Financial modelling in an HMM-modulated regime-switching framework

HMM 调制的制度转换框架中的财务建模

• 批准号: 341780-2012
• 负责人: Mamon, Rogemar
• 金额: $ 1.53万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=572365
• 关键词: Financial; modelling; HMM; modulated; regime

This research programme centres on the theme of regime-switching frameworks in financial modelling. The switching of regimes is governed by either a continuous- or discrete-time hidden Markov chain representing the "state of the world". New practical applications and further theoretical developments of hidden Markov models (HMM) are investigated. First, HMM filtering theory is extended to deal with the long range dependence of time series data illustrating that the Markovian assumption in HMM is not as restrictive as it first appears. This gives rise to weak HMMs driving the stochastic evolution of model parameters thereby capturing both regime-switching and memory properties. Second, Kalman filtering and other non-linear filtering techniques are coupled with optimal HMM filtering theory to produce adaptive and high performance algorithms in the parameter estimation and modelling of financial variables and other phenomena in nonlinear time series. Third, methodologies are devised for efficient valuation of annuity-linked contracts and mortality-linked securities where the dynamics of both financial and demographic factors are assumed correlated, and both interest and mortality rates are HMM-modulated. Fourth, the recovery of time-varying parameters for HMM-based models in option pricing and bond valuation is considered. This inverse problem in finance may be addressed either by using an ansatz approach or by reformulating it as a generalisation of the inverse Stieltjes moment problem of mathematical analysis. In some cases such as in bond pricing, generating functions, which can be viewed as a transform of one of the components of the bond price solution, will be constructed. Whilst all of these investigations have direct relevance to quantitative finance and actuarial science, other fields of applications including economics, engineering and other branches of applied sciences could also positively benefit from the results of this research programme.

该研究方案的中心主题是金融建模中的制度转换框架。政权的切换是由一个连续或离散时间隐马尔可夫链代表的“世界的状态”。隐马尔可夫模型（HMM）的新的实际应用和进一步的理论发展进行了研究。首先，将HMM滤波理论扩展到处理时间序列数据的长程相关性，说明HMM中的马尔可夫假设并不像最初出现的那样严格。这引起了弱HALLESS驱动模型参数的随机演化，从而捕获两个政权切换和记忆特性。其次，卡尔曼滤波和其他非线性滤波技术与最佳HMM滤波理论相结合，以产生自适应和高性能算法，用于参数估计和金融变量建模以及非线性时间序列中的其他现象。第三，设计方法有效的估值年金挂钩的合同和死亡率挂钩的证券，金融和人口因素的动态假设相关，利率和死亡率的HMM调制。第四，考虑了基于HMM的期权定价和债券定价模型中时变参数的恢复问题。金融中的这个逆问题可以通过使用一种分析方法来解决，也可以通过将其重新表述为数学分析的逆Stieltjes矩问题的概括来解决。在某些情况下，如在债券定价，生成函数，这可以被看作是一个转换的债券价格解决方案的组成部分之一，将被构造。虽然所有这些研究都与定量金融和精算科学直接相关，但其他应用领域，包括经济学，工程学和应用科学的其他分支也可以从这项研究计划的成果中受益。