本文使用利率模型定價美元可贖回債券。利用交換選擇權的隱含波動率估計Hull-White和Black-Karasinski兩種利率模型的模型參數，再根據債券合約評價美元可贖回債券。本文提出建構參數因時而變之利率模型的方法，並比較參數為常數以及參數因時而變的可贖回債券評價結果。

This article implements interest rate models to evaluate callable bonds. We use market implied volatilities of swaptions to calibrate the model parameters, mean reversion, and volatility of the Hull-White model and the Black-Karasinski model, respectively, then price callable bonds according to the bond contracts. We propose a method to construct an interest rate model with time-varying parameters. Eventually, we compare the evaluation results of interest rate models with time-varying parameters and the model with constant parameters.

摘要 i
Abstract ii
List of Tables v
List of Figures vi
1 Introduction 1
2 Short Rate Models and Closed Forms 2
2.1 The Hull-White Model 3
2.1.1 The Short Rate Dynamics 3
2.1.2 Closed Forms for Options and Swaptions 4
2.2 The Black-Karasinski Model 5
3 Implementation of Short Rate Models with a Tree 7
3.1 The Construction of a Trinomial Tree (Hull and White, 2001) 7
3.2 Pricing Bonds and Derivatives with a Tree 11
3.2.1 Coupon Bonds11
3.2.2 Swaptions11
3.2.3 Callable Bonds 12
4 Methodology 13
4.1 Zero Rate Curves 13
4.2 Black’s Swaption Model 14
4.3 Relations between Model and Market Parameters 14
4.3.1 The Hull-White Model 15
4.3.2 The Black-Karasinski Model 16
4.4 Calibration to Swaptions 17
5 Numerical Results 19
5.1 Model Parameters 19
5.2 Pricing Callable Bonds 20
5.2.1 Example 1 21
5.2.2 Example 2 23
5.2.3 Example 3 24
5.3 Sensitivity Test 25
6 Conclusion 26
References 27
Figures and Tables 28

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