Optimal switching decisions under stochastic volatility with fast mean reversion

We study infinite–horizon, optimal switching problems under a general class of stochastic volatility models that exhibit “fast” mean–reversion by using techniques from homogenisation theory. This leads to perturbation theory, providing closed–form approximations to the full switching problem which is often intractable, both analytically and numerically. We apply our general results to certain, well–known switching problems and volatility models, providing qualitative information on the effect of multi–scale stochastic volatility on optimal switching decisions and hysteresis. Our results indicate that multi–scale stochastic volatility strongly affects the frequency and the optimal timing of switching between modes. The proposed methodology is of interest to a number of applied problems involving switching flexibility, for example optimal production management of natural resources or foreign direct investment in the face of fluctuating exchange rates. JEL classification: C41; D81; G13