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Protecting pegged currency markets from speculative investors
File(s)
Author(s)
Neumann, Eyal
Schied, Alexander
Type
Journal Article
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.
Date Issued
2022-01-01
Date Acceptance
2021-06-10
Citation
Mathematical Finance, 2022, 32 (1), pp.405-420
URI
DOI
ISSN
0960-1627
Publisher
Wiley
Start Page
405
End Page
420
Journal / Book Title
Mathematical Finance
Volume
32
Issue
1
Copyright Statement
© 2021 Wiley Periodicals LLC. This is the peer reviewed version of the following article, which has been published in final form at https://onlinelibrary.wiley.com/doi/10.1111/mafi.12324. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
Subjects
Social Sciences
Science & Technology
Physical Sciences
Business, Finance
Economics
Mathematics, Interdisciplinary Applications
Social Sciences, Mathematical Methods
Business & Economics
Mathematics
Mathematical Methods In Social Sciences
currency peg
local time
market impact
singular stochastic control
Stackelberg equilibrium
target zone models
TARGET ZONES
Finance
0102 Applied Mathematics
1502 Banking, Finance and Investment
Publication Status
Published
Date Publish Online
2021-06-15