英文标题：
《Hierarchical adaptive sparse grids and quasi Monte Carlo for option
  pricing under the rough Bergomi model》
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作者：
Christian Bayer, Chiheb Ben Hammouda and Raul Tempone
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最新提交年份：
2020
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英文摘要：
  The rough Bergomi (rBergomi) model, introduced recently in [5], is a promising rough volatility model in quantitative finance. It is a parsimonious model depending on only three parameters, and yet remarkably fits with empirical implied volatility surfaces. In the absence of analytical European option pricing methods for the model, and due to the non-Markovian nature of the fractional driver, the prevalent option is to use the Monte Carlo (MC) simulation for pricing. Despite recent advances in the MC method in this context, pricing under the rBergomi model is still a time-consuming task. To overcome this issue, we have designed a novel, hierarchical approach, based on i) adaptive sparse grids quadrature (ASGQ), and ii) quasi-Monte Carlo (QMC). Both techniques are coupled with a Brownian bridge construction and a Richardson extrapolation on the weak error. By uncovering the available regularity, our hierarchical methods demonstrate substantial computational gains with respect to the standard MC method, when reaching a sufficiently small relative error tolerance in the price estimates across different parameter constellations, even for very small values of the Hurst parameter. Our work opens a new research direction in this field, i.e., to investigate the performance of methods other than Monte Carlo for pricing and calibrating under the rBergomi model.
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中文摘要：
最近在[5]中引入的粗糙Bergomi（rBergomi）模型是定量金融中一种很有前景的粗糙波动率模型。这是一个仅依赖三个参数的简约模型，但非常符合经验隐含波动率曲面。在缺乏模型的分析性欧式期权定价方法的情况下，由于分数驱动因素的非马尔可夫性质，流行的期权是使用蒙特卡罗（MC）模拟进行定价。尽管MC方法在这方面取得了最新进展，但rBergomi模型下的定价仍然是一项耗时的任务。为了克服这个问题，我们设计了一种新的分层方法，基于i）自适应稀疏网格求积（ASGQ）和ii）准蒙特卡罗（QMC）。这两种技术都结合了布朗桥构造和Richardson对弱误差的外推。通过揭示可用的规律性，我们的分层方法证明了与标准MC方法相比，当在不同参数星座的价格估计中达到足够小的相对误差容限时，即使对于非常小的赫斯特参数值，我们的分层方法也能获得相当大的计算收益。我们的工作在这一领域开辟了一个新的研究方向，即在rBergomi模型下研究蒙特卡罗以外的定价和校准方法的性能。
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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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