Semimartingale and continuous-time Markov chain approximation for rough stochastic local volatility models

Rough volatility models have recently been empirically shown to provide a good fit historical time series and implied smiles of SPX options. They are continuous-time stochastic models, whose process is driven by fractional Brownian motion with Hurst parameter less than half. Due the challenge that it neither semimartingale nor Markov process, there no unified method not only applies all rough but also computationally efficient. This paper proposes chain (CTMC) approximation approach for general class local (RSLV) models. In particular, we introduce perturbed (PSLV) model as RSLV establish its existence , uniqueness Markovian representation. We propose fast CTMC algorithm prove weak convergence. Numerical experiments demonstrate accuracy high efficiency in pricing European, barrier American Comparing existing literature, significant reduction CPU arrive at same level observed.