SIAM Journal on Financial Mathematics, Volume 11, Issue 3, Page SC-14-SC-25, January 2020.
In this paper we derive an efficient approximation for the price of path-dependent derivatives under the multiscale stochastic volatility models. Using the formulation of this pricing problem under the functional Itô calculus framework and making use of Malliavin calculus formulas for computing the Greeks, we derive a representation for the first-order approximation of the price of path-dependent derivatives in the form of an expectation of the payoff multiplied by a weight function. The weight is known in closed form and depends only on the group market parameters arising from the calibration of the multiscale stochastic volatility to the market's implied volatility. Moreover, only simulations of the Black--Scholes model are required. We exemplify the method for two path-dependent derivatives: arithmetic Asian and barrier options.

中文翻译：

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短沟通：多尺度随机波动率模型下与路径相关的衍生产品的定价：Malliavin表示

SIAM金融数学杂志，第11卷，第3期，第SC-14-SC-25页，2020年1月。
在本文中，我们得出了多尺度随机波动率模型下路径相关衍生产品价格的有效近似。使用在功能性Itô演算框架下的定价问题公式，并利用Malliavin演算公式来计算希腊文，我们得出了路径依赖衍生产品价格的一阶近似的表示形式，其期望值为收益乘以权重函数。权重是封闭形式，仅取决于根据对市场隐含波动率进行多尺度随机波动率校准而产生的组市场参数。而且，仅需要对Black-Scholes模型的仿真。我们举例说明了两种与路径相关的导数的方法：算术亚洲和障碍期权。