英文标题：
《Strong convergence rates for Euler approximations to a class of
  stochastic path-dependent volatility models》
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作者：
Andrei Cozma and Christoph Reisinger
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最新提交年份：
2018
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英文摘要：
  We consider a class of stochastic path-dependent volatility models where the stochastic volatility, whose square follows the Cox-Ingersoll-Ross model, is multiplied by a (leverage) function of the spot price, its running maximum, and time. We propose a Monte Carlo simulation scheme which combines a log-Euler scheme for the spot process with the full truncation Euler scheme or the backward Euler-Maruyama scheme for the squared stochastic volatility component. Under some mild regularity assumptions and a condition on the Feller ratio, we establish the strong convergence with order 1/2 (up to a logarithmic factor) of the approximation process up to a critical time. The model studied in this paper contains as special cases Heston-type stochastic-local volatility models, the state-of-the-art in derivative pricing, and a relatively new class of path-dependent volatility models. The present paper is the first to prove the convergence of the popular Euler schemes with a positive rate, which is moreover consistent with that for Lipschitz coefficients and hence optimal.
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中文摘要：
我们考虑一类随机路径相关波动率模型，其中随机波动率的平方遵循Cox-Ingersoll-Ross模型，乘以现货价格、其运行最大值和时间的杠杆函数。我们提出了一种蒙特卡罗模拟方案，该方案将用于现货过程的对数欧拉方案与用于平方随机波动率分量的全截断欧拉方案或向后欧拉丸山方案相结合。在一些温和的正则性假设和Feller比率的条件下，我们建立了逼近过程在临界时间内的1/2阶（达对数因子）强收敛性。本文研究的模型作为特例包含赫斯顿型随机局部波动率模型、衍生品定价的最新技术以及一类相对较新的路径依赖波动率模型。本文首次证明了流行的Euler格式的正速度收敛性，并且与Lipschitz系数的收敛性一致，因此是最优的。
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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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