英文标题：
《Parallelizing Computation of Expected Values in Recombinant Binomial
  Trees》
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作者：
Sai K. Popuri and Andrew M. Raim and Nagaraj K. Neerchal and Matthias
  K. Gobbert
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最新提交年份：
2018
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英文摘要：
  Recombinant binomial trees are binary trees where each non-leaf node has two child nodes, but adjacent parents share a common child node. Such trees arise in finance when pricing an option. For example, valuation of a European option can be carried out by evaluating the expected value of asset payoffs with respect to random paths in the tree. In many variants of the option valuation problem, a closed form solution cannot be obtained and computational methods are needed. The cost to exactly compute expected values over random paths grows exponentially in the depth of the tree, rendering a serial computation of one branch at a time impractical. We propose a parallelization method that transforms the calculation of the expected value into an \"embarrassingly parallel\" problem by mapping the branches of the binomial tree to the processes in a multiprocessor computing environment. We also propose a parallel Monte Carlo method which takes advantage of the mapping to achieve a reduced variance over the basic Monte Carlo estimator. Performance results from R and Julia implementations of the parallelization method on a distributed computing cluster indicate that both the implementations are scalable, but Julia is significantly faster than a similarly written R code. A simulation study is carried out to verify the convergence and the variance reduction behavior in the proposed Monte Carlo method.
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中文摘要：
重组二叉树是二叉树，其中每个非叶节点有两个子节点，但相邻的父节点共享一个公共子节点。这种树出现在金融学中，当为期权定价时。例如，欧式期权的估值可以通过评估关于树中随机路径的资产回报的预期值来执行。在期权定价问题的许多变体中，无法获得封闭形式的解，需要计算方法。在随机路径上精确计算期望值的成本在树的深度呈指数增长，使得一次对一个分支进行串行计算不切实际。我们提出了一种并行化方法，通过将二叉树的分支映射到多处理器计算环境中的进程，将期望值的计算转化为“令人尴尬的并行”问题。我们还提出了一种并行蒙特卡罗方法，该方法利用映射来减少基本蒙特卡罗估计量的方差。分布式计算集群上并行化方法的R和Julia实现的性能结果表明，这两种实现都是可伸缩的，但Julia的速度明显快于类似编写的R代码。通过仿真研究，验证了所提出的蒙特卡罗方法的收敛性和方差缩减行为。
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分类信息：

一级分类：Statistics        统计学
二级分类：Computation        计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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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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