Equity-linked products

在这个研究项目中，我将开发一个保险责任的随机结构。这种新结构依赖于对未来负债的建模，而不是边际死亡概率。在这种情况下，潜在的短期利率遵循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恒定鞅概率。一旦确定了利率和保险结构，我们就可以扩展鞅度量以包括指数过程（我们对股票指数采用Cox， Ross和Rubinstein模型）。我将使用共冲击模型，层次模型以及copulas来扩展鞅测度，并能够对股票挂钩产品进行估值。我计划对使用无套利理论进行估值的保险产品进行实证研究。目标是确定标准保险费隐含的死亡率负荷，并找到符合观察到的鞅死亡率概率的精算保费原则。与动态再保险市场类似，考虑到出售股票挂钩合约的保险公司可以投资于再保险组合，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）。使用各种风险度量，包括众所周知的风险值和条件尾部预期，我还将分析不同的交易策略对利润风险比的影响。

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.