论文标题
在隐含和局部波动的偏斜和曲率上
On the skew and curvature of implied and local volatilities
论文作者
论文摘要
在本文中，我们研究了局部短端与隐含波动率表面之间的关系。我们的结果基于Malliavin微积分技术，恢复了最近的$ \ frac {1} {h+3/2} $ rule（其中$ h $表示波动性挥发性过程的Hurst参数）（请参阅Bourgey，De Marco，Friz和Pigato（202222），该splotity of Ske skke skke skke skew $ \ frac {1} {h+3/2} $局部波动的相应斜率。此外，我们看到隐含波动率的当地货币短端曲率可以根据当地波动性和Viceversa的短端偏斜和弯曲而写，并且这种关系取决于$ h $。
In this paper, we study the relationship between the short-end of the local and the implied volatility surfaces. Our results, based on Malliavin calculus techniques, recover the recent $\frac{1}{H+3/2}$ rule (where $H$ denotes the Hurst parameter of the volatility process) for rough volatilitites (see Bourgey, De Marco, Friz, and Pigato (2022)), that states that the short-time skew slope of the at-the-money implied volatility is $\frac{1}{H+3/2}$ the corresponding slope for local volatilities. Moreover, we see that the at-the-money short-end curvature of the implied volatility can be written in terms of the short-end skew and curvature of the local volatility and viceversa, and that this relationship depends on $H$.
