Incomplete data, stochastic processes and finance

不完整的数据、随机过程和财务

• 批准号: 8335-2006
• 负责人: McLeish, Don
• 金额: $ 1.46万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=389726
• 关键词: Incomplete; data; stochastic; processes; finance

Incomplete or missing data  and the necessity to impute missing values is a common feature of modern data in finance, economics, sample surveys, biostatistics, and other applications of statistics.  Relevant variables may be ignored either because they are difficult to obtain or  they complicate the analysis.  For example if  stock A is traded at time t, say,   another stock B is highly unlikely to be traded at exactly the same time in which case the fair value of stock B at this time is ``missing''. The usual practice of rounding the trading times up is dangerous in that it introduces biases in the estimates, possibly  of limited consequence for highly liquid equities and benchmark bonds, but much more significant  with thinly traded or illiquid assets.  Naive manufacture or ``imputation'' of data for the convenience of the data analysis runs the risk of introducing bias and undermining the original intent of the analyst; to objectively extract all pertinent information from the data. Ignoring those cases or variables which have missing components is as dangerous as naively filling in data; it too potentially leads to biased results. The objective of  my research is to make exact imputation techniques available to both multivariate and univariate diffusion models, such as those commonly used in finance, and exploit them for estimation of parameters and other problems in which interpolating the values of a diffusion is useful.    In biostatistics, there are often  response or predictor variables that  might help explain the behaviour of a ``response variable'' of interest, but they are not collected simply because of the expense of the data collection.  Similar but less precise information might be easily available from health collection agencies, hospital databases, or a simple cheap test. To what extent can the cheaper variables be used as proxies for the more expensive? Collection of the expensive  variables for even a fraction of the cases will often help assess the degree to which we sacrifice efficiency and bias when we omit these more expensive variables and usually allow for an improvement in efficiency with reduced cost.     My research concerns the "proper" imputation of data, i.e. the imputation of data using the exact distribution consistent with what we observe, so as permit use of simpler complete data techniques on these missing data problems.

不完整或缺失的数据以及需要估算缺失值是金融、经济、抽样调查、生物统计学和其他统计应用中现代数据的共同特征。相关变量可能会被忽略，因为它们难以获得或使分析复杂化。例如，如果股票A在时间t交易， 另一只股票B不太可能在同一时间交易，在这种情况下，此时股票B的公允价值"缺失“。将交易时间向上舍入的通常做法是危险的，因为它会在估计中引入偏差，对流动性高的股票和基准债券可能影响有限，但对交易量小或流动性差的资产影响要大得多，为方便数据分析而天真地制造或“估算”数据有可能引入偏差，破坏分析人员的初衷;客观地从数据中提取所有相关信息。忽略那些缺失成分的案例或变量与天真地填充数据一样危险;它也可能导致有偏见的结果。我的研究的目的是使精确的插补技术可用于多变量和单变量扩散模型，如金融中常用的，并利用它们来估计参数和其他问题，其中插值的扩散值是有用的。 在生物统计学中，通常有响应或预测变量可能有助于解释感兴趣的“响应变量”的行为，但由于数据收集的费用，它们并没有被收集。类似但不太精确的信息可能很容易从健康收集机构，医院数据库或简单的廉价测试中获得。在多大程度上可以使用更便宜的变量作为更昂贵的变量的代理？收集哪怕是一小部分案例的昂贵变量，通常也有助于评估我们在忽略这些更昂贵的变量时牺牲效率和偏差的程度，通常可以在降低成本的情况下提高效率。 我的研究关注的是数据的“适当”插补，即使用与我们观察到的一致的确切分布来插补数据，从而允许在这些缺失数据问题上使用更简单的完整数据技术。