英文标题：
《A new approach for American option pricing: The Dynamic Chebyshev method》
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作者：
Kathrin Glau, Mirco Mahlstedt, Christian P\\\"otz
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最新提交年份：
2018
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英文摘要：
We introduce a new method to price American options based on Chebyshev interpolation. In each step of a dynamic programming time-stepping we approximate the value function with Chebyshev polynomials. The key advantage of this approach is that it allows to shift the model-dependent computations into an offline phase prior to the time-stepping. In the offline part a family of generalised (conditional) moments is computed by an appropriate numerical technique such as a Monte Carlo, PDE or Fourier transform based method. Thanks to this methodological flexibility the approach applies to a large variety of models. Online, the backward induction is solved on a discrete Chebyshev grid, and no (conditional) expectations need to be computed. For each time step the method delivers a closed form approximation of the price function along with the options\' delta and gamma. Moreover, the same family of (conditional) moments yield multiple outputs including the option prices for different strikes, maturities and different payoff profiles. We provide a theoretical error analysis and find conditions that imply explicit error bounds for a variety of stock price models. Numerical experiments confirm the fast convergence of prices and sensitivities. An empirical investigation of accuracy and runtime also shows an efficiency gain compared with the least-square Monte-Carlo method introduced by Longstaff and Schwartz (2001).
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中文摘要：
介绍了一种基于切比雪夫插值的美式期权定价方法。在动态规划时间步长的每一步中，我们用切比雪夫多项式来近似值函数。这种方法的主要优点是，它允许在时间步进之前将依赖于模型的计算转换为脱机阶段。在离线部分，通过适当的数值技术（如蒙特卡罗、偏微分方程或基于傅立叶变换的方法）计算一系列广义（条件）矩。由于这种方法的灵活性，该方法适用于各种各样的模型。在线情况下，反向归纳法在离散切比雪夫网格上求解，无需计算（条件）期望值。对于每个时间步，该方法提供价格函数的闭合形式近似值以及期权的delta和gamma。此外，同一系列（条件）矩会产生多个输出，包括不同行使、到期日和不同支付模式的期权价格。我们提供了一个理论误差分析，并找到了暗示各种股票价格模型显式误差界的条件。数值实验证实了价格和灵敏度的快速收敛性。与Longstaff和Schwartz（2001）提出的最小二乘蒙特卡罗方法相比，精度和运行时间的实证研究也显示了效率的提高。
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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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