2021/05/11 by Florian Bourgey, Bourgey, Florian, Stefano De Marco +1
Economics, Econometrics and Finance · Social Sciences · #Stochastic processes and financial applications #Insurance, Mortality, Demography, Risk Management #Financial Markets and Investment Strategies
paper · pdf · doi:10.48550/arxiv.2105.05356
We consider the pricing of VIX options in the rough Bergomi model. In this setting, the VIX random variable is defined by the one-dimensional integral of the exponential of a Gaussian process with correlated increments, hence approximate samples of the VIX can be constructed via discretization of the integral and simulation of a correlated Gaussian vector. A Monte-Carlo estimator of VIX options based on a rectangle discretization scheme and exact Gaussian sampling via the Cholesky method has a computational complexity of order O(ε-4) when the mean-squared error is set to ε2. We demonstrate that this cost can be reduced to O(ε-2 log2(ε)) combining the scheme above with the multilevel method, and further reduced to the asymptotically optimal cost O(ε-2) when using a trapezoidal discretization. We provide numerical experiments highlighting the efficiency of the multilevel approach in the pricing of VIX options in such a rough forward variance setting.