Before revision:  On the other hand, when the volatilities of the volatilities are independent of this exploding parameter, the volatilities converge to their means and we can have much better approximations. Our aim is to use such approximations to improve the accuracy of certain risk-management methods in markets where fast volatility mean-reversion is observed .
After revision:  On the other hand, when only the mean reversion of the volatility goes to infinity we see a stronger form of convergence of the system to its limit. Our results show that in a fast mean-reverting volatility environment we can accurately estimate the distribution of the loss from a large portfolio by using an approximate constant volatility model which is easier to handle .