英文标题：
《Hybrid scheme for Brownian semistationary processes》
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作者：
Mikkel Bennedsen, Asger Lunde, Mikko S. Pakkanen
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最新提交年份：
2017
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英文摘要：
We introduce a simulation scheme for Brownian semistationary processes, which is based on discretizing the stochastic integral representation of the process in the time domain. We assume that the kernel function of the process is regularly varying at zero. The novel feature of the scheme is to approximate the kernel function by a power function near zero and by a step function elsewhere. The resulting approximation of the process is a combination of Wiener integrals of the power function and a Riemann sum, which is why we call this method a hybrid scheme. Our main theoretical result describes the asymptotics of the mean square error of the hybrid scheme and we observe that the scheme leads to a substantial improvement of accuracy compared to the ordinary forward Riemann-sum scheme, while having the same computational complexity. We exemplify the use of the hybrid scheme by two numerical experiments, where we examine the finite-sample properties of an estimator of the roughness parameter of a Brownian semistationary process and study Monte Carlo option pricing in the rough Bergomi model of Bayer et al. [Quant. Finance 16(6), 887-904, 2016], respectively.
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中文摘要：
我们介绍了一种布朗半平稳过程的模拟方案，该方案基于将过程的随机积分表示在时域中离散化。我们假设过程的核函数在零处有规律地变化。该方案的新特点是通过接近零的幂函数和其他地方的阶跃函数来逼近核函数。这个过程的结果近似是幂函数的维纳积分和黎曼和的组合，这就是为什么我们称这种方法为混合格式。我们的主要理论结果描述了混合格式的均方误差的渐近性，并且我们观察到，与普通的前向黎曼和格式相比，该格式在具有相同计算复杂度的情况下显著提高了精度。我们通过两个数值实验来举例说明混合格式的使用，其中我们检验了布朗半平稳过程粗糙度参数估计量的有限样本性质，并分别研究了拜耳等人[Quant.Finance 16（6），887-9042016]的粗糙Bergomi模型中的蒙特卡罗期权定价。
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分类信息：

一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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