Multilevel Monte Carlo simulation for VIX options in the rough Bergomi model

In this paper we consider the pricing of Chicago Board Options Exchange Volatility Index (VIX) options in rough Bergomi model. setting, VIX random variable is defined by one-dimensional integral exponential a Gaussian process with correlated increments. Hence, approximate samples can be constructed via discretization and simulation vector. A Monte Carlo estimator based on rectangle scheme exact sampling Cholesky method has computational complexity order Ο(ε−4) when mean squared error set to ε2. We demonstrate that cost reduced Ο(ε-2ln-2(ε)) combining above multilevel method, further asymptotically optimal Ο(ε−2) using trapezoidal discretization. provide numerical experiments highlighting efficiency approach such forward variance setting.