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題名 考慮違約風險與隨機利率模型下匯率連結外幣資產選擇權定價
作者 吳宥璇
Wu, Yu-Hsuan
貢獻者 林士貴
Lin, Shih-Kuei
吳宥璇
Wu, Yu-Hsuan
關鍵詞 信用風險
衍生性商品定價
匯率連結外幣資產選擇權
HJM利率模型
Credit risk
Derivatives pricing model
Foreign currency derivatives
HJM interest rate Model
日期 2020
上傳時間 5-Feb-2020 17:31:04 (UTC+8)
摘要 匯率衍生性金融商品皆屬於店頭市場 (over-the-counter, OTC) 交易，且匯率波動與本國及外國之利率有一定的關係，在評價匯率衍生性金融商品時，若忽略交易對手違約風險與利率波動及匯率之相關性，將有失其適用性。因此本文考量違約風險與隨機利率模型兩個因子來評價匯率選擇權，本研究在信用風險因子的模型設定中，進一步加入HJM (Heath, Jarrow and Morton, 1992) 遠期利率模型架構，進而求得隨機利率下考慮違約風險之匯率連動選擇權評價模型。本文將此評價模型應用於最常見的四種匯率連結外幣資產選擇權為範例，探討其在隨機利率與信用風險下合理的價格，以提供投資人來因應匯率風險管理的避險需求。並採用市場歷史資料來估計各個參數，計算四種不同匯率連結外幣資產選擇權價格，針對違約風險、到期日長短、標的資產波動度做敏感度分析，採用數值結果來了解信用風險對於衍生性商品價格的影響。
Most of foreign currency derivatives belong to the over-the-counter (OTC). Moreover, the volatility of exchange rate is greatly affected by the dynamics of both domestic and foreign interest rates. Therefore, if the foreign currency derivatives are priced without the consideration of the counterparty default risk and interest rate, their pricing may cause some pricing error. To solve this problem, this paper presents a pricing formula for foreign currency options with the consideration of the credit risk under the HJM interest rate model. This paper applies this pricing model to the four most common exchange rate-linked options on foreign assets to build its reasonable price with the consideration of the credit risk and interest rate risk. To provide investors manage currency risk. This paper use historical market data to estimate each parameter and calculate the price of four different exchange rate-linked options on foreign assets. Using numerical results to understand the impact of default risk, maturity, and the volatility of underlying asset on the prices of derivative commodity.
參考文獻 [1]Amin K., and Jarrow R.A. (1991), “Pricing Foreign Currency Options under Stochastic Interest Rate, ” Journal of International Money and Finance, Vol.10,310-329.
[2]Black, F., M., Scholes, 1973, “The Pricing of Options and Corporate Liabilities,” Journal of Political & Economy, Vol.81,637-659.
[3]Bodurtha, J., and Courtadon, G., 1987, “Tests of an American Option Pricing Model on the Foreign Currency Options Market,” Journal of Financial and Quantitative Analysis, Vol.22,153-167.
[4]Grabbe, J. O., 1983, “The Pricing of Call and Put Option on Foreign Exchange,” Journal of International Money and FinanceVol.2, 239-253.
[5]Heath, D. C., Jarrow, R.A., Morton, A. J., 1992, “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation,” Econometrica, Vol.60(1), 77-105.
[6]Hilliard, J.E., J. Madura and A.L. Tucker, 1991, “Currency Option Pricing with Stochastic Domestic and Foreign Interest Rates,” Journal of Financial and Quantitative Analysis, Vol.26(2),139-151.
[7]Hull, J. C., A., White, 1995, “The Impact of Default Risk on the Prices of Options and Other Derivative Securities,” Journal of Banking & Finance, Vol.19, 299-322.
[8]Johnson, H., R., Stulz, 1987, “The Pricing of Options with Default Risk,” Journal of Finance, Vol.42, 267-280.
[9]Jarrow, R. A., S. M., Turnbull, 1995, “Pricing Derivatives on Financial Securities Subject to Credit Risk,” Journal of Finance, Vol.50, 53-85.
[10]Jarrow, R. A., and Turnbull, S. M. 2000, “The Intersection of Market and Credit Risk,” Journal of Banking & Finance, Vol.24, 271-299.
[11]Jarrow, R. A., and Yu, F. 2001, “Counterparty Risk and the Pricing of Defaultable Securities,” Journal of Finance, Vol.56, 1765-1799.
[12]Klein, P. C., 1996, “Pricing Black-Scholes Options with Correlated Credit Risk,” Journal of Banking and Finance, Vol. 20, 1211-1229.
[13]Klein, P.C., Inglis, M., 2001 ,“Pricing Vulnerable European Options when the Option`s Payoff can Increase the Risk of Financial Distress,” Journal of Banking and Finance, Vol. 25, 993-1012.
[14]Li, G., and Zhang, C., 2019, “Counterparty Credit Risk and Derivatives Pricing,” Journal of Financial Economics, Vol.134, 647-668.
[15]Pan, G. G., and Wu, T. C. , 2008, “Pricing Vulnerable Options,” Journal of Financial Studies, Vol.16, 131-158.
[16]Reiner, E., 1992, “Quanto Mechanics,” From Black-Scholes to Black Holes, Risk Magazine, Vol.5, 147-151.
[17]Rabinovitch, R., 1989, “Pricing Stock and Bond Option when Default-Rate is Stochastic,” Journal of Financial and Quantitative Analysis, Vol.24, 447-457.
[18]Shreve, S. E., 2004. “Stochastic Calculus for Finance II: Continuous-Time Models,” Springer-Verlag, New York.
[19]Tian, L.H., Wang, G.Y., Wang, X.C. and Wang, Y.J., 2014, “Pricing Vulnerable Options with Correlated Credit Risk Under Jump‐Diffusion Processes. ” The Journal of Futures Markets, Vol. 34, 957-979.
描述 博士
國立政治大學
金融學系
100352504
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0100352504
資料類型 thesis
dc.contributor.advisor 林士貴zh_TW
dc.contributor.advisor Lin, Shih-Kueien_US
dc.contributor.author (Authors) 吳宥璇zh_TW
dc.contributor.author (Authors) Wu, Yu-Hsuanen_US
dc.creator (作者) 吳宥璇zh_TW
dc.creator (作者) Wu, Yu-Hsuanen_US
dc.date (日期) 2020en_US
dc.date.accessioned 5-Feb-2020 17:31:04 (UTC+8)-
dc.date.available 5-Feb-2020 17:31:04 (UTC+8)-
dc.date.issued (上傳時間) 5-Feb-2020 17:31:04 (UTC+8)-
dc.identifier (Other Identifiers) G0100352504en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/128565-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 金融學系zh_TW
dc.description (描述) 100352504zh_TW
dc.description.abstract (摘要) 匯率衍生性金融商品皆屬於店頭市場 (over-the-counter, OTC) 交易，且匯率波動與本國及外國之利率有一定的關係，在評價匯率衍生性金融商品時，若忽略交易對手違約風險與利率波動及匯率之相關性，將有失其適用性。因此本文考量違約風險與隨機利率模型兩個因子來評價匯率選擇權，本研究在信用風險因子的模型設定中，進一步加入HJM (Heath, Jarrow and Morton, 1992) 遠期利率模型架構，進而求得隨機利率下考慮違約風險之匯率連動選擇權評價模型。本文將此評價模型應用於最常見的四種匯率連結外幣資產選擇權為範例，探討其在隨機利率與信用風險下合理的價格，以提供投資人來因應匯率風險管理的避險需求。並採用市場歷史資料來估計各個參數，計算四種不同匯率連結外幣資產選擇權價格，針對違約風險、到期日長短、標的資產波動度做敏感度分析，採用數值結果來了解信用風險對於衍生性商品價格的影響。zh_TW
dc.description.abstract (摘要) Most of foreign currency derivatives belong to the over-the-counter (OTC). Moreover, the volatility of exchange rate is greatly affected by the dynamics of both domestic and foreign interest rates. Therefore, if the foreign currency derivatives are priced without the consideration of the counterparty default risk and interest rate, their pricing may cause some pricing error. To solve this problem, this paper presents a pricing formula for foreign currency options with the consideration of the credit risk under the HJM interest rate model. This paper applies this pricing model to the four most common exchange rate-linked options on foreign assets to build its reasonable price with the consideration of the credit risk and interest rate risk. To provide investors manage currency risk. This paper use historical market data to estimate each parameter and calculate the price of four different exchange rate-linked options on foreign assets. Using numerical results to understand the impact of default risk, maturity, and the volatility of underlying asset on the prices of derivative commodity.en_US
dc.description.tableofcontents 第一章 緒論 7
第一節 研究動機與目的 7
第二節 研究架構 11
第二章 模型設定 11
第一節 模型基本假設 11
第二節 測度轉換 18
第三章 匯率連結外幣資產選擇權在考慮違約風險下的評價 23
第一節 違約風險下的彈性匯率外幣資產選擇權 23
第二節 違約風險下的合成選擇權 25
第三節 違約風險下的固定匯率外幣資產選擇權 26
第四節 違約風險下的外幣資產連結匯率選擇權 28
第四章 匯率連結外幣資產選擇權在考慮隨機利率模型下的評價 30
第一節 隨機利率模型下的彈性匯率外幣資產選擇權 30
第二節 隨機利率模型下的合成選擇權 31
第三節 隨機利率模型下的固定匯率外幣資產選擇權 32
第四節 隨機利率模型下的外幣資產連結匯率選擇權 33
第五章 匯率連結外幣資產選擇權在考慮違約風險與隨機利率模型下的評價 34
第一節 違約風險與隨機利率模型下的彈性匯率外幣資產選擇權 34
第二節 違約風險與隨機利率模型下的合成選擇權 36
第三節 違約風險與隨機利率模型下的固定匯率外幣資產選擇權 37
第四節 違約風險與隨機利率模型下的外幣資產連結匯率選擇權 39
第六章 數值分析 41
第一節 參數設定與數值結果 41
第二節 敏感度分析－發行公司資產波動度 43
第三節 敏感度分析－到期日長短 47
第四節 敏感度分析－標的資產波動度 51
第七章 穩健性檢視 55
第一節 敏感度分析－發行公司資產波動度 56
第二節 敏感度分析－到期日長短 64
第三節 敏感度分析－標的資產波動度 71
第八章 結論 77
參考文獻 78
Appendix A. 風險中立測度、輔助測度下相對價格之動態過程 80
Appendix B. 國內遠期測度、輔助測度下相對價格之動態過程 85
Appendix C. 違約風險下的彈性匯率外幣資產選擇權 87
Appendix D. 違約風險下的合成選擇權 89
Appendix E. 違約風險下的固定匯率外幣資產選擇權 92
Appendix F. 違約風險下的外幣資產連結匯率選擇權 94
Appendix G. 隨機利率模型下的彈性匯率外幣資產選擇權 97
Appendix H. 隨機利率模型下的合成選擇權 98
Appendix I. 隨機利率模型下的固定匯率外幣資產選擇權 99
Appendix J. 隨機利率模型下的外幣資產連結匯率選擇權 101
Appendix K. 違約風險與隨機利率模型下的彈性匯率外幣資產選擇權 102
Appendix L. 違約風險與隨機利率模型下的合成選擇權 105
Appendix M. 違約風險與隨機利率模型下的固定匯率外幣資產選擇權 107
Appendix N. 違約風險與隨機利率模型下的外幣資產連結匯率選擇權 110		zh_TW
dc.format.extent 2507978 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0100352504en_US
dc.subject (關鍵詞) 信用風險zh_TW
dc.subject (關鍵詞) 衍生性商品定價zh_TW
dc.subject (關鍵詞) 匯率連結外幣資產選擇權zh_TW
dc.subject (關鍵詞) HJM利率模型zh_TW
dc.subject (關鍵詞) Credit risken_US
dc.subject (關鍵詞) Derivatives pricing modelen_US
dc.subject (關鍵詞) Foreign currency derivativesen_US
dc.subject (關鍵詞) HJM interest rate Modelen_US
dc.title (題名) 考慮違約風險與隨機利率模型下匯率連結外幣資產選擇權定價zh_TW
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1]Amin K., and Jarrow R.A. (1991), “Pricing Foreign Currency Options under Stochastic Interest Rate, ” Journal of International Money and Finance, Vol.10,310-329.
[2]Black, F., M., Scholes, 1973, “The Pricing of Options and Corporate Liabilities,” Journal of Political & Economy, Vol.81,637-659.
[3]Bodurtha, J., and Courtadon, G., 1987, “Tests of an American Option Pricing Model on the Foreign Currency Options Market,” Journal of Financial and Quantitative Analysis, Vol.22,153-167.
[4]Grabbe, J. O., 1983, “The Pricing of Call and Put Option on Foreign Exchange,” Journal of International Money and FinanceVol.2, 239-253.
[5]Heath, D. C., Jarrow, R.A., Morton, A. J., 1992, “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation,” Econometrica, Vol.60(1), 77-105.
[6]Hilliard, J.E., J. Madura and A.L. Tucker, 1991, “Currency Option Pricing with Stochastic Domestic and Foreign Interest Rates,” Journal of Financial and Quantitative Analysis, Vol.26(2),139-151.
[7]Hull, J. C., A., White, 1995, “The Impact of Default Risk on the Prices of Options and Other Derivative Securities,” Journal of Banking & Finance, Vol.19, 299-322.
[8]Johnson, H., R., Stulz, 1987, “The Pricing of Options with Default Risk,” Journal of Finance, Vol.42, 267-280.
[9]Jarrow, R. A., S. M., Turnbull, 1995, “Pricing Derivatives on Financial Securities Subject to Credit Risk,” Journal of Finance, Vol.50, 53-85.
[10]Jarrow, R. A., and Turnbull, S. M. 2000, “The Intersection of Market and Credit Risk,” Journal of Banking & Finance, Vol.24, 271-299.
[11]Jarrow, R. A., and Yu, F. 2001, “Counterparty Risk and the Pricing of Defaultable Securities,” Journal of Finance, Vol.56, 1765-1799.
[12]Klein, P. C., 1996, “Pricing Black-Scholes Options with Correlated Credit Risk,” Journal of Banking and Finance, Vol. 20, 1211-1229.
[13]Klein, P.C., Inglis, M., 2001 ,“Pricing Vulnerable European Options when the Option`s Payoff can Increase the Risk of Financial Distress,” Journal of Banking and Finance, Vol. 25, 993-1012.
[14]Li, G., and Zhang, C., 2019, “Counterparty Credit Risk and Derivatives Pricing,” Journal of Financial Economics, Vol.134, 647-668.
[15]Pan, G. G., and Wu, T. C. , 2008, “Pricing Vulnerable Options,” Journal of Financial Studies, Vol.16, 131-158.
[16]Reiner, E., 1992, “Quanto Mechanics,” From Black-Scholes to Black Holes, Risk Magazine, Vol.5, 147-151.
[17]Rabinovitch, R., 1989, “Pricing Stock and Bond Option when Default-Rate is Stochastic,” Journal of Financial and Quantitative Analysis, Vol.24, 447-457.
[18]Shreve, S. E., 2004. “Stochastic Calculus for Finance II: Continuous-Time Models,” Springer-Verlag, New York.
[19]Tian, L.H., Wang, G.Y., Wang, X.C. and Wang, Y.J., 2014, “Pricing Vulnerable Options with Correlated Credit Risk Under Jump‐Diffusion Processes. ” The Journal of Futures Markets, Vol. 34, 957-979.		zh_TW
dc.identifier.doi (DOI) 10.6814/NCCU202000075en_US