论文标题
在多尺度随机波动率模型下定价路径依赖性导数：malliavin表示
Pricing Path-Dependent Derivatives under Multiscale Stochastic Volatility Models: a Malliavin Representation
论文作者
论文摘要
在本文中，我们得出了有效的蒙特卡洛近似值，该近似值是在fouque \ textit {et al}的多尺度随机波动率模型下的路径依赖性衍生物的价格。利用在功能性ITôCilculus框架下的该定价问题的表述，并利用Malliavin Cilculus的希腊公式，我们得出了一个代表路径依赖衍生物价格的一阶近似值，以$ \ \ \ m athbbbb {e} [e} [e} [e} [\ mbox {\ mbox} {\ mbox {reveef} \ time times \ mbox \ mbox \ mbox \ mbox \ mbox \ mbox \ mbox} $ {重量以封闭形式知道，仅取决于由校准多尺度随机波动到市场隐含波动率的群体市场参数。此外，仅需要对黑色choles模型进行仿真。我们说明了夫妇依赖性衍生物的方法。
In this paper we derive a efficient Monte Carlo approximation for the price of path-dependent derivatives under the multiscale stochastic volatility models of Fouque \textit{et al}. Using the formulation of this pricing problem under the functional Itô calculus framework and making use of Greek formulas from Malliavin calculus, we derive a representation for the first-order approximation of the price of path-dependent derivatives in the form $\mathbb{E}[\mbox{payoff} \times \mbox{weight}]$. 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 is required. We exemplify the method for a couple path-dependent derivatives.
