Hedging derivatives: from finance to actuarial science

对冲衍生品：从金融到精算科学

• 批准号: 355946-2013
• 负责人: Badescu, Alexandru
• 金额: $ 0.8万
• 依托单位: University of Calgary
• 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=635823
• 关键词: Hedging; derivatives; finance; actuarial; science

The pricing, hedging and risk management of financial and insurance products have been key objects of study in over two decades. Although tremendous research efforts have addressed important aspects, there are still 'puzzles' yet to be solved. This research project focus on two main strands from the financial econometrics and actuarial science literature. The first part of the project investigates the pricing and hedging of financial derivatives, in particular options and volatility derivatives. Although a vast majority of the mathematical finance literature examines these in continuous time, mainly due to the tractability offered by this setup, quantities of interest are in general sampled at fixed dates and therefore, a discrete-time setting might be more appropriate. In this project we develop new methods for pricing and hedging of options and variance swaps based on a broad class of non-linear time series models and we illustrate the interplay with their continuous time limits, by studying the convergence between the corresponding quantities of interest. We further plan to investigate how these methods can be applied to hedging insurance products. In the second part of the proposal, we explore one of the major challenges faced by an insurance company regarding the quantification of its minimum required capital and its optimal investment into a well-diversified portfolio of financial assets. Motivated by the Solvency II Directives, we propose new optimization problems for non-life insurance companies, with different solvency constraints imposed by regulators. These optimization problems will be implemented in both static, and dynamic settings.

在二十年中，金融和保险产品的定价，对冲和风险管理一直是研究的关键对象。尽管巨大的研究工作已经解决了重要方面，但仍有“难题”尚未解决。该研究项目着重于金融计量经济学和精算科学文献中的两个主要链。该项目的第一部分调查了金融衍生品的定价和对冲，特别是选择和波动性衍生品。尽管绝大多数数学金融文献都在连续的时间内检查了这些文献，这主要是由于这种设置提供的障碍性，但通常在固定日期进行了采样数量，因此，离散的时间设置可能更合适。在这个项目中，我们开发了基于广泛的非线性时间序列模型的选择和方差互换定价和套期保值的新方法，我们通过研究相应的兴趣量之间的收敛性来说明与它们连续的时间限制的相互作用。我们进一步计划调查如何将这些方法应用于对冲保险产品。在提案的第二部分中，我们探讨了一家保险公司在量化其最低要求的资本以及其最佳投资对金融资产投资组合的最佳投资方面面临的主要挑战之一。在偿付能力II指令中，我们为非生活保险公司提出了新的优化问题，该公司对监管机构施加了不同的偿付能力约束。这些优化问题将在静态和动态设置中实现。