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都是在连续时间内制定的，但实际上它们仅在离散时间内使用，这种方法的一个重要例子是德尔塔对冲，其中使用从连续时间模型获得的对市场风险的敏感性。由于该问题的重要性，许多研究都旨在描述引起的对冲误差的不同属性，然而，大多数结果都涉及欧式期权，尽管大多数研究都是针对欧式期权的。交易的期权取决于标的资产的价格路径我最近证明了亚洲期权的 Delta 对冲策略的效率明显低于最优风险最小化对冲策略，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。对于其他路径相关期权，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。