本文以遠期利率的二次樣條插值法,以及美國名目債券和美國抗通膨債
券(TIPS)報價,分別配適名目和實質利率期限結構。根據費雪方程式,我將名
目減去實質利率期限結構,得到盈虧平衡通膨(BEI)期限結構。此外,為了配適
出合理的實質利率,對於TIPS中的通膨補償機制,我嘗試納入三種不同的通膨
預期假設。接下來,我利用上述模型推導的BEI即期利率期限結構,將其轉換為
交易信號,以建構基於不同天期與共整合的BEI配對交易策略。結果表明,幾何
增長假設下的通膨補償所得到的BEI期限結構,最接近現有數據。此外,推測由
於即期利率和債券價格之間的差異與有無票息的差異,從BEI即期利率生成的
交易信號並非對於所有債券價格交易皆很實用,但對於零息通膨交換(inflation
swap)交易則有不錯的成效。總而言之,在合理通膨補償與實質即期利率下導出
的BEI即期利率,對零息商品而言,可以做為良好的獲利交易訊號。

In this thesis, I endeavor to utilize quadratic spline interpolation of forward rate approach, and the U.S. nominal bonds as well as TIPS quotes to fit the nominal and real term structures respectively. By Fisher’s equation, I subtract real rate from the nominal rate with the same maturity to obtain the break-even inflation (BEI) term structure. Moreover, I attempt to incorporate three different inflation expectation assumptions for TIPS to obtain the most reasonable real rate. Furthermore, I transform the BEI spot rates into trading signals to construct BEI pair trading strategies based on different maturities and cointegration. The results suggest that the BEI term structure derived from the TIPS inflation compensation under the assumption of geometric growth is closest to existing data. And trading
signals generated from BEI spot rates may not be universally useful for all bond price trading due to differences between spot rates and bond prices as well as coupon, but they are effective for zero-coupon inflation swap (ZCIS) trading. All in all, the BEI spot rates derived from reasonable inflation compensations and real spot rates can serve as a good trading signals for profit in zero-coupon securities.

Abstract (Chinese) I
Abstract II

Acknowledgements (Chinese) III
Contents IV

List of Figures VI
List of Tables VIII

1 Introduction 1

2 Preliminaries 9
2.1 Nominal Bonds, and TIPS Pricing Formulae . . . . . . . . . . . . . 9
2.1.1 Forward rates, Spot rates, and Discount Factors . . . . . . . 9
2.1.2 T-Bills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.3 T-Notes and T-Bonds . . . . . . . . . . . . . . . . . . . . . 10
2.1.4 TIPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 Quadratic Spline Interpolation of Forward Rates . . . . . . . 11
2.2.2 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.3 Cointegration-Based Pair . . . . . . . . . . . . . . . . . . . . 15

3 Data Description 16
3.0.1 CPI-U Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.0.2 Treasury Coupon Bonds Price Data . . . . . . . . . . . . . . 18
3.0.3 Nominal Coupon Bonds Price Data . . . . . . . . . . . . . . 20
3.0.4 TIPS Price Data . . . . . . . . . . . . . . . . . . . . . . . . 21
3.0.5 Break-even Inflation Data . . . . . . . . . . . . . . . . . . . 22
3.0.6 Inflation Swap Data . . . . . . . . . . . . . . . . . . . . . . 22
4 Methodology 24
4.0.1 Definition of Inflation Compensation . . . . . . . . . . . . . 24
4.0.2 Selection of Fitting Bonds . . . . . . . . . . . . . . . . . . . 29
5 Estimating Results and the Break-even Inflation Term Structure 31
5.0.1 No Growth of Inflation : by Jarrow and Yildirim . . . . . . 33
5.0.2 Geometric Growth of Inflation . . . . . . . . . . . . . . . . . 37
5.0.3 TIPS Break-even Inflation . . . . . . . . . . . . . . . . . . . 41
5.0.4 Comprehensive Comparison . . . . . . . . . . . . . . . . . . 45
6 Cointegration Break-even Inflation Pair Trading Strategies 48
6.0.1 Nominal Bonds and TIPS BEI Pairs . . . . . . . . . . . . . 48
6.0.2 ZCIS BEI Pairs . . . . . . . . . . . . . . . . . . . . . . . . . 54

7 Conclusion 57
A. Solving Quadratic Spline Interpolation of Forward 59
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