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: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635972
• 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是在连续时间中制定的，但实际上它们只在离散时间中使用。这种方法的一个重要例子是delta套期保值，其中使用从连续时间模型获得的对市场风险的敏感性来创建局部静态对冲投资组合。由于这个问题的重要性，许多研究都旨在描述诱导套期误差的不同性质。然而，大多数结果都与欧洲期权有关，尽管大多数交易期权依赖于基础证券的价格路径。我最近证明了亚洲期权的delta套期保值的效率明显低于最佳风险最小化套期保值策略。这一结果具有重要的现实意义，我计划在这一领域扩大和加强我的研究。一个方向是为其他依赖路径的期权提供类似的分析，包括美国期权和障碍期权。第二个方向是考虑适用于其他应用领域的模型，例如保险。