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研究生： 鄭立誠
Li-Cheng Cheng
論文名稱： 跨通貨利率衍生性商品之評價與討論
Valuing Cross-Currency Interest Rate Derivatives
指導教授： 張森林
San-Lin Chung
口試委員:
學位類別： 碩士
Master
系所名稱： 管理學院 - 財務金融學系
Department of Finance
畢業學年度： 89
語文別： 中文
論文頁數： 69
中文關鍵詞： 跨通貨 、Hull & White 模型 、利率衍生性商品 、quanto 、差額交換 、買權賣權評價理論
外文關鍵詞： cross-currency, Hull & White Model, interest rate derivatives, quanto, diff swap, put-call parity
相關次數： 點閱：9  下載：0 
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    • 在本文中，我們將著重於三個有趣的議題上。一個是quanto形式的利率衍生性工具，其標的為外國的浮動利率但卻以本國貨幣的本金來計算損益。另一個議題是差額型利率衍生性工具，其標的為外國與本國浮動利率差額但卻只以本國貨幣的本金來計算損益。最後一個是這些跨通貨利率衍生性商品間的關係，例如我們可以透過quanto cap、quanto floor、swap來組成diff swap等等。
    另外我們也推導這些商品的封閉解並指出quanto caplet與diff caplet的特徵；利用這些公式，我們可以得到這些商品的敏感度分析。


    In this article we focus on three interesting issues. One is quanto interest rate instruments where the underlying asset is the foreign rate on floating notes, but measured in domestic currency. Another subject is currency protected spread rate (diff) instruments whereby the underlying asset is the difference between the foreign and domestic floating rate.
    They are also measured in domestic currency. The other issue is the relationship between these cross-currency interest rate derivatives such as the relationship among diff swaps, quanto caps, quanto floors, and domestic swaps or the relationship among quanto caps, diff caps, floors, and domestic swaps, etc. We will additionally derive the closed-formed solution and show many characteristics of quanto interest rate and diff instruments. By using these pricing methods, we will show the sensitivity analysis of diff caplets and quanto caps.

    1 Introduction 1 2 Literature Review 4 2.1 Wei (1994) 4 2.2 Hull and White (1994a)(1994b) 7 2.2.1 Constructing an Interest Rate Tree 8 2.2.2 Building the Tree of Two Interest Rates 14 2.2.3 Constructing the Tree--Zero Correlation 16 2.2.4 Constructing the Tree--Non-Zero Correlation 17 3 Quanto Caplets and Quanto Floorlets 19 3.1 Pricing Quanto Caplets and Quanto Floorlets 19 3.2 Sensitivity Analysis of Quanto Caplets 20 4 Diff Caplet and Diff Floorlet 21 4.1 Pricing Diff Caplets or Floorlets 21 4.2 Sensitivity Analysis of Diff Caplets 23 4.3 Comparing Di® Caplet With The Combination of Domestic Floorlets and Quanto Caplets 24 4.4 An Example--Quanto Notes 26 5 Block-Building of Cross-Currency Interest Rate Derivatives 27 5.1 General Case 27 5.1.1 Quanto Put-Call Parity 27 5.1.2 Diff Put-Call Parity 29 5.1.3 Diff Swaps, Quanto Swaps, and Swaps 30 5.1.4 Quanto Caps, Quanto Floors and Diff Swaps 31 5.1.5 The Relationship among Domestic, Quanto and Diff Instruments 33 5.2 Under Vasicek Model Assumption 35 5.2.1 The Dynamic Duplicate 35 6 Conclusion 36 A Appendix I--Quanto Caps and Quanto Floors 39 A.1 Foreign Caplets Denominated in Domestic Currency 39 A.2 Foreign Floorlets Denominated in Domestic Currency 42 A.3 Domestic Caplets Denominated in Foreign currency 43 A.4 Domestic Floorlets Denominated in Foreign Currency 45 B Appendix II{Di® Caps and Floors with K = 0 46 B.1 Diff Caplets Denominated in Domestic Currency with K = 0 46 B.2 Di® Floorlets Denominated in Domestic Currency with K = 0 49

    1. Chan, K. C., G. A. Karolyi, F. A. Longstaff, and A. B. Sanders, 1992, "Empirical Comparison of Alternative Models of the Short-Term Interest Rate." The Journal of Finance, 47, 3, 1209-1227.
    2. Chang, C. C., S. L. Chung and M. T. Yu "Valuation and Hedging of Differential Swaps." Journal of Future Market, SSCI (2001 Dec/2002 Jan, Forthcoming).
    3. Chung, S.L., 1999, "American Option Valuation under Stochastic Interest Rates." Review of Derivatives Research, 3(3), 283-307.
    4. Das, S., 1992a, "Differential Strip-Down." Risk, 5, 6, 65-72.
    5. Hull, J. and A. White, 1994, "Numerical Procedures For Implementing Term Structure Models I: Single-Factor Models." Journal of Derivatives, 2, 1, 7-16.
    6. Hull, J. and A. White, 1994, "Numerical Procedures For Implementing Term Structure Models II: Two-Factor Models." Journal of Derivatives, 2, 2, 37-47.
    7. Hull, John C. "Options, Futures, & Other Derivatives." (4nd ed) Prentice-Hall International, Inc.
    8. Michalisin, M. D. and T. Carey, 1999, "The Diff Swap: Strategy, Structure, And Financial Reporting." Bank Accounting & Finance, 12, 2, 43-49.
    9. Wei, J. Z., 1994, "Valuing Differential Swaps." Journal of Derivatives, 1, 3(Spring 1994), 64-76.
    10. Vasicek, O., 1977, "An Equilibrium Characterization of the Term Structure." Journal of Financial Economics, 5 (1977), 177-188.

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