Capital Ideas: Optimal Capital Reserve Strategies for a Bank and Its Regulator

36 Pages Posted: 28 Aug 2012 Last revised: 28 Sep 2020

See all articles by Kristoffer J. Glover

Kristoffer J. Glover

University of Technology Sydney (UTS) - UTS Business School; Financial Research Network (FIRN)

Paul V. Johnson

University of Manchester; University of Manchester

Geoffrey Evatt

School of Mathematics, University of Manchester

Mingliang Cheng

University of Manchester

Date Written: September 26, 2020

Abstract

We formulate a continuous-time model of a deposit taking bank, operating subject to capital adequacy regulation, and where the bank's loans are exposed to default risk. The bank maximises their market value of equity by appropriately controlling loan and equity issuance, dividend payments, and endogenous closure. Of interest to regulators, we show how the bank responds to the span of capital adequacy requirements and to changes in default variance. We find a nonmonotonic response of bank lending to increased capital requirements (initially increasing and then decreasing). We also find that the probability of early closure (through either insolvency or endogenous closure) can be minimised for a well-chosen capital adequacy ratio. Moreover, the level of capital requirement that minimises the probability of early closure and maximises lending is fairly robust to changes in the bank's default variance/risk; contributing to the ongoing discussion on optimal bank capital.

Keywords: capital requirements, banking, real options, optimal control

JEL Classification: G21, G28, C61

Suggested Citation

Glover, Kristoffer J. and Johnson, Paul V. and Evatt, Geoffrey and Cheng, Mingliang, Capital Ideas: Optimal Capital Reserve Strategies for a Bank and Its Regulator (September 26, 2020). Available at SSRN: https://ssrn.com/abstract=2136977 or http://dx.doi.org/10.2139/ssrn.2136977

Kristoffer J. Glover (Contact Author)

University of Technology Sydney (UTS) - UTS Business School ( email )

Sydney
Australia

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Paul V. Johnson

University of Manchester ( email )

Oxford Road
Manchester, N/A M13 9PL
United Kingdom
+44 (0) 161 306 3660 (Phone)

HOME PAGE: http://www.maths.manchester.ac.uk/~pjohnson/

University of Manchester ( email )

Oxford Road
Manchester, N/A M13 9PL
United Kingdom
+44 (0) 161 306 3660 (Phone)

HOME PAGE: http://www.maths.manchester.ac.uk/~pjohnson/

Geoffrey Evatt

School of Mathematics, University of Manchester ( email )

United Kingdom

Mingliang Cheng

University of Manchester ( email )

Oxford Road
Manchester, N/A M13 9PL
United Kingdom

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