Optimal switching decisions under stochastic volatility with fast mean reversion

• Study optimal switching problems under “fast” mean-reverting stochastic volatility.
• Derive closed-form approximations of the full problem via homogenization theory.
• Apply our general solution to well-known switching problems and volatility models.
• Proposed method is of interest to applied problems involving switching flexibility.

We study infinite-horizon, optimal switching problems for underlying processes that exhibiting “fast” mean-reverting stochastic volatility. We obtain closed-form analytic approximations of the solution for the resulting quasi-variational inequalities, that provide quantitative and qualitative results for the effects of multi-scale variability of the underlying process on the optimal switching rule. The proposed methodology is applicable to a number of operations research problems involving switching flexibility.