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研究生： 林詩茜
Lin, Shih-Cian
論文名稱： 使用立基於Hull-White 雙因子模型的三元樹演算法評價可贖回債券
Evaluation of Callable Bonds Using Trinomial Tree Based on Hull-White Two-Factor Model
指導教授： 鍾經樊
Chung, Ching-Fan
口試委員: 張焯然
Chang, Jow-Ran
曾祺峰
Tzeng, Chi-Feng
張森林
Chung, San-Lin
學位類別： 碩士
Master
系所名稱： 科技管理學院 - 計量財務金融學系
Department of Quantitative Finance
論文出版年： 2022
畢業學年度： 110
語文別： 英文
論文頁數： 48
中文關鍵詞： 利率模型 、美元可贖回債券 、利率三元樹 、校正參數 、單因子利率模型 、雙因子利率模型
外文關鍵詞： Hull-White Model, Callable Bond, Interest Rate Tree, Parameter Calibration, One-Factor Model, Two-Factor Model
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    • 本文將根據Hull-White 雙因子短利模型編寫可模擬未來利率期間結構並計算可贖回債券價格的R 語言程式，其中模型參數將根據交換選擇權的隱含波動率市場資料進行估計，並將針對Federal Agricultural Mortgage Corporation 在04/20/2021 發行的五年期美元可贖回債券，以及其他三檔可贖回債券為例進行評價。

    This thesis proposed a valuation method of the callable bond based on the Hull-White two-factor interest rate model. We construct a trinomial tree to simulate interest rate term structure and valuate interest rate derivatives in R language. After using the implied volatilities of swaptions observed in market data to calibrate the model parameters, a valuation of a 5-year US callable bond issued on 04/20/2021 by Federal Agricultural Mortgage Corporation is reported as an example.

    Contents Abstract (Chinese) I Abstract II Contents III List of Figures V List of Tables VI 1 Introduction 1 2 The Short Rate Dynamics 3 2.1 Hull-White One-Factor Model . . . . . . . . . . . . . . . . . . . . . 4 2.2 Hull-White Two-Factor Model . . . . . . . . . . . . . . . . . . . . . 5 3 Construct a Trinomial Tree 7 3.1 Hull-White one-factor model . . . . . . . . . . . . . . . . . . . . . . 7 3.1.1 The process r∗ t . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.1.2 The Corresponding Tree for rt . . . . . . . . . . . . . . . . . 9 3.2 Hull-White two-factor model . . . . . . . . . . . . . . . . . . . . . . 10 3.3 Building Trees for the Hull-White two-factor model . . . . . . . . . 11 3.4 Pricing Callable Bonds with a Tree . . . . . . . . . . . . . . . . . . 13 4 Calibrate the Model Parameter 14 4.1 Calibration Using Real-Market Data . . . . . . . . . . . . . . . . . 14 4.2 The Loss Function Problem . . . . . . . . . . . . . . . . . . . . . . 15 4.3 Pricing Swaption under the Black’s Model . . . . . . . . . . . . . . 15 4.4 Pricing Swaptions under the One-Factor Model . . . . . . . . . . . 16 5 Numerical Result 18 5.1 Pricing Callable Bonds . . . . . . . . . . . . . . . . . . . . . . . . . 18 5.1.1 Example 1: April 20, 2021 . . . . . . . . . . . . . . . . . . . 18 5.1.2 Example 2: June 30, 2021 . . . . . . . . . . . . . . . . . . . 20 5.1.3 Example 3: August 12, 2021 . . . . . . . . . . . . . . . . . . 21 5.1.4 Example 4: November 28, 2017 . . . . . . . . . . . . . . . . 23 6 Conclusion 25 Reference 27

    [1] Brigo D. and Mercurio F. (2006). Interest Rate Models Theory and Practice, pages 127–171. Springer Finance, second edition., 2001.
    [2] Hull J and White A. (1990). Pricing Interest-Rate-Derivative Securities. Review of Financial Studies, 3:573–92.
    [3] Hull J and White A. (1994). Numerical Procedures for Implementing Term Structure Models II. The Journal of Derivatives, 2:37–48.
    [4] Hull J and White A. (2000) The General Hull-White Model and Super Calibration. 57.
    [5] Vincenzo R. and Gabriele T. (2019). Calibration of one-factor and two-factor Hull–white models using swaptions. Computational Management Science, 16.
    [6] Vincenzo R. and Frank J. Fabozzi. (2017) Pricing Coupon Bond Options and Swaptions under the Two-Factor Hull-White Model. The Journal of Fixed Income, 27(2):30–36.27

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