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題名 隨機利率下，跨通貨投資組合選擇權之定價與避險策略
Pricing and Hedging Cross-Currency Portfolio Option with Stochastic Interest Rates
作者 王祥安
Wang , Hsiang-An
貢獻者 胡聯國<br>廖四郎
Hu, Lien-Kuo<br>Liao, Szu-Lang
王祥安
Wang , Hsiang-An
關鍵詞 投資組合選擇權
平賭測度
遠期平賭
利率模型
隨機利率
Portfolio Option
Martingale
Forward Measure Approach
Interest Rate Models
Stochastic Interest Rates
HJM
Cross Currency
日期 2003
上傳時間 18-九月-2009 14:08:14 (UTC+8)
摘要 在WTO成立，各國國際化程度日益提高的同時，企業與個人進行跨國投資的情形也愈來愈普遍，跨國投資除了要考慮標的資產之報酬與波動性之外，尚須考量匯率變動所產生之風險與不確定性。當某一國外資產具有正向預期報酬率的同時，實現後的報酬率卻又不一定為正，正是因為匯率波動所產生的影響。又，傳統財務理論告訴我們，藉由增加投資組合中所有非完全正相關的資產個數可以有效的降低投資組合的非系統風險，因此投資人在進行投資時往往採用建構投資組合的方式取代持有少數資產的型態。然而，在建構跨通貨避險投資組合時，若是對於投資組合中的各項資產與外幣分別進行避險（分別利用衍生性商品避險），往往是費時、費力又不具有效率。因此，對於整個投資組合進行避險反而是一個比較好的方法，當投資組合價值發生變動時，可以即時對於各項資產部位與外幣分別做調整，遠較於對個別資產進行避險來的方便、快速且有效。
In most cases, investment is made of building a portfolio rather than single asset. Therefore, it is necessary to develop techniques of valuing portfolio derivatives. Moreover, we consider a cross-currency portfolio that account for currency and interest rate risk. As interest rate is stochastic, we use Heath-Jarrow Morton (HJM) Approach to describe its dynamics. Applying Vorst (1992); Geman, Karoui and Rochet(1995), we derive the approximated close-form of the cross-currency portfolio option.

In HJM Approach, it is difficult to acquire hedge ratios of options. We apply another method to build a hedging portfolio. Then, we perform numerical simulations to test its hedging efficiency and sensitivity with respect to different variables.
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2. 呂桔誠、廖四郎、王昭文，組合型選擇權之評價與其在投資組合避險策略上之應用，亞太經濟管理評論，6卷2期，2003/3，p1-20.
3. 陳松男、鄭翔尹，『組合型權證的正確評價與避險方法』，證券市場發展季刊，1999，11卷4期，p1-23.
4. 陳兆維，利率波動結構對標準與平均利率上限契約評價的影響，國立台灣大學財務金融學研究所，2002。
5. 張雅琪，隨機利率下外幣選擇權定價理論與模擬，國立政治大學金融學系研究所，1999。
6. 張士琦，Heath-Jarrow-Morton 架構下，四種外國債券選擇權之評價與避險，世新大學管理學院經濟學系研究所，2001。
7. Alziary B., Decamps J-P and Koehl P-F, “A PDE Approach to Asian Options: Analysis and Numerical Evidence”, Journal of Banking and Finance, Vol.21, 1997, p613-640.
8. Amin, K. I. and Jarrow R., ”Pricing Foreign Currency Options under Stochastic Interest Rates”, Journal of International Money Finance, Vol.10, 1991, P310-329.
9. Amin K. I. and Morton A., “Implied Volatility Functions in Arbitrage-Free Term Structure Models”, Journal of Financial Economics. Vol.35, 1994, p141-180.
10. Black Fischer and Scholes Myron, “The Pricing of Options and Corporate Liabilities”, Journal of Political Economy, Vol.81, 1973, p637-654.
11. Bouaziz L; Briys E. and Crouhy M., “The Pricing of Forward-Start Asian Options”, Journal of Banking and Finance”, Vol.18, 1994, p823-839.
12. Boyle P., “Options: A Monte Carlo Approach”, Journal of Financial Economics, Vol.4, 1977, p323-338.
13. Brace A., Gatarek D. and Musiela M., “The Market Model of Interest Rate Dynamics”, Mathematical Finance, Vol.7, 1997, p127-155.
14. Briys E., Mai H. M., Bellalah M. and de Varenne F., “Options, Futures and Exotic Derivatives”, John Wiley & Sons, 1998.
15. Carverhill A. and Clewlow L., “Flexible Convolution”, Risk, Vol.5, 1990, p25-29.
16. Chacko G. and Das S., “Average Interest”, Working Paper, Harvard Business School, 1997.
17. Clewlow Les and Strickland Chris, “Implementing Derivatives Models”, John Wiley & Sons, 1998.
18. Corwin J.; Boyle P. and Tang K., “Quasi-Monte Carlo Methods in Numerical Finance”, Management Science, Vol.42, 1996, p1705-1711.
19. Cox, J. C. and Ross S. A., “The Valuation of Options for Alternative Stochastic Process”, Journal of Financial Economics, Vol.7:3, 1976, p229-264.
20. Cox, J. C., Ingersoll J. E. and Ross S. A., “A Intertemporal General Equilibrium Model of Asset Prices”, Econometrica, Vol.53, 1985a, p363-384.
21. Cox, J. C., Ingersoll J. E. and Ross S. A., “A Theory of Term Structure of Interest Rates”, Econometrica, Vol.53, 1985b, p385-407.
22. Curran, M., “Valuing Asian and Portfolio Options by Conditioning on Geometric Mean Price”, Management Science, Vol.40, 1994, p1705-1711.
23. Derosa David, “Currency Derivatives”, John Wiley & Sons, 1998.
24. Derosa David, “Options on Foreign Exchange”, 2nd edition, John Wiley & Sons, 2000.
25. Dewynne J. and Wilmott P., “Aisan Options as Linear Complementarity Problems”, Advances in Futures and Options Research, Vol.8, 1995, p145-173.
26. El Karoui N., Rochet J. C., “A Pricing Formula for Options on Coupon Bonds”, Working Paper, SDEES, 1989.
27. Filipovic D., “Consistency Problems for HJM Interest Rate Models”, Unpublished Doctoral Dissertation. Swiss Federal Institute of Technology, 2000.
28. Geman H., “The Importance of the Forward Neutral Probability in a Stochastic Approach of Interest Rates”, Working Paper, ESSEC, 1989.
29. Geman H., and El Karoui N., Rochet J. C., “Change of Numeraire, Change of Probability Measures and Pricing of Options”, Journal of Applied Probability, Vol.32, 1995, p443-458.
30. Geman H., and Yor M., “Bessel Process, Asian Options and Perpetuities”, Mathematical Finance, Vol.3, 1993, p349-375.
31. Gentle D., “Basket Weaving”, Risk, Vol.6, 1993, p51-52.
32. Hakala J□rgen and Wystup Uwe, Foreign Exchange Risk: Models, Instruments and Strategies, Risk Books, 2002.
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35. Harrison J. M. and S. R. Pliska, “A Stochastic Calculus Model of Continuous Trading: Complete Markets”, Stochastic Process and Their Applications, Vol.15, 1983, p313-365.
36. Haykov J., “A Better Control Variate for Pricing Standard Asian Options”, Journal of Financial Engineering, Vol.1993, p207-216.
37. Heath D., Jarrow R. and Morton A., “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation”, Econometrica, Vol.60, 1922, p77-105.
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39. Hull, John C. “Options, Futures, & Other Derivatives” 5th Edition, Pretice-Hall, 2003.
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42. Hull John C. and White Alan, “Efficient Procedures for Valuing European and American Path-Dependent Options”, Journal of Derivatives, Vol.1, 1993b, p21-31.
43. Hyunh C. B., “Back to Baskets”, Risk, Vol.7, 1994, p55-61.
44. J□ckel Peter, “Monte Carlo Methods in Finance”, John Wiley & Sons, 2002.
45. Jamshidian F., “LIBOR and Swap Market Models and Measures”, Finance and Stochastic, Vol.1, 1997, p293-330.
46. Jarrow R., “The Pricing of Commodity Option with Stochastic Interest Rates”, Advances in Futures and Options Research, Vol.2, 1987, p19-45.
47. Jarrow R. and Rudd A. “Option Pricing”, Irwin, 1983.
48. Ju N., “Fourier Transformation, Martingale and the Pricing of Average Rate Derivatives”, Ph.D. Thesis, U. California-Berkley, 1997.
49. Kemma A. and Vorst T., “A Pricing Method for Options Based on Average Asset Values”, Journal of Banking and Finance, Vol.14, 1990, p113-129.
50. Kramkov D. and Mordecky E., “Integral Options”, Theory of Probability and Its Applications, Vol.39, 1994, p162-171.
51. Kuo I. D., “Implied Volatility Functions for One and Two Factor Heath, Jarrow, and Morton Models, 2002 現代財務論壇，台中東海大學。
52. Levy E., “Pricing European Average Rate Currency Options”, Journal of International Money and Finance, Vol.11, 1992, p474-491.
53. Li A., Ritchken P. and Sankarasubramanian L., “Lattice Models for Pricing American Interest Rate Claims”, Journal of Finance, Vol.50, 1995, 719-737
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描述 碩士
國立政治大學
國際經營與貿易研究所
91351020
92
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0091351020
資料類型 thesis
dc.contributor.advisor 胡聯國<br>廖四郎zh_TW
dc.contributor.advisor Hu, Lien-Kuo<br>Liao, Szu-Langen_US
dc.contributor.author (作者) 王祥安zh_TW
dc.contributor.author (作者) Wang , Hsiang-Anen_US
dc.creator (作者) 王祥安zh_TW
dc.creator (作者) Wang , Hsiang-Anen_US
dc.date (日期) 2003en_US
dc.date.accessioned 18-九月-2009 14:08:14 (UTC+8)-
dc.date.available 18-九月-2009 14:08:14 (UTC+8)-
dc.date.issued (上傳時間) 18-九月-2009 14:08:14 (UTC+8)-
dc.identifier (其他 識別碼) G0091351020en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/35090-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 國際經營與貿易研究所zh_TW
dc.description (描述) 91351020zh_TW
dc.description (描述) 92zh_TW
dc.description.abstract (摘要) 在WTO成立，各國國際化程度日益提高的同時，企業與個人進行跨國投資的情形也愈來愈普遍，跨國投資除了要考慮標的資產之報酬與波動性之外，尚須考量匯率變動所產生之風險與不確定性。當某一國外資產具有正向預期報酬率的同時，實現後的報酬率卻又不一定為正，正是因為匯率波動所產生的影響。又，傳統財務理論告訴我們，藉由增加投資組合中所有非完全正相關的資產個數可以有效的降低投資組合的非系統風險，因此投資人在進行投資時往往採用建構投資組合的方式取代持有少數資產的型態。然而，在建構跨通貨避險投資組合時，若是對於投資組合中的各項資產與外幣分別進行避險（分別利用衍生性商品避險），往往是費時、費力又不具有效率。因此，對於整個投資組合進行避險反而是一個比較好的方法，當投資組合價值發生變動時，可以即時對於各項資產部位與外幣分別做調整，遠較於對個別資產進行避險來的方便、快速且有效。zh_TW
dc.description.abstract (摘要) In most cases, investment is made of building a portfolio rather than single asset. Therefore, it is necessary to develop techniques of valuing portfolio derivatives. Moreover, we consider a cross-currency portfolio that account for currency and interest rate risk. As interest rate is stochastic, we use Heath-Jarrow Morton (HJM) Approach to describe its dynamics. Applying Vorst (1992); Geman, Karoui and Rochet(1995), we derive the approximated close-form of the cross-currency portfolio option.

In HJM Approach, it is difficult to acquire hedge ratios of options. We apply another method to build a hedging portfolio. Then, we perform numerical simulations to test its hedging efficiency and sensitivity with respect to different variables.		en_US
dc.description.tableofcontents Abstract
1. Introduction
2. Review of Interest Rate Models
2.1 Models for Short-Term Interest Rates
2.2 Models for Forward Rates
3. The Security Economy
3.1 Dynamics of the Security Economy
3.2 Arbitrage-Free Condition
3.3 Forward Measure Approach
4. Valuation of Portfolio Options
5. Hedging Strategy
6. Numerical Simulation
6.1 Portfolio Hedging Analysis
6.2 Call Price Simulations
7. Conclusion
Reference
Appendix		zh_TW
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0091351020en_US
dc.subject (關鍵詞) 投資組合選擇權zh_TW
dc.subject (關鍵詞) 平賭測度zh_TW
dc.subject (關鍵詞) 遠期平賭zh_TW
dc.subject (關鍵詞) 利率模型zh_TW
dc.subject (關鍵詞) 隨機利率zh_TW
dc.subject (關鍵詞) Portfolio Optionen_US
dc.subject (關鍵詞) Martingaleen_US
dc.subject (關鍵詞) Forward Measure Approachen_US
dc.subject (關鍵詞) Interest Rate Modelsen_US
dc.subject (關鍵詞) Stochastic Interest Ratesen_US
dc.subject (關鍵詞) HJMen_US
dc.subject (關鍵詞) Cross Currencyen_US
dc.title (題名) 隨機利率下，跨通貨投資組合選擇權之定價與避險策略zh_TW
dc.title (題名) Pricing and Hedging Cross-Currency Portfolio Option with Stochastic Interest Ratesen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) 1. 王銘杰，無匯率風險的國外權益資產取得策略，國立暨南大學國際企業系，2002。zh_TW
dc.relation.reference (參考文獻) 2. 呂桔誠、廖四郎、王昭文，組合型選擇權之評價與其在投資組合避險策略上之應用，亞太經濟管理評論，6卷2期，2003/3，p1-20.zh_TW
dc.relation.reference (參考文獻) 3. 陳松男、鄭翔尹，『組合型權證的正確評價與避險方法』，證券市場發展季刊，1999，11卷4期，p1-23.zh_TW
dc.relation.reference (參考文獻) 4. 陳兆維，利率波動結構對標準與平均利率上限契約評價的影響，國立台灣大學財務金融學研究所，2002。zh_TW
dc.relation.reference (參考文獻) 5. 張雅琪，隨機利率下外幣選擇權定價理論與模擬，國立政治大學金融學系研究所，1999。zh_TW
dc.relation.reference (參考文獻) 6. 張士琦，Heath-Jarrow-Morton 架構下，四種外國債券選擇權之評價與避險，世新大學管理學院經濟學系研究所，2001。zh_TW
dc.relation.reference (參考文獻) 7. Alziary B., Decamps J-P and Koehl P-F, “A PDE Approach to Asian Options: Analysis and Numerical Evidence”, Journal of Banking and Finance, Vol.21, 1997, p613-640.zh_TW
dc.relation.reference (參考文獻) 8. Amin, K. I. and Jarrow R., ”Pricing Foreign Currency Options under Stochastic Interest Rates”, Journal of International Money Finance, Vol.10, 1991, P310-329.zh_TW
dc.relation.reference (參考文獻) 9. Amin K. I. and Morton A., “Implied Volatility Functions in Arbitrage-Free Term Structure Models”, Journal of Financial Economics. Vol.35, 1994, p141-180.zh_TW
dc.relation.reference (參考文獻) 10. Black Fischer and Scholes Myron, “The Pricing of Options and Corporate Liabilities”, Journal of Political Economy, Vol.81, 1973, p637-654.zh_TW
dc.relation.reference (參考文獻) 11. Bouaziz L; Briys E. and Crouhy M., “The Pricing of Forward-Start Asian Options”, Journal of Banking and Finance”, Vol.18, 1994, p823-839.zh_TW
dc.relation.reference (參考文獻) 12. Boyle P., “Options: A Monte Carlo Approach”, Journal of Financial Economics, Vol.4, 1977, p323-338.zh_TW
dc.relation.reference (參考文獻) 13. Brace A., Gatarek D. and Musiela M., “The Market Model of Interest Rate Dynamics”, Mathematical Finance, Vol.7, 1997, p127-155.zh_TW
dc.relation.reference (參考文獻) 14. Briys E., Mai H. M., Bellalah M. and de Varenne F., “Options, Futures and Exotic Derivatives”, John Wiley & Sons, 1998.zh_TW
dc.relation.reference (參考文獻) 15. Carverhill A. and Clewlow L., “Flexible Convolution”, Risk, Vol.5, 1990, p25-29.zh_TW
dc.relation.reference (參考文獻) 16. Chacko G. and Das S., “Average Interest”, Working Paper, Harvard Business School, 1997.zh_TW
dc.relation.reference (參考文獻) 17. Clewlow Les and Strickland Chris, “Implementing Derivatives Models”, John Wiley & Sons, 1998.zh_TW
dc.relation.reference (參考文獻) 18. Corwin J.; Boyle P. and Tang K., “Quasi-Monte Carlo Methods in Numerical Finance”, Management Science, Vol.42, 1996, p1705-1711.zh_TW
dc.relation.reference (參考文獻) 19. Cox, J. C. and Ross S. A., “The Valuation of Options for Alternative Stochastic Process”, Journal of Financial Economics, Vol.7:3, 1976, p229-264.zh_TW
dc.relation.reference (參考文獻) 20. Cox, J. C., Ingersoll J. E. and Ross S. A., “A Intertemporal General Equilibrium Model of Asset Prices”, Econometrica, Vol.53, 1985a, p363-384.zh_TW
dc.relation.reference (參考文獻) 21. Cox, J. C., Ingersoll J. E. and Ross S. A., “A Theory of Term Structure of Interest Rates”, Econometrica, Vol.53, 1985b, p385-407.zh_TW
dc.relation.reference (參考文獻) 22. Curran, M., “Valuing Asian and Portfolio Options by Conditioning on Geometric Mean Price”, Management Science, Vol.40, 1994, p1705-1711.zh_TW
dc.relation.reference (參考文獻) 23. Derosa David, “Currency Derivatives”, John Wiley & Sons, 1998.zh_TW
dc.relation.reference (參考文獻) 24. Derosa David, “Options on Foreign Exchange”, 2nd edition, John Wiley & Sons, 2000.zh_TW
dc.relation.reference (參考文獻) 25. Dewynne J. and Wilmott P., “Aisan Options as Linear Complementarity Problems”, Advances in Futures and Options Research, Vol.8, 1995, p145-173.zh_TW
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