Hierarchical adaptive sparse grids and quasi-Monte Carlo for option pricing under the rough Bergomi model
Hierarchical adaptive sparse grids and quasi-Monte Carlo for option pricing under the rough Bergomi model
复制标题
粗略贝尔戈米模型下的分层自适应稀疏网格和准蒙特卡罗期权定价
DOI：
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
R. Tempone
中科院分区：
文献类型：
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作者：
Christian Bayer;Chiheb Ben Hammouda;R. Tempone
粗糙Bergomi（rBergomi）模型，最近在拜耳等人[粗糙波动下的定价。定量Finance，2016，16（6），887-904]，是数量金融学中一个很有前途的粗糙波动率模型。这是一个只依赖于三个参数的简约模型，但非常适合经验隐含波动率表面。在缺乏分析的欧式期权定价方法的模型，由于非马尔可夫性质的分数驱动器，流行的选择是使用蒙特卡洛（MC）模拟定价。尽管MC方法在这方面取得了最新进展，但在rBergomi模型下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，分层的方法，基于：（i）自适应稀疏网格正交（ASGQ），和（ii）准蒙特卡罗（QMC）。这两种技术是再加上布朗桥建设和Richardson外推的弱错误。通过揭示可用的规律性，我们的分层方法相对于标准MC方法表现出大量的计算增益。他们达到了足够小的相对误差容限的价格估计在不同的参数星座，即使是非常小的值的赫斯特参数。我们的工作开辟了一个新的研究方向，在这一领域，即调查的性能，而不是蒙特卡洛定价和校准下的rBergomi模型的方法。
The rough Bergomi (rBergomi) model, introduced recently in Bayer et al. [Pricing under rough volatility. Quant. Finance, 2016, 16(6), 887–904], is a promising rough volatility model in quantitative finance. It is a parsimonious model depending on only three parameters, and yet remarkably fits 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. They reach 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.
粗略分数波动率模型中的短期近货币偏斜
影响因子：
1.3
作者：
C. Bayer;P. K. Friz;A. Gulisashvili;B. Horvath;B. Stemper
通讯作者：
B. Stemper
影响因子：
1.6
作者：
Christian;Peter K;Gassiat;Martin;Stemper;Benjamin
通讯作者：
Benjamin