Pricing and Hedging Equity-Linked Products Using Risk Measures

使用风险措施对股票挂钩产品进行定价和对冲

• 批准号: RGPIN-2014-04020
• 负责人: Gaillardetz, Patrice
• 金额: $ 1.31万
• 依托单位: Concordia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=610787
• 关键词: Pricing; Hedging; Equity; Linked; Products

The main objective of this project is to develop pricing and hedging techniques for equity-indexed annuities based on risk measures. An equity-indexed annuity (EIA) is an insurance product with benefits linked to the performance of an equity market. It provides limited participation in the performance of an equity index (e.g. S&P 500) while guaranteeing a minimum rate of return. First introduced by Keyport Life Insurance Co in 1995, EIAs have been the most innovative annuity product over the last 20 years. They have become increasingly popular since their debut; the sales of EIAs have steadily increased and hit a record high of $33.9 billion in 2012, as indicated in the fourth quarter 2012 U.S. Individual Annuities Sales survey from Life Insurance and Market Research Association (LIMRA).Equity-indexed annuities are usually wrapped with some death, surrender, withdrawal, and accumulation guarantees that protect policyholders. The costs of these guarantees are evaluated based on financial and actuarial models. Research on evaluating these products has been carried using various approaches; see Hardy ("Investment Guarantees: Modeling and Risk Management for Equity-Linked life Insurance", 2003) and the references therein. I am primarily interested in the application of optimization techniques to reduce the risk of equity-indexed annuity portfolios. In a complete market, all financial claims can be hedged perfectly. However, in an incomplete financial market, the number of securities is less than the number of possible outcomes. In this case, the perfect hedge is unattainable. This is the appropriate framework when complex underlying asset models, mortality risks, and withdrawals are considered. There are different pricing and hedging techniques that could be used in such cases; we shall focus on risk measures. Two different objectives could be achieved while defining the hedging strategy using risk measures. On the one hand, the insurance company could minimize the hedging cost for a given risk level. On the other hand, the issuer could minimize the risk associated to a hedging strategy chosen among self-financing ones. Gaillardetz and Moghtadai (Equity-Linked Product Evaluation Using Iterated Risk Measures, 2013) focus on the latter where the hedging strategy is formed of the underlying risky and risk-free assets. Using the result of Rockafeller and Uryasev (Conditional value-at-risk for general loss distributions, 2002), which converts the evaluation of the tail value-at-risk into a linear programming problem, we propose to generalize the hedging strategies to multiple risky assets. We will also restrict our hedging strategies to self-financing strategies and try to minimize a given risk measure. This could be solved using the linear programming approach with state variables. Surrender and withdrawal options are usually priced assuming that policyholders are rational. It requires that the investors be fully informed of the financial market and thus can always take optimal decisions. This strong assumption leads to an upper bound for prices since it considers the worse case scenario for the issuer. Under the proposed risk measure approach, surrender and withdrawal processes will be modeled under the physical probability measures, which means that some endogenous and exogenous effects will be used.

该项目的主要目标是开发基于风险衡量的股票指数年金的定价和对冲技术。股票指数年金（EIA）是一种保险产品，其福利与股票市场的表现挂钩。它提供对股票指数（例如标准普尔 500）表现的有限参与，同时保证最低回报率。 EIA 由 Keyport Life Insurance Co 于 1995 年首次推出，是过去 20 年来最具创新性的年金产品。自出道以来，他们的受欢迎程度越来越高；根据人寿保险和市场研究协会 (LIMRA) 的 2012 年第四季度美国个人年金销售调查显示，EIA 的销售额稳步增长，并在 2012 年创下了 339 亿美元的历史新高。 股票指数年金通常包含一些死亡、退保、提款和累积保证，以保护保单持有人。这些担保的成本是根据财务和精算模型进行评估的。已经使用各种方法对这些产品进行了评估研究；参见 Hardy（“投资担保：股权挂钩人寿保险的建模和风险管理”，2003 年）及其参考文献。我主要对应用优化技术来降低股票指数年金投资组合的风险感兴趣。在一个完整的市场中，所有的金融债权都可以完美地对冲。然而，在不完全的金融市场中，证券的数量少于可能结果的数量。在这种情况下，完美的对冲是不可能实现的。当考虑复杂的基础资产模型、死亡风险和提款时，这是合适的框架。在这种情况下可以使用不同的定价和对冲技术；我们要重点关注风险措施。使用风险衡量指标定义对冲策略时可以实现两个不同的目标。一方面，保险公司可以最大限度地降低给定风险水平的对冲成本。另一方面，发行人可以最大限度地降低与自筹资金策略中选择的对冲策略相关的风险。 Gaillardetz 和 Moghtadai（使用迭代风险测量的股票挂钩产品评估，2013）重点关注后者，其中对冲策略由潜在的风险和无风险资产组成。利用 Rockafeller 和 Uryasev（一般损失分布的条件风险价值，2002）的结果，将尾部风险价值的评估转化为线性规划问题，我们建议将对冲策略推广到多种风险资产。我们还将对冲策略限制为自负盈亏策略，并尽量减少给定的风险措施。这可以使用状态变量的线性规划方法来解决。 退保和退保选择的定价通常假设投保人是理性的。它要求投资者充分了解金融市场，从而能够做出最优决策。这一强有力的假设导致了价格上限，因为它考虑了发行人最坏的情况。根据所提出的风险度量方法，退保和退出过程将在物理概率度量下建模，这意味着将使用一些内生和外生效应。