市场化进程中的利率模型研究—从随机微分到量子金融的分析

Interest rate liberalization is the important part of China’s financial system reform, which will bring new challenges for the current financial products pricing mechanism and risk management. Based on the research of dynamic process and evolution mechanism of interest rates, the project targets at solving the key problems arising from China’s financial market on both theoretical and practical ways. In the aspects of theories, following the main track of “from Stochastic Calculus to Quantum Finance”, the theoretical models will be developed to describe the stochastic volatility and jump process of interest rates. In order to develop interest rate market models, the stochastic processes in stochastic volatility models and jump diffusion models will be generalized to stochastic fields. Furthermore, Libor Hamiltonian market model and particle tunneling model will be developed fully built on quantum field theory, which realize the evolution from Stochastic Calculus to Quantum Finance. In the aspects of applications, in order to conduct the asset pricing, the treasury bond yield curve will be fitted by using Libor market model. Furthermore, the economic meanings of yield curve will be revealed. The pricing of treasury bond and futures will be studied by using interest rate models, and the arbitraging and hedging of portfolios will be simulated. The theoretical and practical research of this projects can provide important theoretical support and practice guidance for China’s policy authorities and financial institutes on enhancing interest rate risk management.

利率市场化是我国金融体制改革的重要内容，将对我国现有的金融产品定价机制和风险管理形成新的挑战。本项目通过研究利率的动态过程和演化机制，分别在理论和应用方面解决我国金融市场存在的关键性实际问题。理论方面，基于“随机微分—量子金融”这一主线，构建理论模型用以描述利率的随机波动和跳跃行为；分别将随机波动率模型和跳跃扩散模型中的随机过程扩展为更一般的波动场，并构建利率市场模型；进一步构建完全基于量子场论的Libor 哈密顿量市场模型和粒子遂穿模型，实现从随机微分到量子金融的理论进化。应用方面，基于Libor市场模型，拟合出能够指导基础定价的国债收益率曲线，并揭示其经济含义；运用利率模型对国债和国债期货进行定价研究，并指导组合的套利和套期保值仿真交易。本项目的理论和应用研究可以为我国政策当局、金融机构加强利率风险管理提供重要的理论支持和实践指导。

利率的随机演变特征及其模型构建一直以来是金融工程和金融数学研究的重点，本课题研究了我国利率的随机波动和跳跃特征，以及利率模型在我国金融市场的应用。首先，在量子金融的背景下，研究了Libor市场模型的哈密顿量，提出了可以很好地描述多个不同到期期限利率的利率市场模型，极大地提高了利率模型的解释能力，且提出了市场时间的概念。其次，通过使用物理理论中的transfer entropy的方法刻画了金融机构之间和全球金融市场之间的风险传递网络，为研究资产价格的跳跃特征和风险提供了全新的视角和方法。最后，本课题分别在国债收益率曲线拟合、国债期货、利率信息含量等方面实现了利率模型在我国金融市场的应用研究。此外，基于本课题的研究成果，对Zipf ranking、统计经济学模型、股票收益率和基准利率的状态转换等相关领域做了研究。本课题丰富了量子理论和物理理论在金融数学中的相关理论，可为我国监管层和金融机构加强利率风险管理提供理论和方法。