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題名 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
貢獻者 林士貴<br>蔡紋琦
Lin, Shih Kuei<br>Tsai, Wen Chi
朱苡榕
Zhu, Yi Rong
關鍵詞 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
上傳時間 20-Jul-2016 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.
[3] Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy, 81: 637-654.
[4] Bodurtha, J. N., Courtadon G. R., 1987. Tests of an American option pricing model on the foreign currency options market. Journal of Financial and Quantitative Analysis, 22(2): 153-167.
[5] Barndorff-Nielsen, O. E., 1997. Normal inverse Gaussian distributions and stochastic volatility modelling. Scandinavian Journal of Statistics, 24: 1-13.
[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.
[13] Eraker, B., 2004. Do stock prices and volatility jump? Reconciling evidence from spot and option prices. Journal of Finance, 59, 1367-1404.
[14] Garman, M., Kohlhagen, S., 1983. Foreign currency option values. Journal of
International Money and Finance, 2: 231–237.

[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.
[17] Heston, S. L., Nandi, S., 2000. A closed-form GARCH option valuation model. Review of Financial Studies, 13: 585-625.
[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
資料類型 thesis
dc.contributor.advisor 林士貴<br>蔡紋琦zh_TW
dc.contributor.advisor Lin, Shih Kuei<br>Tsai, Wen Chien_US
dc.contributor.author (Authors) 朱苡榕zh_TW
dc.contributor.author (Authors) Zhu, Yi Rongen_US
dc.creator (作者) 朱苡榕zh_TW
dc.creator (作者) Zhu, Yi Rongen_US
dc.date (日期) 2016en_US
dc.date.accessioned 20-Jul-2016 16:52:24 (UTC+8)-
dc.date.available 20-Jul-2016 16:52:24 (UTC+8)-
dc.date.issued (上傳時間) 20-Jul-2016 16:52:24 (UTC+8)-
dc.identifier (Other Identifiers) G0103354023en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/99312-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 103354023zh_TW
dc.description.abstract (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。zh_TW
dc.description.abstract (摘要) 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.en_US
dc.description.tableofcontents 第一章 緒論 1
1.1 研究動機 1
1.2 研究目的 3
第二章 文獻回顧 4
2.1 匯率選擇權評價模型 4
2.2 隨機波動度選擇權評價 5
2.3 GARCH 選擇權評價 6
第三章 GARCH-Lévy 匯率選擇權評價模型 9
3.1 報酬率與 Lévy 跳躍風險模型 9
3.2 GARCH 動態過程 14
3.3 測度轉換 16
3.4 匯率選擇權評價公式 19
3.5 參數估計方法 21
第四章 實證分析 23
4.1 匯率選擇權資料描述 23
4.2 匯率報酬率與匯率選擇權之敘述統計 25
4.3 模擬分析 27
4.4 模型評價表現 27
第五章 結論 29
參考文獻 30
附錄
附錄 A：測度轉換 32
附錄 B：特徵函數推導 37
附錄 C：匯率選擇權評價公式推導 42		zh_TW
dc.format.extent 1186747 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0103354023en_US
dc.subject (關鍵詞) 匯率選擇權評價zh_TW
dc.subject (關鍵詞) GARCHzh_TW
dc.subject (關鍵詞) Lévy過程zh_TW
dc.subject (關鍵詞) 跳躍風險zh_TW
dc.subject (關鍵詞) 波動聚集zh_TW
dc.subject (關鍵詞) Currency option pricing formulaen_US
dc.subject (關鍵詞) GARCHen_US
dc.subject (關鍵詞) Lévy-processen_US
dc.subject (關鍵詞) Jump risken_US
dc.subject (關鍵詞) Volatility clusteringen_US
dc.title (題名) GARCH-Lévy匯率選擇權評價模型 與實證分析zh_TW
dc.title (題名) Pricing Model and Empirical Analysis of Currency Option under GARCH-Lévy processesen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (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.
[3] Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy, 81: 637-654.
[4] Bodurtha, J. N., Courtadon G. R., 1987. Tests of an American option pricing model on the foreign currency options market. Journal of Financial and Quantitative Analysis, 22(2): 153-167.
[5] Barndorff-Nielsen, O. E., 1997. Normal inverse Gaussian distributions and stochastic volatility modelling. Scandinavian Journal of Statistics, 24: 1-13.
[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.
[13] Eraker, B., 2004. Do stock prices and volatility jump? Reconciling evidence from spot and option prices. Journal of Finance, 59, 1367-1404.
[14] Garman, M., Kohlhagen, S., 1983. Foreign currency option values. Journal of
International Money and Finance, 2: 231–237.

[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.
[17] Heston, S. L., Nandi, S., 2000. A closed-form GARCH option valuation model. Review of Financial Studies, 13: 585-625.
[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.		zh_TW