Annals of Finance

, Volume 15, Issue 1, pp 125–153 | Cite as

Vanishing central bank intervention in stochastic impulse control

  • Gregory GagnonEmail author
Research Article


Stochastic control of exchange rates when a central bank employs anti-inflationary stochastic differential equation (SDE) monetary policy is the key topic of our paper. Despite low money growth SDE policy means exchange rates invariably violate the central bank’s targets. Monetary policy also incorporates interventions reflected by sudden money supply jumps that moderate deviations from targets. Controlling exchange rates involves minimizing target deviation and intervention costs. Restrictions on these costs ensure intervention vanishes under the optimal control, implying the central bank engineers freely floating exchange rates instead of managed floating or fixed exchange rates. Econometric evidence suggests discretionary interventions may be ineffective or generate excess volatility and speculation in currency markets. Our result demonstrates mathematically that such collateral damage discourages intervention.


Stochastic impulse control Semimartingale Value function 

JEL Classification

C61 E58 F31 G12 



Many thanks to the referee whose comments significantly improved the paper. Thanks are also due to my parents, Linda Gagnon and Philip Gagnon, for their constant encouragement. Great thanks are due to Ruby Mack, recently retired Academic Councillor of UTM Economics, for her dedicated service over the years. The paper is dedicated to my departed feline friends Emerald, Athos, Sekhmet, Cicero Toodle, Scipio Toodle, Mycenae and Athena who helped make life worthwhile.


  1. Abhyankar, A., Sarno, L., Valente, G.: Exchange rates and fundamentals: evidence on the economic value of predictability. J Int Econ 66, 325–348 (2005)CrossRefGoogle Scholar
  2. Cadenillas, A., Zapatero, F.: Optimal central bank intervention in the foreign exchange market. J Econ Theory 87, 218–242 (1999)CrossRefGoogle Scholar
  3. Cadenillas, A., Zapatero, F.: Classical and stochastic impulse control of the exchange rate using interest rates and reserves. Math Finance 10, 141–156 (2000)CrossRefGoogle Scholar
  4. Chang, Y., Taylor, S.: Intra-daily effects of foreign exchange intervention by the Bank of Japan. J Int Money Finance 17, 191–210 (1998)CrossRefGoogle Scholar
  5. Dembo, A., Zeitouni, O.: Large Deviations Theory and Applications. New York: Springer (2010)Google Scholar
  6. Dominguez, K.: Central bank intervention and exchange rate volatility. J Int Money Finance 17, 161–190 (1998)CrossRefGoogle Scholar
  7. Engle, R., Ito, T., Lin, W.: Meteor showers or heat waves? Heteroskedastic intra-daily volatility in the foreign exchange market. Econometrica 58, 525–542 (1990)CrossRefGoogle Scholar
  8. El Karoui, N., Peng, S., Quenez, M.: Backward stochastic differential equations in finance. Math Finance 17, 1–71 (1997)CrossRefGoogle Scholar
  9. Elliott, R., Shen, J.: Dynamic optimal capital structure with regime switching. Ann Finance 11, 199–220 (2015)CrossRefGoogle Scholar
  10. Flood, R., Garber, P.: A model of stochastic process switching. Econometrica 51, 537–551 (1983)CrossRefGoogle Scholar
  11. Fatum, R., Hutchison, M.: Foreign exchange intervention and monetary policy in Japan 2003–2004. IEEP 2, 241–260 (2005)CrossRefGoogle Scholar
  12. Gagnon, G.: Stochastic impulse control of exchange rates with Freidlin–Wentzell perturbations. J Appl Probab 54, 23–41 (2017)CrossRefGoogle Scholar
  13. Gagnon, G.: Semimartingale property for a backward exchange rate process. Unpublished manuscript (2018)Google Scholar
  14. Harrison, J.M., Taksar, M.: Impulse control of a Brownian motion. Math Oper Res 8, 439–453 (1983)CrossRefGoogle Scholar
  15. Hu, Y., Yong, J.: Forward–backward stochastic differential equations with non-smooth coefficients. Stoch Processes Appl 87, 93–106 (2000)CrossRefGoogle Scholar
  16. Ito, T.: Interventions and Japanese economic recovery. IEEP 2, 219–239 (2005)CrossRefGoogle Scholar
  17. Jeanblanc-Piqué, M.: Impulse control method and exchange rate. Math Finance 8, 161–177 (1993)CrossRefGoogle Scholar
  18. Kharroubi, I., Ma, J., Pham, H., Zhang, J.: Backward SDEs with constrained jumps and quasi-variational inequalities. Ann Probab 38, 794–840 (2010)CrossRefGoogle Scholar
  19. LeBaron, B.: Technical trading rule profitability and foreign exchange market intervention. J Int Econ 49, 125–143 (1999)CrossRefGoogle Scholar
  20. Mark, N.C., Sul, D.: Nominal exchange rates and monetary fundamentals: evidence from a small post-Bretton Woods sample. J Int Econ 53, 29–52 (2001)CrossRefGoogle Scholar
  21. MacDonald, R., Taylor, M.: The monetary approach to the exchange rate: rational expectations, long run equilibrium, and forecasting. IMF Staff Pap 40, 89–107 (1993)CrossRefGoogle Scholar
  22. MacDonald, R., Taylor, M.: The monetary model of the exchange rate: long run relationships, short run dynamics and how to beat a random walk. J Int Money Finance 13, 276–290 (1994)CrossRefGoogle Scholar
  23. Meese, R.A., Rogoff, K.: Empirical exchange rate models of the seventies: do they fit out of sample? J Int Econ 14, 3–24 (1983)CrossRefGoogle Scholar
  24. Mundaca, G., Øksendal, B.: Optimal stochastic intervention control with application to the exchange rate. J Math Econ 29, 225–243 (1998)CrossRefGoogle Scholar
  25. Peng, S., Shi, Y.: Infinite horizon forward–backward stochastic differential equations. Stoch Processes Appl 85, 75–92 (2000)CrossRefGoogle Scholar
  26. Protter, P.: Stochastic Integration and Differential Equations. New York: Springer (1990)Google Scholar
  27. Rapach, D., Wohar, M.: Testing the monetary model of exchange rate determination: new evidence from a century of data. J Int Econ 58, 359–385 (2002)CrossRefGoogle Scholar
  28. Smith, G.: Exchange rate discounting. J Int Money Finance 14, 659–666 (1995)CrossRefGoogle Scholar
  29. Wang, P.: The Economics of Foreign Exchange and Global Finance. New York: Springer (2009)Google Scholar
  30. Yong, J., Zhou, X.Y.: Stochastic Controls. New York: Springer (1999)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of Toronto MississaugaMississaugaCanada

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