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Protecting pegged currency markets from speculative investors
Author(s) -
Neuman Eyal,
Schied Alexander
Publication year - 2022
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12324
Subject(s) - position (finance) , stackelberg competition , currency , economics , monetary economics , central bank , global game , foreign exchange swap , foreign exchange reserves , financial economics , foreign exchange market , microeconomics , finance , monetary policy
We consider a stochastic game between a trader and a central bank in a target zone market with a lower currency peg. This currency peg is maintained by the central bank through the generation of permanent price impact, thereby aggregating an ever‐increasing risky position in foreign reserves. We describe this situation mathematically by means of two coupled singular control problems, where the common singularity arises from a local time along a random curve. Our first result identifies a certain local time as that central bank strategy for which this risk position is minimized. We then consider the worst‐case situation the central bank may face by identifying that strategy of the strategic investor that maximizes the expected inventory of the central bank under a cost criterion, thus establishing a Stackelberg equilibrium in our model.