论文标题
粗略波动的数值方案的错误率较弱
Weak error rates of numerical schemes for rough volatility
论文作者
论文摘要
粗糙波动率模型的模拟涉及随机积分的离散化，其中集成是Hurst索引$ h \ in（0,1/2）$的（相关）分数Brownian运动的函数。在特殊情况下，当集成剂是FBM本身或测试函数是立方体时，我们获得了此类近似值弱误差的收敛速率的结果。我们的结果指出，融合为$（3H+ \ frac {1} {2}）\ wedge 1 $，用于精确的左点离散化，以及$ h+ \ frac {1} {2} {2} {2} $，用于使用精心选择的权重。
Simulation of rough volatility models involves discretization of stochastic integrals where the integrand is a function of a (correlated) fractional Brownian motion of Hurst index $H \in (0,1/2)$. We obtain results on the rate of convergence for the weak error of such approximations, in the special cases when either the integrand is the fBm itself, or the test function is cubic. Our result states that the convergence is of order $(3H+ \frac{1}{2}) \wedge 1$ for exact left-point discretization, and of order $H+\frac{1}{2}$ for the hybrid scheme with well-chosen weights.
