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.

这一建议涉及超越经典的多变量几何布朗运动的金融市场的多变量建模，通过使用对现代数学金融理论做出贡献的创新思想、概念和技术。值得特别注意的是不同资产之间的依赖结构的建模。所提出的模型引入了跳跃、随机波动、随机协方差、分数过程，有时还引入了这些特征的组合。对于所提出的模型，本方案考虑了定价和灵敏度分析等基本问题，采用了精确定价和近似定价两种方法。对于所提出的一些模型，主要是那些包含分数布朗运动分量的模型，因此可能不是半鞅，因此研究套利机会的存在性及其相关的套期保值策略是有意义的。这种方法强调轨迹的精细结构，而不是模型的概率结构。这些多变量模型的参数的统计推断也构成了一个非常相关的问题，将被研究。对这些模型的研究，特别是对资产之间相关性结构的研究，可以更好地理解金融市场的动态，这从风险管理的角度来看是很重要的。