英文标题：
《Smoothing the payoff for efficient computation of Basket option prices》
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作者：
Christian Bayer, Markus Siebenmorgen, Raul Tempone
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最新提交年份：
2017
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英文摘要：
  We consider the problem of pricing basket options in a multivariate Black Scholes or Variance Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical integration techniques may not be directly available, requiring the use of methods like Monte Carlo specifically designed to work for non-regular problems. We propose to use the inherent smoothing property of the density of the underlying in the above models to mollify the payoff function by means of an exact conditional expectation. The resulting conditional expectation is unbiased and yields a smooth integrand, which is amenable to the efficient use of adaptive sparse grid cubature. Numerical examples indicate that the high-order method may perform orders of magnitude faster compared to Monte Carlo or Quasi Monte Carlo in dimensions up to 35.
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中文摘要：
我们考虑多变量Black-Scholes或方差Gamma模型中的篮子期权定价问题。从数值角度来看，此类期权的定价对应于具有非光滑被积函数的中高维数值积分问题。由于缺乏规律性，高阶数值积分技术可能无法直接使用，需要使用专门用于处理非规则问题的蒙特卡罗等方法。我们建议使用上述模型中基础密度的固有平滑特性，通过精确的条件期望来缓和支付函数。由此产生的条件期望是无偏的，并产生一个光滑的被积函数，这有利于有效地使用自适应稀疏网格体积。数值算例表明，与蒙特卡罗或准蒙特卡罗相比，高阶方法在35维以下的维度上执行速度可能快几个数量级。
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Mathematics        数学
二级分类：Numerical Analysis        数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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