Abstract
Creditors, banks and bank regulators should evaluate whether a borrower is likely to default. I apply several techniques in the extensive mathematical literature of stochastic optimal control/dynamic programming to derive an optimal debt in an environment where there are risks on both the asset and liabilities sides. The vulnerability of the borrowing firm to shocks from either the return to capital, the interest rate or capital gain, increases in proportion to the difference between the Actual and Optimal debt ratio, called the excess debt. As the debt ratio exceeds the optimum, default becomes ever more likely. This paper is “A Tale of Two Crises” because the same analysis is applied to the agricultural debt crisis of the 1980s and to the subprime mortgage crisis of 2007. A measure of excess debt is derived, and we show that it is an early warning signal of a crisis in both cases.
References
Blanchet-Scalliet, C., A. Diop, R. Gibson, D. Talay, and E. Tancré (2007). Technical analysis compared to mathematical models based methods under parameters mis-specification. Journal of Banking and Finance 31 (5): 1351–1374.Search in Google Scholar
Demyanyk, Y., and O. Van Hemert (2007). Understanding the Subprime Mortgage Crisis. Supervisory Policy Analysis Working Papers 2007-05. Federal Reserve Bank of St. Louis.Search in Google Scholar
Federal Deposit Insurance Corporation (FDIC) (1997). An Examination of the Banking Crises of the 1980s and Early 1990s. History of the Eighties – Lessons for the Future, Vol. I. URL: http://www.fdic.gov/bank/historical/history/vol1.html.Search in Google Scholar
Doms, M., F. Furlong, and J. Krainer (2007). Housing Prices and Subprime Mortgage Delinquencies. Economic Letter 2007-8. Federal Reserve Bank of San Francisco.Search in Google Scholar
Federal Reserve Bank St. Louis, Economic Data – FRED.Search in Google Scholar
Fleming, W. H. (1999). Controlled Markov Processes and Mathematical Finance. In F. H. Clarke and R. J. Stern (eds.), Nonlinear Analysis, Differential Equations and Control. Dordrecht: Kluwer.Search in Google Scholar
Fleming, W. H., and H. M. Soner (2006). Controlled Markov Processes and Viscosity Solutions. New York: Springer.Search in Google Scholar
Fleming, W. H., and J. L. Stein (2004). Stochastic Optimal Control, International Finance and Debt. Journal of Banking and Finance 28 (5): 979–996.Search in Google Scholar
Guidolin, M., and E. La Jeunesse, The Decline in the U.S. Personal Saving Rate: Is It Real and Is It a Puzzle? Review (Federal Reserve Bank of St. Louis) 89 (6): 419–514.10.20955/r.89.491-514Search in Google Scholar
OFHEO, Office of Federal Housing Enterprise Oversight (2009).Search in Google Scholar
Øksendal, B. K. (1995). Stochastic Differential Equations: An Introduction with Applications. Berlin: Springer.10.1007/978-3-662-03185-8Search in Google Scholar
Stein, J. L. (2004). A Stochastic Optimal Control Modeling of Debt Crises. In G. Yin and Q. Zhang (eds.), Mathematics of Finance. American Mathematical Society 351: 319–332.Search in Google Scholar
Stein, J. L. (2005). Optimal Debt and Endogenous Growth in Models of International Finance. Australian Economic Papers 44 (4): 389–413.Search in Google Scholar
Stein, J. L. (2006). Stochastic Optimal Control, International Finance, and Debt Crises. Oxford: Oxford University Press.10.1093/0199280576.001.0001Search in Google Scholar
Stein, J. L. (2007). United States Current Account Deficits: A Stochastic Optimal Control Analysis. Journal of Banking and Finance 31 (5) 1321–1350.10.1016/j.jbankfin.2006.10.016Search in Google Scholar
United States Department of Agriculture (USDA), Economic Research Service (ERS) (2002). Farm Income and Balance Sheet Indicators, 1929–2002, November 26, 2002.Search in Google Scholar
© 2010 Jerome L. Stein, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.
