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研究生:陳尚群
研究生(外文):Shang-Chiun Chen
論文名稱:利率上限及交換選擇權之定價-多因子市場利率模型
論文名稱(外文):Prices of Caps and Swaptions under Multi-Factor LIBOR Market Models
指導教授:岳夢蘭岳夢蘭引用關係
指導教授(外文):Meng-Lan Yueh
學位類別:碩士
校院名稱:國立中央大學
系所名稱:財務金融研究所
學門:商業及管理學門
學類:財務金融學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:英文
論文頁數:50
中文關鍵詞:交換選擇權定價校準蒙地卡羅模擬利率上限波動性結構利率市場模型
外文關鍵詞:CalibrationMonte Carlo SimulationPricingSwaptionCapVolatility StructureLIBOR Market Model
相關次數:
  • 被引用被引用:1
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  • 下載下載:6
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本篇論文中,結論顯示在波動性為時間齊次或是常態的假設下,以三因子模型去評價利率上限,其定價較為精準,但是以單因子及二因子模型來評價,則表現普遍不佳;若是以三因子模型去評價交換選擇權,在選擇權到期年限為兩年或是三年的情況下,其定價比單因子及二因子模型精準,但是在選擇權到期年限為七年的情況下,並不保證三因子模型定價比單因子及二因子模型精準。此外也發現市場模型中的波動性參數如果採用時間齊次性假設,則定價表現較佳。這是個很重要的結果,因為在文獻上,大部分的學者總是採用Rebonato (1998)所建議的參數化波動性假設來評價利率衍生性商品,然而本文卻發現此種假設的定價表現不佳。
In this paper, we find that for caps, when we assume volatilities are time-homogeneous or flat, 3-factor model is better than 1- and 2-factor model. For swaptions, no matter how many years expiration is, if the tenor is shorter (2 or 3 year), the pricing performance in the 3-factor mode is better than others. But if the tenor is longer (7 year), the pricing performance of the 3-factor model is not guaranteed to be better than that of other models. If we use time-homogeneous volatilities to evaluate caps or swaptions, pricing performance is very well in most situations. We have to notice this result. Because in the literatures, most of researchers always use parametric instantaneous volatilities (case 3) that are suggested by Rebonato (1998) to evaluate interest rate derivatives. However, we show in this paper that the pricing performance under a parametric instantaneous volatilities assumption might be not very satisfactory.
1. Introduction 1
2. Caps and Swaptions 4
2.1. Caps 4
2.1.1. The Definition 4
2.1.2. The Market Price for Caps 4
2.2. Swaptions 5
2.2.1. The Definition 5
2.2.2. The Market Price for Swaptions 6
3. Data Descriptions 7
4. The Model 9
4.1. General Setup of the LIBOR Market Model 9
4.2. Calibrating the LIBOR Market Model 10
4.2.1. The Instantaneous Volatility Function 11
4.2.2. The Instantaneous Correlation Function 13
4.3. Monte Carlo Simulation 16
4.4. Pricing of Vanilla Instruments 17
4.4.1. Pricing Caps under the LIBOR Market Model 17
4.4.2. Pricing Swaptions under the LIBOR Market Model 18
5. Empirical Results 19
5.1. Initial Inputs 19
5.2. Term Structures of Piecewise-Constant Instantaneous Volatilities 19
5.2.1. Case 1: Time-Homogeneous Instantaneous Volatility 19
5.2.2. Case 2: Constant Instantaneous Volatility 20
5.2.3. Case 3: Parametric Instantaneous Volatility 20
5.3. The Instantaneous Correlation Matrix 21
5.4. The Valuation of Caps and Swaptions 22
5.4.1. How Many Factors? 22
5.4.2. What Kind of Volatilities? 23
6. Conclusions 24
Reference 43
Appendix 46
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Bühler, W., Uhrig-Homburg, M., Walter, U., Weber, T. (1999), “An Empirical Comparison of Forward-Rate and Spot-Rate Models for Valuing Interest-Rate Options,” Journal of Finance, 54, 269-305.

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Brace, A., Dun, T., and Barton, G. (1998), “Towards a Central Interest Rate Model,” FMMA notes working paper.

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Fan, R., A. Gupta, and P. Ritchken (2001), “On Pricing and Hedging in the Swaption Market: How Many Factors, Really?”, working paper, Case Western Reserve University.

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Longstaff, F., P. Santa-Clara, and E. Schwartz (2001), “The Relative Valuation of Caps and Swaptions: Theory and Empirical Evidence,” Journal of Finance, 56, 2067-2109.

Miltersen, K.R., Sandmann K., Sondermann D. (1997), “Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates,” Journal of Finance, 52, 409-430.

Musiela, M., and Rutkowski, M. (1997), “Continuous-Time Term Structure Models: Forward Measure Approach,” Finance and Stochastics, 4, 261-292.

Pelsser, A. (2000), Efficient Methods for Valuing Interest Rate Derivatives, Springer, Heidelberg.

Peterson, S., R. Stapleton, and M. Subrahmanyam (2001), “The Valuation of Caps, Floors and Swaptions in a Multi-Factor Spot-Rate Model,” working paper, Stern School of Business, New York University.

Rebonato, R. (1999), “On the Simultaneous Calibration of Multifactor Lognormal Interest Rate Models to Black Volatilities and to the Correlation Matrix,” Journal of Computational Finance, 4, 5-27.

Riccardo Rebonato (2002), Modern Pricing of Interest-Rate Derivatives - The LIBOR Market Model and Beyond, Princeton University Press.
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