Protecting Pegged Currency Markets from Speculative Investors

TL;DR

This paper models a stochastic game between a trader and a central bank in a pegged currency market, analyzing strategies to minimize risk and identify worst-case scenarios through coupled control problems.

Contribution

It introduces a mathematical framework using coupled singular control problems to determine optimal and worst-case strategies in a currency peg market.

Findings

Identifies a local time strategy minimizing central bank risk.

Establishes a Stackelberg equilibrium between trader and central bank.

Provides a mathematical characterization of strategic interactions in target zone markets.

Abstract

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.