本课题对金融理论中的单一收益率曲线的无套利利率期限结构模型进行创新，构建出以核心国债收益率曲线为基准、与同币种多条次级收益率曲线的联合无套利模型，次级收益率曲线与核心收益率曲线的利差被系统违约风险、市场流动性风险及个体风险所定价。这一高维无套利框架既兼顾收益率的期限关系，又同时刻画不同收益率曲线之间的因子结构特征，可以应用于对“外围-中心”型债券收益率体系的动态关系进行联合建模和实时监控。课题分别根据美国、欧洲和中国债券市场的具体特征对该经济体内多条收益率曲线在这一框架下进行联合建模、估计，识别系统性风险与个体风险及其交互影响，为政策制定者和市场投资者在债务系统的结构性、动态性和复杂性条件下的定价、分析和预测提供有效工具。在这一理论建模框架下，我们还将进一步引入状态空间的时变系数模型，使用贝叶斯计量方法适应性地实时更新模型参数和风险观测，为动态掌握债市风险演变路径和政策调整提供科学手段。

Based on the affine arbitrage-free term structural model for single yield curve modeling supported by financial theory, this project develops a novel framework to jointly model multiple yield curves with no-arbitrage restrictions. In this framework, there is one benchmark yield curve, typically the sovereign yield curve of an economy, and multiple yield curves of higher risks. The states of these curves contain three types of factors: 1) the benchmark yield factors, which are basis for all curves; 2) two common factors for yield spreads of yield curves with higher risk, i.e., the common credit risk and market liquidity risk; and 3) specific risk factors for each yield curve other than the benchmark. No-arbitrage restrictions exist not only between yields of different maturities across a yield curve, but also across yield curves with the underlying factor structure. This framework ensures consistency of pricing of bonds in a high-dimension world, and is useful for bond portfolio management, risk analysis and management. It is particular helpful for policy analysis on systemic risks of the bond market, which can disentangle common risks from asset specific risks and to quantify risks in a unified and consistent way with underlying economic foundations. Moreover, we will also introduce a time-varying parameter VAR model to the state to build a model accommodating possible structural breaks, which is more realistic in studying a crisis scenario. With Bayesian Markov chain Monte Carlo method and adaptive modeling techniques, we can estimate the model for bond markets of Europe, US and China, and bring rich insights to the structural debt problems pertinent to these economies in the recent decade, and provide effective tools for risk monitoring and policy analysis in real time.