Multivariate modelling of financial markets

金融市场的多元建模

• 批准号: RGPIN-2014-04203
• 负责人: Alvarez, Alexander
• 金额: $ 0.73万
• 依托单位: Ryerson University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=566365
• 关键词: Multivariate; modelling; financial; markets

This proposal concerns the multivariate modeling of financial Markets beyond the classical Multivariate Geometric Brownian motion, by using innovative ideas, concepts and techniques that contribute to the theory of modern mathematical finance. Special attention is deserved to the modeling of the dependence structure between the different assets. The proposed models introduce jumps, stochastic volatility, stochastic covariance, fractional processes and sometimes combinations of theses features. For the proposed models, fundamental problems as pricing and sensitivity analysis are considered in this proposal, using both exact and approximate pricing approaches. For some of the proposed models, mainly for those that include a Fractional Brownian motion component and therefore may not be semimartingales, it is relevant to study the existence of arbitrage opportunities, and the hedging strategies associated to them. This approach emphasize on the fine structure of the trajectories instead of the probabilistic structure of the model. The statistical inference of the parameters of these multivariate models constitute also a very relevant problem that will be studied. The study of these models, and in particular the study of the dependence structure between the assets, provides a better understanding of the dynamics of financial markets, which is important from the risk management perspective.

该提案涉及通过使用创新的思想，概念和技术来有助于现代数学金融理论的创新思想，概念和技术，涉及超出经典多元几何布朗运动以外的金融市场的多元建模。应特别注意不同资产之间依赖性结构的建模。提出的模型引入了跳跃，随机波动率，随机协方差，分数过程以及有时的这些特征组合。对于拟议的模型，使用精确和近似定价方法在此提案中考虑了作为定价和灵敏度分析的基本问题。对于某些提议的模型，主要是针对包括分数布朗运动组成部分并且可能不是半明星的模型，它与研究套利机会的存在以及与之相关的对冲策略是相关的。这种方法强调了轨迹的精细结构，而不是模型的概率结构。这些多元模型的参数的统计推断也构成了一个非常相关的问题。对这些模型的研究，尤其是对资产之间的依赖结构的研究，可以更好地理解金融市场的动态，从风险管理的角度来看，这很重要。