Statistical and computational topics from modern finance and insurance

现代金融和保险的统计和计算主题

• 批准号: RGPIN-2015-04059
• 负责人: Kolkiewicz, Adam
• 金额: $ 1.02万
• 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: 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=589569
• 关键词: Statistical; computational; topics; modern; finance

While many mathematical models used in modern finance are formulated in continuous time, in practice they are used in discrete time only. An important example of such an approach is delta hedging, where sensitivity to the market risk obtained from a continuous-time model is used to create a locally static hedge portfolio. Due to the importance of the problem, numerous studies have been aimed at describing different properties of the induced hedging error. The majority of the results, however, deal with European options, despite the fact that most of the traded options depend on the price-path of the underlying security. I recently demonstrated that delta hedging for Asian options is significantly less efficient than optimal risk-minimizing hedging strategies. This result has important practical implications, and I plan to broaden and intensify my research in this area. One direction is to provide similar analysis for other path-dependent options, including American and barrier options. Second direction is to consider models suitable in other areas of applications, such as insurance.

虽然现代金融中使用的许多数学模型都是在连续时间内制定的，但实际上它们只在离散时间内使用。这种方法的一个重要例子是delta对冲，其中从连续时间模型获得的市场风险的敏感性被用来创建一个局部静态对冲投资组合。由于该问题的重要性，许多研究旨在描述不同性质的诱导套期保值错误。大多数的结果，然而，处理欧式期权，尽管事实上，大多数的交易期权依赖于价格路径的基础证券。 我最近证明了亚式期权的Delta对冲比最优风险最小化对冲策略的效率低得多。这一结果具有重要的实际意义，我计划扩大和加强我在这一领域的研究。一个方向是为其他路径依赖期权提供类似的分析，包括美式期权和障碍期权。 第二个方向是考虑适用于其他应用领域的模型，例如保险。