Assessing the Costs of Protection in a Context of Switching Stochastic Regimes

We consider the problem of cost assessment in the context of switching stochastic regimes. The dynamics of a given asset include a background noise, described by a Brownian motion and a random shock, the impact of which is characterized by changes in the coefficient diffusions. A particular economic agent that is directly exposed to variations in the underlying asset price, incurs some costs, <inline-formula> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ramf_a_642615_o_ilm0001.gif"/> </inline-formula>, when the underlying asset price reaches a certain threshold, L. Ideally, the agent would make advance provision, or hedge, for these costs at time 0. We evaluate the amount of provision, or the hedging premium, <inline-formula> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ramf_a_642615_o_ilm0002.gif"/> </inline-formula>, for these costs in the disrupted environment, with changes in the regime for a given time horizon, and analyse the sensitivity of this amount to possible model misspecifications.