英文标题：
《Recursive Marginal Quantization of Higher-Order Schemes》
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作者：
T. A. McWalter, R. Rudd, J. Kienitz, E. Platen
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最新提交年份：
2017
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英文摘要：
  Quantization techniques have been applied in many challenging finance applications, including pricing claims with path dependence and early exercise features, stochastic optimal control, filtering problems and efficient calibration of large derivative books. Recursive Marginal Quantization of the Euler scheme has recently been proposed as an efficient numerical method for evaluating functionals of solutions of stochastic differential equations. This method involves recursively quantizing the conditional marginals of the discrete-time Euler approximation of the underlying process. By generalizing this approach, we show that it is possible to perform recursive marginal quantization for two higher-order schemes: the Milstein scheme and a simplified weak order 2.0 scheme. As part of this generalization a simple matrix formulation is presented, allowing efficient implementation. We further extend the applicability of recursive marginal quantization by showing how absorption and reflection at the zero boundary may be incorporated, when this is necessary. To illustrate the improved accuracy of the higher order schemes, various computations are performed using geometric Brownian motion and its generalization, the constant elasticity of variance model. For both processes, we show numerical evidence of improved weak order convergence and we compare the marginal distributions implied by the three schemes to the known analytical distributions. By pricing European, Bermudan and Barrier options, further evidence of improved accuracy of the higher order schemes is demonstrated.
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中文摘要：
量化技术已被应用于许多具有挑战性的金融应用中，包括具有路径依赖和早期行使特征的债权定价、随机最优控制、过滤问题和大型衍生品账簿的有效校准。欧拉格式的递归边际量化是最近提出的一种有效的数值方法，用于计算随机微分方程解的泛函。该方法涉及递归量化基础过程的离散时间Euler近似的条件边缘。通过推广这种方法，我们证明了可以对两种高阶方案执行递归边缘量化：Milstein方案和简化的弱阶2.0方案。作为这一推广的一部分，提出了一个简单的矩阵公式，可以有效地实现。我们进一步扩展了递归边缘量子化的适用性，展示了在必要时如何将零边界处的吸收和反射合并。为了说明高阶格式精度的提高，使用几何布朗运动及其推广，即常弹性方差模型进行了各种计算。对于这两个过程，我们给出了改进的弱阶收敛性的数值证据，并将三种格式所隐含的边缘分布与已知的解析分布进行了比较。通过对欧式期权、百慕大期权和障碍期权的定价，进一步证明了高阶方案精度的提高。
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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：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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