Continuous-time Markov chain approximation for pricing Asian options under rough stochastic local volatility models

We propose a general framework for pricing both discretely and continuously monitored arithmetic average Asian options whose underlying asset price satisfies the rough stochastic local volatility model. We use a semimartingale approximation approach for the rough stochastic local volatility model to obtain its Markovian representation. For each type of Asian options, we use the double-layer continuous-time Markov chain to approximate the transformed underlying asset price, and derive the double transform of the Asian option price in terms of the unique bounded solution to a related functional equation. We invert the analytical double transforms of Asian option prices under the approximate continuous-time Markov chain numerically to obtain the approximations for Asian option prices. Monte Carlo simulation demonstrates the accuracy and efficiency of the proposed method for Asian option pricing.