论文标题
粗糙波动率模型的错误估计较弱
Weak error estimates for rough volatility models
论文作者
论文摘要
我们考虑了一类具有粗糙随机波动率的随机过程，其中包括粗糙的Bergomi和粗糙的Stein-Stein模型，这些模型在定量融资方面具有非常重要的意义。 此类（非马尔可）模型的一个基本问题涉及有效的数值方案。虽然良好的利率已经充分理解（$ h $），但我们在这里解决了复杂的费率问题。我们的主要结果断言，对于相当大的测试功能，弱点本质上是$ \ min \ {3H+\ tfrac12，1 \} $，其中$ h \ in（0,1/2] $是hurst brownian运动的hurst参数，这是构成粗暴波动性过程的分数布朗运动。 有趣的是，$ h = 1/6 $的相变与两个驱动因素之间的相关性有关，因此给出了随机波动率模型中至关重要的数量的额外含义。您的结果与下限相辅相成，这表明所获得的较弱率确实是最佳的。
We consider a class of stochastic processes with rough stochastic volatility, examples of which include the rough Bergomi and rough Stein-Stein model, that have gained considerable importance in quantitative finance. A basic question for such (non-Markovian) models concerns efficient numerical schemes. While strong rates are well understood (order $H$), we tackle here the intricate question of weak rates. Our main result asserts that the weak rate, for a reasonably large class of test function, is essentially of order $\min \{ 3H+\tfrac12, 1 \}$ where $H \in (0,1/2]$ is the Hurst parameter of the fractional Brownian motion that underlies the rough volatility process. Interestingly, the phase transition at $H=1/6$ is related to the correlation between the two driving factors, and thus gives additional meaning to a quantity already of central importance in stochastic volatility modelling.Our results are complemented by a lower bound which show that the obtained weak rate is indeed optimal.
