We consider a large portfolio limit where the asset prices evolve according certain stochastic volatility models with default upon hitting a lower barrier. When the asset prices and the volatilities are correlated via systemic Brownian Motions, that limit exist and it is described by a SPDE on the positive half-space with Dirichlet boundary conditions which has been studied in \cite{HK17}. We study the convergence of the total mass of a solution to this stochastic initial-boundary value problem when the mean-reversion coefficients of the volatilities are multiples of a parameter that tends to infinity. When the volatilities of the volatilities are multiples of the square root of the same parameter, the convergence is extremely weak. 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.
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