Interest rate term structure and fixed income security pricing

Author: Li Hejin et al.
Publisher:
Publish Date: 2005-01-01
Features: China is steadily advancing the reform of interest rate liberalization. Currently, the level of interest rate liberalization has been significantly improved, with commercial interest rates other than bank deposit and loan rates fully liberalized. In particular, medium- and long-term government bond rates are determined through open bidding, providing market-based, independent, and time-preference-driven interest rates, which offer clear price guidance signals for the launch and trading of financial products. As the reform of interest rate liberalization deepens, government bond rates, as risk-free rates, will become the benchmark interest rates for financial markets. The yield curve composed of government bond yields of different maturities will have a significant impact on the pricing of financial products, including stocks, bonds, and derivative securities. At the same time, China will vigorously develop the bond market, including rapid growth in government bonds and corporate bonds, and various hybrid bond products with embedded options will emerge. The yield curve will play a crucial role in the design and pricing of these hybrid bonds. Against this backdrop, this book primarily focuses on the yield curve as the research subject, systematically analyzing it from theoretical research to empirical research, and further to applied research and policy research. The main contributions and conclusions of this book are as follows:
Building on existing theories of the yield curve, this book employs principles of stochastic processes and non-parametric kernel function estimation methods to establish a non-parametric yield curve model based on diffusion-jump processes. This non-parametric model overcomes the limitations of traditional parametric models, which assume a priori the probability distribution and parameter forms of interest rates, by relying on data-driven analysis. It also considers the impact of sudden market factors on the jump components of the interest rate stochastic process.
Using data from the Shanghai Stock Exchange's government bond repurchase rates as a sample, this book empirically tests the established non-parametric yield curve model and compares it with typical parametric yield curve models, such as the Vasicek model and the CIR model. The empirical results indicate that the parametric models exhibit specification errors. The author argues that the non-parametric model proposed in this book can more accurately describe the yield curve of China's government bond rates compared to traditional parametric models.
As an application of the established non-parametric yield curve model, this book conducts pricing research on three types of hybrid bonds: oil bonds, convertible bonds, and reverse floating-rate bonds. These hybrid bonds are representative financial products in reality whose pricing still needs improvement.
This book designs futures-linked oil bonds and options-linked oil bonds, whose interest payments are linked to oil futures prices, differing from traditional fixed-rate and floating-rate bonds. These oil hybrid bonds exhibit the characteristics of futures and call options, respectively. The correlation between interest rates and oil prices is tested, revealing a small correlation coefficient and frequent inconsistencies between interest rate and oil price fluctuations, providing a practical basis for the design of oil hybrid bonds.
Limits (upper, lower, and dual) are set for oil futures prices for these two types of oil bonds, and their pricing is studied using the established non-parametric yield curve model, with comparisons made to pricing under constant interest rates. The results suggest that issuing these hybrid bonds by oil companies can effectively diversify and transfer oil price volatility risks, overcoming the shortcomings of traditional fixed-rate and floating-rate bonds in hedging against oil price fluctuations. The non-parametric model's pricing results differ from those under constant interest rates, indicating that these hybrid bonds carry certain interest rate risks. Setting limits on oil futures prices can provide a degree of protection for issuers or investors, and the risk of options-linked oil bonds is lower than that of futures-linked oil bonds.
This book also conducts pricing research on convertible bonds under stochastic interest rates. Taking the Airport Convertible Bond traded on the Shanghai Stock Exchange as an example, the conversion option, redemption option, and put option of the bond are priced and compared using both the established non-parametric model and the traditional Black-Scholes model. The results indicate that the non-parametric yield curve model's pricing method for convertible bonds is superior to the Black-Scholes model's method.
Additionally, this book improves some design terms of the Airport Convertible Bond, designing a floating-rate convertible bond and pricing it using the non-parametric model. The results show that issuing floating-rate convertible bonds is beneficial for protecting investors' interests when interest rates are low.
This book also conducts pricing research on reverse floating-rate bonds. By decomposing and combining reverse floating-rate bonds, it designs reverse floating-rate bonds with interest rate upper limits, lower limits, and dual limits, and studies their pricing using the non-parametric model. It also highlights the importance of issuing reverse floating-rate bonds in China.
Furthermore, this book explores policy research on establishing a benchmark government bond yield curve for China's financial market and proposes specific policy recommendations. Additionally, it examines fundamental theories, systems, domestic and international comparisons, and practical operational frameworks in areas such as bond market financial innovation, credit risk modeling, and bond rating.
The main innovations of this book are as follows:
1. It establishes a non-parametric yield curve model based on diffusion-jump processes. This non-parametric model does not assume a priori the probability distribution of interest rates or the parameter form of the model, overcoming the defects of traditional parametric models that rely on such assumptions. At the same time, it considers the stochastic process of short-term interest rates as a diffusion-jump process, addressing the limitation of traditional models that assume short-term interest rates follow only diffusion processes while ignoring market jumps.
2. It uses government bond repurchase rate data to empirically test the established non-parametric yield curve model, with results indicating that the non-parametric model outperforms traditional parametric models.
3. It designs futures-linked oil bonds and options-linked oil bonds, whose interest payments are linked to oil futures prices, effectively diversifying and transferring oil price volatility risks. Pricing research on these bonds is conducted using the established non-parametric model.
4. It uses the established non-parametric model to price convertible bonds and compares the results with the traditional Black-Scholes model's pricing method, showing that the proposed method is superior. It also designs floating-rate convertible bonds to address some defects in China's convertible bond design terms and prices them using the non-parametric model.
5. It uses the established non-parametric model to conduct pricing research on reverse floating-rate bonds.
With the deepening of interest rate liberalization in China, the role of interest rates in pricing financial products is becoming increasingly significant. The yield curve model established in this book overcomes the limitations of traditional models, offering substantial guidance for the design and pricing of financial products. The designed oil bonds can effectively help oil companies hedge against oil price volatility risks. This book provides a new pricing method for convertible bonds emerging in China's capital market. The designed reverse floating-rate bonds can be used by financial institutions to manage interest rate risks and conduct hedging.
Based on the theory of the yield curve, this book employs principles of stochastic processes and non-parametric kernel function estimation methods to establish a non-parametric yield curve model based on diffusion-jump processes. It uses government bond repurchase rate data from the Shanghai Stock Exchange to empirically test the model. Additionally, it applies the model to pricing research on oil bonds, convertible bonds, and reverse floating-rate bonds. The book also explores policy research on establishing a benchmark government bond yield curve for China's financial market and proposes specific policy recommendations.