A moment approach to bounding exotic options under regime switching

Abstract

The switching of market regimes has a significant impact on derivative pricing that exposes investors to an additional level of risk. However, deriving the exact price of exotic options under regime switching is still at the early stages of development. In this article, we consider deriving tight upper and lower bounds for the price of a wide class of exotic options under regime switching. We show that the additional complexity introduced by the regime-switching dynamics can be greatly reduced by exploiting the additive structure of the infinitesimal generator of the regime-switching process. As a result, the problem of bounding the option price under regime switching can be reformulated as a semidefinite programming problem, which can be solved efficiently in practice. The effectiveness of our approach is illustrated through numerical examples.

Keywords:

• exotic options
• regime switching
• moment approach
• semidefinite programming