARCH-Lévy currency option pricing model. The empirical results show that either in-sample pricing error or out-of-sample hedging performance, the infinite-activity Lévy process, GARCH-VG and GARCH-NIG option pricing model is better than finite-activity Lévy process, GARCH-MJ option pricing model. Overall, we find using GARCH-NIG currency option pricing model can achieve the lower in-sample and out-of sample pricing error.
    參考文獻: [1] Amin, K., Jarrow, R. A., 1991. Pricing foreign currency options under stochastic interest rates. Journal of International Money and Finance, 10: 310-329.
    [2] Bakshi, G., Cao, C., & Chen, Z. W., 1997. Empirical performance of alternative option pricing models. Journal of Finance, 52: 2003-2049.
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    [6] Bates, D. S., 1996. Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options. Review of Financial Studies, 9: 69-107.
    [7] Biger, N., Hull, J., 1983. The valuation of currency options. Financial Management, 12: 24-28.

    [8] Bollerslev, T., 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31: 307-327.
    [9] Christoffersen, P., Jacobs, K., & Mimouni, K., 2010. Volatility dynamics for the S&P500: Evidence from realized volatility, daily returns, and option prices. Review of Financial Studies, 23: 3141-3189.
    [10] Christoffersen, P., Jacobs, K., & Ornthanalai, C., 2012. Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options. Journal of Financial Economics, 106: 447-472.
    [11] Christoffersen, P., Feunou, B., & Jeon, Y., 2015. Option valuation with observable volatility and jump dynamics. Journal of Banking and Finance, 61: 101-120.
    [12] Duan, J.C., 1995. The GARCH option pricing model. Mathematical Finance, 5: 13-32.
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    [15] Grabbe, J. O., 1983. The pricing of call and put options on foreign exchange. Journal of International Money and Finance, 2(3): 239-253.
    [16] Heston, S. L., 1993. A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 6: 327-343.
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    [18] Hull, J., White, A., 1987. The pricing of options on assets with stochastic volatilities. Journal of Finance, 42(2): 281-300.

    [19] Madan, D. B., Seneta, E., 1990. The variance gamma (V.G.) model for share market returns. Journal of Business, 63: 511-524.
    [20] Merton, R. C., 1976. Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics, 63: 3-50.

    [21] Nelson, D. B., 1991. Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59: 347-370.
    [22] Ornthanalai, C., 2014. Lévy jump risk: Evidence from options and returns. Journal of Financial Economics, 112: 69-90.
    [23] Sato, K., 1999. Lévy processes and infinitely divisible distributions. Cambridge University Press.
    描述: 碩士
    國立政治大學
    統計學系
    103354023
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0103354023
    数据类型: thesis
    显示于类别:[統計學系] 學位論文

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