英文标题：
《Fast Numerical Method for Pricing of Variable Annuities with Guaranteed
  Minimum Withdrawal Benefit under Optimal Withdrawal Strategy》
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作者：
Xiaolin Luo and Pavel Shevchenko
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最新提交年份：
2014
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英文摘要：
  A variable annuity contract with Guaranteed Minimum Withdrawal Benefit (GMWB) promises to return the entire initial investment through cash withdrawals during the policy life plus the remaining account balance at maturity, regardless of the portfolio performance. Under the optimal withdrawal strategy of a policyholder, the pricing of variable annuities with GMWB becomes an optimal stochastic control problem. So far in the literature these contracts have only been evaluated by solving partial differential equations (PDE) using the finite difference method. The well-known Least-Squares or similar Monte Carlo methods cannot be applied to pricing these contracts because the paths of the underlying wealth process are affected by optimal cash withdrawals (control variables) and thus cannot be simulated forward in time. In this paper we present a very efficient new algorithm for pricing these contracts in the case when transition density of the underlying asset between withdrawal dates or its moments are known. This algorithm relies on computing the expected contract value through a high order Gauss-Hermite quadrature applied on a cubic spline interpolation. Numerical results from the new algorithm for a series of GMWB contract are then presented, in comparison with results using the finite difference method solving corresponding PDE. The comparison demonstrates that the new algorithm produces results in very close agreement with those of the finite difference method, but at the same time it is significantly faster; virtually instant results on a standard desktop PC.
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中文摘要：
具有最低取款保障福利（GMWB）的可变年金合同承诺，无论投资组合表现如何，在保单有效期内通过现金取款以及到期时的剩余账户余额来返还全部初始投资。在投保人的最优退出策略下，带有GMWB的可变年金定价成为一个最优随机控制问题。到目前为止，文献中仅通过使用有限差分法求解偏微分方程（PDE）来评估这些契约。众所周知的最小二乘法或类似的蒙特卡罗方法无法应用于这些合同的定价，因为潜在财富过程的路径受最优现金提取（控制变量）的影响，因此无法及时模拟。在本文中，我们提出了一个非常有效的新算法，用于在标的资产在提款日期或其时刻之间的转移密度已知的情况下对这些合同进行定价。该算法依赖于通过应用于三次样条插值的高阶Gauss-Hermite求积来计算期望的合同价值。然后给出了一系列GMWB合同的新算法的数值结果，并与用有限差分法求解相应偏微分方程的结果进行了比较。比较表明，新算法产生的结果与有限差分法非常接近，但同时速度显著加快；在标准台式PC上几乎可以即时获得结果。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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