Protecting Target Zone Currency Markets from Speculative Investors. (arXiv:1801.07784v1 [q-fin.MF])

We consider a stochastic game between a trader and the central bank on target zone markets. In this type of markets the price process is modeled as a diffusion which is reflected at one or more barriers. Such models arise when a currency exchange rate is kept above a certain threshold due to central bank intervention. We consider a trader who wishes to liquidate a large amount of currency, where for whom prices are optimal at the barrier. The central bank, who wishes to keep the currency exchange rate above this barrier, therefore needs to buy its own currency. The permanent price impact, which is created by the transactions of both sides, turns the optimal trading problems of the trader and the central bank into coupled singular control problems, where the common singularity arises from a local time along a random curve. We first solve the central bank's control problem by means of the Skorokhod map and then derive the trader's optimal strategy by solving a sequence of approximated control problems, thus establishing a Stackelberg equilibrium in our model.