# 臺灣博碩士論文加值系統

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 本論文透過蒙地卡羅模擬探討在市場利率模型下利率上限契約的評價與避險。吾人將本論文分為兩部分分析，第一部分著重在間斷型態利率界限選擇權的評價。由於界限選擇權相對於標準歐式選擇權來的便宜，而成為近年來市場上風險管理者所喜愛的避險工具。因此我們將探討隨著市場利率模型中遠期利率波動度的變動，對間斷型態界限利率上限選擇權價值的影響。第二部分著重在利率上限契約的避險。我們選用不同到期日的零息債券當作避險工具，至於這些零息債券的到期日及數目的選擇則是我們所要討論的主題。由模擬的結果顯示，我們可簡化成只選用四張不同到期日的債券便可達到與選用N+1張不同到期日債券相似的結果(N為利率上限契約的重設次數)。
 In this paper, the LIBOR Market Model is implemented to price and hedge interest rate caps by Monte Carlo simulation. The study falls into two parts. In the first part, we focus on pricing discrete interest rate barrier caps. Barrier caps, less expensive than vanilla caps, have become very popular in recent year as useful hedging instruments for risk management strategies, and we use Monte Carlo procedure to value discrete barrier caps based on the LIBOR Market Model. In the second part of the study, we focus on the hedging of vanilla caps. The choices of the number and maturity of the hedging instruments which use the zero coupon bonds are the subject in this paper. We replicate numbers of hedging portfolios of interest rate caps and test the hedging performance of these portfolios by simulation. The numerical results of the hedging of interest rate caps show that we can simplify zero coupon bonds with N+1 maturities to be using zero coupon bonds with four maturities. Here, N is the number of reset dates. The result suggests that we can choose zero coupon bonds with four maturities, as hedging instruments of interest rate cap, mature most closely at the initial and end life of the interest rate cap respectively.
 Contents1. Introduction………………………………………………………………………12. Interest Rate Cap and Discrete Barrier Cap Agreements……………………42.1 Interest Rate Caps………………………………………...………………42.2 Discrete Barrier Interest Rate Caps………………...……………………63. The Model……………………………………………………………………83.1 LIBOR Market Model…………………………………………………..83.2 Interest Rate Cap Prices…………………….………………………114. Simulation………………………………………………………………………144.1 Simulation Routine……………………………………………………….144.2 Discounting Procedures………………………………….…………165. Numerical Results……………………………………………………………..185.1 Discrete Barrier Caps…………………………………………………...185.2 Effects of Volatility Structures………………………………………….196. Hedging Strategy………………………………………………………………236.1 Hedging Portfolios Constructions………………………………………236.2 Hedging Performance……………………………………………………267. Conclusion……………………………………………………………………….40Reference…………………………………………………………………………….41Table ContentsTable 4.1 Paths of LIBOR rates…………...…………………………………………16Table 5.1 Prices of discrete barrier caps…….….……………….…………….…..…19Table 5.2 Valuation of Up-and Out Barrier Cap at Different VolatilityLevels…….....21Table 5.3 Valuation of Up-and Out Barrier Cap at Different Volatility Levels……...22Table 6.1 Price Sensitivities of Hedging Portfolios…………………………………27Table 6.2 Price Sensitivities of Hedging Portfolios of Different Maturity Caps..…..28Table 6.3 Price Sensitivities in Upward Term Structure………………..………..…30Table 6.4 Price Sensitivities in Downward Term Structure……………..…………30Table 6.5 Hedging Performance of 2-year Interest Rate Cap……………..………32Table 6.6 Hedging Performance of 4-year Interest Rate Cap……………..………33Table 6.7 Hedging Performance of 6-year Interest Rate Cap……………..………34Figure ContentsFigure 6.1 The shape of upward term structure………………………………….29Figure 6.2 The shape of downward term structure………………………………29Figure 6.3 2-year Cap Hedge Results……………………………………………35Figure 6.4 4-year Cap Hedge Results……………………………………………35Figure 6.5 6-year Cap Hedge Results……………………………………………36Figure 6.6 2-year Cap Hedge Results under upward term structure……………..36Figure 6.7 4-year Cap Hedge Results under upward term structure……………..37Figure 6.8 6-year Cap Hedge Results under upward term structure……………..37Figure 6.9 2-year Cap Hedge Results under downward term structure………….38Figure 6.10 4-year Cap Hedge Results under downward term structure………….38Figure 6.11 6-year Cap Hedge Results under downward term structure………….39
 ReferenceAhn, D.H., S. Figlewski, and B. Gao, 1999, Pricing discrete barrier options with an adaptive mesh, The Journal of Derivatives, Summer, Vol. 6, pp. 33-43Brace, A., D. Gatarek, and M. Musiela, 1997, The market model of interest rate dynamics, Mathematical Finance, April, Vol. 7, No. 2, pp. 127-147Brace, A., T. Dun, and G. Barton, 1998, Towards a central interest rate model, Tech. Rep., Conference Global Derivatives, 98Brace, A., 1998, Simulation in the GHJM and LFM models, FMMA NOTES, 19 FebruaryDriessen, J., P. Klaasen, and B. Melenberg, 2003, The performance of multi-factor term structure models for pricing and hedging caps and swaption, Journal of Financial & Quantitative Analysis, September, Vol. 38, Issue 3, pp. 635Dun, T., S. Erik, and B. Geoff, 1999, Simulated swaption hedging in the lognormal forward LIBOR model, Working paper, June, University of Technology, SydenyDun, T., S. Erik, and B. Geoff, 2000, Simulated swaption delta-hedging in the lognormal forward LIBOR model, 2001, International Journal of Theoretical and Applied Finance, Vol. 4, No. 4, pp. 677-709Gupta, A. and M. G. Subrahmanyam, 2001, An examination of the static and dynamic performance of interest rate option pricing models in the dollar cap-floor markets, Working paper, SeptemberHull, J., and A. White, 1990, Pricing interest-rate-derivative securities, The Review of Financial studies, Vol. 3, No. 4 (1990), pp. 573-592Hull, John C., 2003, Options, Futures, and Other Derivatives, 5th ed., (United States of America: Prentice-Hall, Inc.)Kuan, G.C.H., and N. Webber, 2003, Pricing barrier options with one-factor interest rate models, The Journal of Derivatives, Summer, Vol. 10, pp. 33-50Longstaff, F. A., 1990, The valuation of options on yield, Journal of Financial Economics, 26, pp. 97-121Longstaff, F. A., 1995, Hedging interest rate risk with options on average interest rates, Journal of Fixed Income, March, pp. 37-45Miltersen, K.R., K. Sandmann, and D. Sondermann, 1997, Closed form solutions for term structure derivatives with log-normal interest rates, The Journal of Finance 52, March, pp. 409-430Pelsser, A., 2000, Efficient Methods for Valuing Interest Rate Derivatives (Springer)
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 1 利率選擇權評價與避險之分析 2 結構型商品之定價與設計－以TargetRedemptionNotes為例 3 利率上限及交換選擇權之定價－多因子市場利率模型

 1 4、李承訓，軍隊與民主憲政（上），軍法專刊，38卷2期。 2 9、陳樸生，軍事審判與司法審判之共通性與特殊性，軍法專刊，7卷1期。

 1 利率選擇權評價與避險之分析 2 為他人選擇對妥協效果之影響 3 利率上限及交換選擇權之定價－多因子市場利率模型 4 抵押房貸證劵化之評價 5 利率上限避險契約與銀行放款利率管理─選擇權評價模式分析 6 新奇利率衍生性金融商品--平均利率上限契約之評價、避險及應用 7 銀行往來關係對公司首次在公開市場發行的債券融資成本之影響 8 探討金融危機下融資方式對借款人績效表現的影響 9 影響跨國債券發行者選擇發行地的因素-以投資者保護探討 10 營造業進入中國市場之工程契約風險研究 11 雲端服務契約的重要條款之檢視-從法律及風險之觀點 12 心理契約、組織承諾與留任意願關係之研究－以南部基層派遣員工為例 13 併購契約之法律風險管理 14 情事變更對工程契約爭議之探討 15 遠期美元契約避險效能之研究

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