Equity-linked products

在这个研究项目中，我将建立一个保险责任的随机结构。这种新的结构依赖于对未来负债的建模，而不是对令人震惊的死亡率概率的建模。在这种情况下，基础短期利率遵循Ho和Lee模型。保险责任结构应具有与Ho和Lee的利率模型相似的假设，例如恒定波动率和非常数鞅概率。一旦定义了利率和保险结构，我们就可以扩展鞅度量以包括指数过程(我们使用了股票指数的考克斯、罗斯和鲁宾斯坦模型)。我将使用共同冲击模型、分层模型以及Copula来扩展鞅度量，并能够对与股票挂钩的产品进行估值。我计划对使用无套利理论评估的保险产品进行一项实证研究。其目标是确定标准保险费所隐含的死亡率负荷，并找到符合观察到的鞅死亡率概率的精算保费原则。与动态的再保险市场类似，我也计划研究不同的对冲策略(均值-方差对冲、有效对冲(分位数对冲)、超级复制等)。考虑到销售股权挂钩合同的保险公司可以投资于再保险组合。运用风险价值和条件尾部预期等多种风险度量方法，分析了不同交易策略对收益风险比的影响。

In this research project, I will develop a stochastic structure for insurance liabilities. This new structure relies on the modelling of future liabilities instead of martingale mortality probabilities. In this setup, the underlying short-term rate follows the Ho and Lee model. The insurance liability structure should have similar assumptions to those of Ho and Lee for interest rate models, for instance constant volatility and non-constant martingale probabilities. Once the interest rate and insurance structures are defined, we can extend the martingale measure to include the index process (we employ the Cox, Ross and Rubinstein model for the stock index). I will use common-shock models, hierarchal models as well as copulas to extend the martingale measure and be able to valuate equity-linked products. I plan to conduct an empirical study on insurance products valuated using arbitrage-free theory. The goal is to identify the mortality loadings implied by standard insurance premiums and find actuarial premium principles that fit the observed martingale mortality probabilities. Similar to dynamic reinsurance markets, I also plan to investigate different hedging strategies (mean-variance hedging, efficient hedging (quantile hedging), super-replication, etc.) considering that insurance companies selling equity-linked contracts can invest in a reinsurance portfolio. Using various risk measures including the well-known Value at Risk and Conditional Tail Expectation, I will also analyze the effect of the different trading strategies on the profit-risk ratio.