Markovian approximations of stochastic Volterra equations with the fractional kernel
针对粗糙Bergomi和粗糙Heston模型中方差过程非马尔可夫、非半鞅且模拟成本高的问题，提出用N维扩散过程近似随机Volterra方程，证明在Lipschitz系数下强收敛速度超多项式，并用于计算欧式看涨期权的隐含波动率微笑。
We consider rough stochastic volatility models where the variance process satisfies a stochastic Volterra equation with the fractional kernel, as in the rough Bergomi and the rough Heston model. In particular, the variance process is therefore not a Markov process or semimartingale, and has quite low H\"older-regularity. In practice, simulating such rough processes thus often results in high computational cost. To remedy this, we study approximations of stochastic Volterra equations using an $N$-dimensional diffusion process defined as solution to a system of ordinary stochastic differential equation. If the coefficients of the stochastic Volterra equation are Lipschitz continuous, we show that these approximations converge strongly with superpolynomial rate in $N$. Finally, we apply this approximation to compute the implied volatility smile of a European call option under the rough Bergomi and the rough Heston model.