论文标题
通过连续时间马尔可夫链近似分析可变年金中VIX连接的费用激励措施
Analysis of VIX-linked fee incentives in variable annuities via continuous-time Markov chain approximation
论文作者
论文摘要
我们考虑在流行的随机波动率模型（例如赫斯顿，赫尔 - 白人，斯科特，$α$ - hypheremetric，$ 3/2 $和$ 4/2 $型号）下的可变年金（VA）定价（VAS）具有一般费用结构。特别是，我们分析了具有保证最低成熟度（GMMB）的VA合同最佳投降策略的不同VIX挂钩费用结构的影响。在假设可以在到期之前交出VA合同的假设，VA合同的定价对应于具有无限，时间依赖和不连续的收益功能的最佳停止问题。我们开发有效的算法，用于使用两层连续的马尔可夫链近似为基金价值过程的VA合同定价。当合同保留直到到期并在一般费用结构下，我们表明合同的价值可以通过封闭形式的矩阵表达式近似。我们还提供了一种快速而简单的方法来确定通过递归算法确定早期投降的价值，并提供简单的程序以近似最佳的投降表面。我们从数字上表明，当费用链接到VIX索引时，最佳的投降策略对于帐户价值的波动性的变化更为强大。
We consider the pricing of variable annuities (VAs) with general fee structures under popular stochastic volatility models such as Heston, Hull-White, Scott, $α$-Hypergeometric, $3/2$, and $4/2$ models. In particular, we analyze the impact of different VIX-linked fee structures on the optimal surrender strategy of a VA contract with guaranteed minimum maturity benefit (GMMB). Under the assumption that the VA contract can be surrendered before maturity, the pricing of a VA contract corresponds to an optimal stopping problem with an unbounded, time-dependent, and discontinuous payoff function. We develop efficient algorithms for the pricing of VA contracts using a two-layer continuous-time Markov chain approximation for the fund value process. When the contract is kept until maturity and under a general fee structure, we show that the value of the contract can be approximated by a closed-form matrix expression. We also provide a quick and simple way to determine the value of early surrenders via a recursive algorithm and give an easy procedure to approximate the optimal surrender surface. We show numerically that the optimal surrender strategy is more robust to changes in the volatility of the account value when the fee is linked to the VIX index.
