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    政大機構典藏 > 商學院 > 金融學系 > 學位論文 >  Item 140.119/76173
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/76173


    Title: LMM利率模型下可取消利率交換評價與風險管理
    Cancelable Swap Pricing and Risk Management under LIBOR Market Model
    Authors: 廖家揚
    Liao, Chia Yang
    Contributors: 廖四郎
    Liao, Szu Lang
    廖家揚
    Liao, Chia Yang
    Keywords: 可取消利率交換
    百慕達利率交換選擇權
    市場利率模型
    最小平方蒙地卡羅法
    敏感度分析
    風險值
    Cancellable Swap
    Bermudan Swaption
    Libor Market Model
    Least Squares Monte Carlo Method
    Sensitivity Analysis
    Value at Risk
    Date: 2014
    Issue Date: 2015-07-01 14:45:33 (UTC+8)
    Abstract: 許多公司在發行公司債的時候,會給此公司債一個可提前贖回的特性,此種公司債稱為可贖回公司債(Callable Bond),用來規避利率變動風險的金融商品也與我們熟知的利率交換不同,稱為可取消利率交換(Cancelable Swap)。其實可取消利率交換可以拆解成百慕達利率交換選擇權(Bermudan Swaption)加上利率交換,由於利率交換之評價較簡單也有市場一致的評價方法,因此百慕達利率交換選擇權便成為評價的重點。
    評價的部分,由於百慕達式的商品有提前履約的特性,造成其封閉解不存在,因此需要利用其他的近似解或是數值方法來求它的價格。由於本文採用BGM(1997)的市場利率模型(Libor Market Model),其高維度的性質導致數狀方法與有限差分法使用起來較無效率,因此本文選擇使用蒙地卡羅法做為評價的方法,同時利用Longstaff and Schwartz(2001)的最小平方蒙地卡羅法(Least Squares Monte Carlo Method)來解決提前履約的問題。
    最後,本文將採用2種利率波動度假設與2種不同利率間相關係數的假設,共4種組合,在歐式利率交換選擇權的市場波動度下進行校準,使用校準出來的參數進行評價來得到4種價格。再進行商品的敏感度分析(Sensitivity Analysis)和風險值(Value at Risk)的計算。
    Reference: 中文文獻
    [1] 王祥帆 (2005) 百慕達式利率交換選擇權。
    [2] 蔡宏彬 (2009) 在BGM模型下固定交換利率商品之效率避險與評價。
    英文文獻
    [1] Alpsten, H., (2003), Pricing bermudan swap options using the BGM model with arbitrage – free discretisation and boundary based option exercise, Working paper, Department of mathematics royal institute of technology.
    [2] Andersen, L., (2000), A Simple Approach to the Pricing of Bermudan Swaptions in the Multi – Factor Libor Market Model, Journal of Computational Finance 3(2), 1-32.
    [3] Brace, A., D. Gatarek, and M. Musiela, (1997), The market model of interest rate dynamics, Mathematical Finance 7(2), 127-155.
    [4] Brigo, D. and Mercurio, F. (2007). Interest rate models, theory and practice, Springer Science + Business Media.
    [5] Cox, J., Ingersoll J. and Ross, S. A theory of the term structure of interest rates, Econometrica, 53(2) (1985) 385-407.
    [6] Coffey, C. and Schoenmakers, J(2002). Systematic generation of parametric correlation structures for the libor market model, International Journal of Theoretical and Applied Finance.
    [7] Glasserman, P. (2004). Monte carlo methods in financial engineering, Springer Science + Business Media.
    [8] Hull, J., White, A. (1993). One-factor interest rate models and the valuation of interest rate derivative securities. Journal of Financial and Quantitative Analysis 28, 235-254.
    [9] Jorion, P. (1997): Value at Risk – The New Benchmark for Controlling Market Risk. McGraw-Hill, New York
    [10] Lvov, D. (2005). Monte carlo methods for pricing and hedging: Applications to bermudan swaptions and convertible bonds, PhD dissertation, ISMA Centre, University of Reading.
    [11] Longstaff, F. A., and Schwartz, E. S. (2001), “Valuing American Potions by Simulation: A Simple Least – Squares Approach”, The Review of Financial Studies 14(1), 113-147.
    [12] Pedersen, M. B, (1999), Bermudan Swaptions in the LIBOR market model, Financial Research Department, Preprint.
    [13] Pietersz, R. and A. Pelsser, (2003), Risk managing bermudan swaptions in the LIBOR BGM Model, Preprint.
    [14] Piterbarg, V. (2005). A practitioner’s guide to pricing and hedging callable libor exotics in forward libor models, Working paper.
    [15] Rebonato, R. (2002). Modern pricing of interest rate derivatives: The libor market model and beyond, Princeton University Press.
    [16] Steffen Hippler, (2008). Pricing bermudan swaptions in the LIBOR market model, master dissertation, university of Oxford.
    [17] Svoboda, S., (2004), Interest rate modelling, published by Palgrave Macmillan.
    [18] Tavella, D., (2002), Quantitative methods in derivatives pricing: An Introduction to Computational Finance, Published by John Wiley & Sons, Ltd.
    [19] Vasicek, O. (1997), An equilibrium characterization of the term structure, Journal of Financial Economics 5, 177-188.
    [20] Weigel, P., (2004), Optimal calibration of LIBOR market models to correlations, The Journal of Derivatives, Winter 2004, 43-50.
    Description: 碩士
    國立政治大學
    金融研究所
    102352014
    103
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0102352014
    Data Type: thesis
    Appears in Collections:[金融學系] 學位論文

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