A Monte-Carlo approach for pricing arithmetic Asian rainbow options under the mixed fractional Brownian motion

We derive a closed-form solution for pricing geometric Asian rainbow options under the mixed geometric frac- tional Brownian motion (FBM). In particular, the number of underlying assets is allowed to be arbitrary, and fully correlated fractional Brownian motions are taken into account. The analytical solution obtained is used as a con- trol variate for Monte Carlo based computations of the price of arithmetic Asian rainbow options. Numerical ex- periments are presented in which options on two, three, four and ten underlying assets are considered. Results reveal that the proposed control variate technique is very effective to reduce the variance of the Monte Carlo es- timator and yields a reliable approximation of the Asian rainbow option price.