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題名 可違約互換率之匯率連動選擇權的評價
Valuation of Quanto Options on Defaultable Swap Rates
作者 陳宏銘
貢獻者 陳松男<br>林建秀
Chen, Son Nan<br>Lin, Chien Hsiu
陳宏銘
關鍵詞 匯率交換選擇權
LIBOR 市場模型
違約風險
信用衍生性商品
違約比率
Quanto swaptions
LIBOR market model
default risk
credit derivative
default ratio
日期 2015
上傳時間 17-Aug-2015 14:08:50 (UTC+8)
摘要 本文探討可違約互換率之匯率連動選擇權的評價，外國以及本國違約交
     換率的動態是建立在LIBOR 市場模型的框架。為了簡化推導過程，我們將
     原本本國以及外國交換率的雙動態轉為單一動態, 因此違約以及履約價將轉
     換為一個固定的常數比率來評價可違約互換率之匯率連動選擇權。由於商品
     本身是考量違約的情況，因此使用遠期的存活測度來評價可違約互換率之匯
     率連動選擇權。最後在數值分析的部分我們使用蒙地卡羅來模擬可違約互換
     率之匯率連動選擇權，理論值與模擬值的結果接近。
This study prices quanto options on defaultable swap rates (QODSR) in which domestic and foreign defaultable swap rates are considered in the LIBOR market model. We use two fixed ratios to price the QODSR with the default and strike rate
     property. The forward default-swap measure provides a simple method for valuing the QODSR. Numerical analysis is performed and compared with the Monte Carlo method to investigate the effects of volatility and default on the QODSR.
參考文獻 Amin, K. and Jarrow, R. (1991), ‘Pricing foreign currency options under stochastic interest
     rates’, Journal of International Money and Finance 10(3), 310–329.
     Bennett, M. N. . and Kennedy, J. E. . (2004), ‘Quanto pricing with copulas’, The Journal of
     Derivatives 12(1), 26–45.
     Bielecki, T. R. and Rutkowski, M. (2002), Credit risk: modeling, valuation and hedging,
     Springer.
     Brace, A., Gmatarek, D. and Musiela, M. (1997), ‘The market model of interest rate dynamics’,
     Mathematical Finance 7(2), 127–155.
     Brigo, D. and Mercurio, F. (2007), Interest Rate Models - Theory and Practice With Smile,
     Inflation and Credit, Springer finance, Springer-Verlag Berlin Heidelberg.
     Eberlein, E. and Koval, N. (2006), ‘A cross-currency levy market model’, Quantitative Finance
     6(6), 465–480.
     Flavell, R. R. (2011), Swaps and other derivatives, John Wiley & Sons.
     Geman, H., El Karoui, N. and Rochet, J. (1995), ‘Changes of numeraire, changes of probability
     measure and option pricing’, Journal of applied Probability 32(2), 443–458.
     Heath, D., Jarrow, R. and Morton, A. (1992), ‘Bond pricing and the term structure of interest
     rates: A new methodology for contingent claims valuation’, Econometrica 60(1), 77–105.
     Hull, J. and White, A. (2000), ‘Valuing Credit Default Swaps I: No Counterparty Default Risk’,
     The Journal of Derivatives 8(1), 29–40.
     Hull, J. and White, A. (2003), ‘The valuation of credit default swap options’, Journal of Derivatives
     10, 40–50.
     Jamshidian, F. (1997), ‘Libor and swap market models and measures’, Finance and Stochastics
     1(4), 293–330.
     Jamshidian, F. (2004), ‘Valuation of credit default swaps and swaptions’, Finance and Stochastics
     8(3), 343–371.
     Lando, D. (1998), ‘On Cox Processes and Credit Risky Securities’, Review of Derivatives Research
     2(2/3), 99–120.
     Li, D., Moshirian, F., Wee, T. and Wu, E. (2009), ‘Foreign exchange exposure: Evidence
     from the us insurance industry’, Journal of International Financial Markets, Institutions and
     Money 19(2), 306–320.
     Musiela, M. and Rutkowski, M. (2006), Martingale methods in financial modelling, Springer-
     Verlag Berlin Heidelberg.
     Schönbucher, P. (2000), ‘A libor market model with default risk’, Available at SSRN 261051 .
     Yong, H. H. A., Faff, R. and Chalmers, K. (2009), ‘Derivative activities and asia-pacific banks’
     interest rate and exchange rate exposures’, Journal of international financial markets, institutions
     and money 19(1), 16–32.
描述 博士
國立政治大學
金融研究所
97352502
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0097352502
資料類型 thesis
dc.contributor.advisor 陳松男<br>林建秀zh_TW
dc.contributor.advisor Chen, Son Nan<br>Lin, Chien Hsiuen_US
dc.contributor.author (Authors) 陳宏銘zh_TW
dc.creator (作者) 陳宏銘zh_TW
dc.date (日期) 2015en_US
dc.date.accessioned 17-Aug-2015 14:08:50 (UTC+8)-
dc.date.available 17-Aug-2015 14:08:50 (UTC+8)-
dc.date.issued (上傳時間) 17-Aug-2015 14:08:50 (UTC+8)-
dc.identifier (Other Identifiers) G0097352502en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/77558-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 金融研究所zh_TW
dc.description (描述) 97352502zh_TW
dc.description.abstract (摘要) 本文探討可違約互換率之匯率連動選擇權的評價，外國以及本國違約交
     換率的動態是建立在LIBOR 市場模型的框架。為了簡化推導過程，我們將
     原本本國以及外國交換率的雙動態轉為單一動態, 因此違約以及履約價將轉
     換為一個固定的常數比率來評價可違約互換率之匯率連動選擇權。由於商品
     本身是考量違約的情況，因此使用遠期的存活測度來評價可違約互換率之匯
     率連動選擇權。最後在數值分析的部分我們使用蒙地卡羅來模擬可違約互換
     率之匯率連動選擇權，理論值與模擬值的結果接近。		zh_TW
dc.description.abstract (摘要) This study prices quanto options on defaultable swap rates (QODSR) in which domestic and foreign defaultable swap rates are considered in the LIBOR market model. We use two fixed ratios to price the QODSR with the default and strike rate
     property. The forward default-swap measure provides a simple method for valuing the QODSR. Numerical analysis is performed and compared with the Monte Carlo method to investigate the effects of volatility and default on the QODSR.		en_US
dc.description.tableofcontents 致謝
     中文摘要ii
     Abstract iii
     1 Introduction 1
     2 Model and Notations 4
     2.1 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
     2.2 Change of Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
     2.3 First Hitting Time and Joint Probability Law . . . . . . . . . . . . . . 9
     2.4 Dynamic Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
     3 Valuation of Quanto Options on Defaultable Swap Rates 14
     3.1 Default Swaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
     4 Numerical Results 20
     4.1 Results of QODSR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
     5 Conclusion 24
     A Proof of theorem 3.1 32
     參考文獻 35		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0097352502en_US
dc.subject (關鍵詞) 匯率交換選擇權zh_TW
dc.subject (關鍵詞) LIBOR 市場模型zh_TW
dc.subject (關鍵詞) 違約風險zh_TW
dc.subject (關鍵詞) 信用衍生性商品zh_TW
dc.subject (關鍵詞) 違約比率zh_TW
dc.subject (關鍵詞) Quanto swaptionsen_US
dc.subject (關鍵詞) LIBOR market modelen_US
dc.subject (關鍵詞) default risken_US
dc.subject (關鍵詞) credit derivativeen_US
dc.subject (關鍵詞) default ratioen_US
dc.title (題名) 可違約互換率之匯率連動選擇權的評價zh_TW
dc.title (題名) Valuation of Quanto Options on Defaultable Swap Ratesen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Amin, K. and Jarrow, R. (1991), ‘Pricing foreign currency options under stochastic interest
     rates’, Journal of International Money and Finance 10(3), 310–329.
     Bennett, M. N. . and Kennedy, J. E. . (2004), ‘Quanto pricing with copulas’, The Journal of
     Derivatives 12(1), 26–45.
     Bielecki, T. R. and Rutkowski, M. (2002), Credit risk: modeling, valuation and hedging,
     Springer.
     Brace, A., Gmatarek, D. and Musiela, M. (1997), ‘The market model of interest rate dynamics’,
     Mathematical Finance 7(2), 127–155.
     Brigo, D. and Mercurio, F. (2007), Interest Rate Models - Theory and Practice With Smile,
     Inflation and Credit, Springer finance, Springer-Verlag Berlin Heidelberg.
     Eberlein, E. and Koval, N. (2006), ‘A cross-currency levy market model’, Quantitative Finance
     6(6), 465–480.
     Flavell, R. R. (2011), Swaps and other derivatives, John Wiley & Sons.
     Geman, H., El Karoui, N. and Rochet, J. (1995), ‘Changes of numeraire, changes of probability
     measure and option pricing’, Journal of applied Probability 32(2), 443–458.
     Heath, D., Jarrow, R. and Morton, A. (1992), ‘Bond pricing and the term structure of interest
     rates: A new methodology for contingent claims valuation’, Econometrica 60(1), 77–105.
     Hull, J. and White, A. (2000), ‘Valuing Credit Default Swaps I: No Counterparty Default Risk’,
     The Journal of Derivatives 8(1), 29–40.
     Hull, J. and White, A. (2003), ‘The valuation of credit default swap options’, Journal of Derivatives
     10, 40–50.
     Jamshidian, F. (1997), ‘Libor and swap market models and measures’, Finance and Stochastics
     1(4), 293–330.
     Jamshidian, F. (2004), ‘Valuation of credit default swaps and swaptions’, Finance and Stochastics
     8(3), 343–371.
     Lando, D. (1998), ‘On Cox Processes and Credit Risky Securities’, Review of Derivatives Research
     2(2/3), 99–120.
     Li, D., Moshirian, F., Wee, T. and Wu, E. (2009), ‘Foreign exchange exposure: Evidence
     from the us insurance industry’, Journal of International Financial Markets, Institutions and
     Money 19(2), 306–320.
     Musiela, M. and Rutkowski, M. (2006), Martingale methods in financial modelling, Springer-
     Verlag Berlin Heidelberg.
     Schönbucher, P. (2000), ‘A libor market model with default risk’, Available at SSRN 261051 .
     Yong, H. H. A., Faff, R. and Chalmers, K. (2009), ‘Derivative activities and asia-pacific banks’
     interest rate and exchange rate exposures’, Journal of international financial markets, institutions
     and money 19(1), 16–32.		zh_TW