Exchange rate dynamics under limits of arbitrage and heterogeneous expectations

  • Soumya DattaEmail author
Regular Article


Following the failure of Lehman Brothers in September 2008, with the liquidity drying up in the interbank lending markets, the scope for short-term arbitrage in forex markets has reduced substantially. Increased counterparty risk and strengthening of prudential norms have resulted in limits of arbitrage. This paper attempts to theoretically examine the impact of limits of arbitrage in a purely deterministic continuous-time model of exchange rates with boundedly rational agents having heterogeneous expectations. The rate of exchange depends on a combination of fundamental factors and speculative behavior by heterogeneous agents in foreign exchange markets. However, given that our focus is primarily on speculators, we keep the determination of the fundamentals outside the scope of our model. We find that under certain situation the limits of arbitrage might increase the stability of the fundamental equilibrium. However, the limits of arbitrage might indirectly destabilize the fundamental equilibrium by causing a reduction in the number of professional arbitrageurs.


Exchange rate Heterogeneous expectations 

JEL Classification

C62 D84 E03 F31 



  1. Akram F, Rime D, Sarno L (2008) Arbitrage in the foreign exchange market: turning on the microscope. J Int Econ 76:237–253CrossRefGoogle Scholar
  2. Angelini P, Nobili A, Picillo C (2011) The interbank market after August 2007: what has changed, and why? J Money Credit Bank 43(5):923–958CrossRefGoogle Scholar
  3. Baba N, Packer F (2009a) From turmoil to crisis: dislocations in the fx swap market before and after the failure of lehman brothers. J Int Money Finance 28(8):1350–1374CrossRefGoogle Scholar
  4. Baba N, Packer F (2009b) Interpreting deviations from covered interest parity during the financial market turmoil of 200708. J Bank Finance 33(11):1953–1962CrossRefGoogle Scholar
  5. Bekaert G, Hodrick R (2012) International financial management, 2nd edn. Pearson Education Inc., New JerseyGoogle Scholar
  6. Brock WA, Hommes CH (1997) A rational route to randomness. Econometrica 65(5):1059–1095CrossRefGoogle Scholar
  7. Brock WA, Hommes CH (1998) Heterogeneous beliefs and routes to chaos in a simple asset pricing model. J Econ Dyn Control 22(8):1235–1274CrossRefGoogle Scholar
  8. Cecchetti SG, Schoenholtz KL (2017) Money, banking, and financial markets, 5th edn. McGraw-Hill College, New YorkGoogle Scholar
  9. Cecchetti SG, Schoenholtz KL (2018) Bank financing: the disappearance of interbank lending. Accessed 29 Nov 2018
  10. Chiarella C, He X-Z (2002) Heterogeneous beliefs, risk and learning in a simple asset pricing model. Comput Econ 19(1):95–132CrossRefGoogle Scholar
  11. Chiarella C, He X-Z (2003) Heterogeneous beliefs, risk, and learning in a simple asset-pricing model with a market maker. Macroecon Dyn 7(4):503–536CrossRefGoogle Scholar
  12. Chiarella C, He X-Z, Zheng M (2013) Heterogeneous expectations and exchange rate dynamics. Eur J Finance 19(5):392–419CrossRefGoogle Scholar
  13. Cifarelli G, Paladino G (2018) Can the interaction between a single long-term attractor and heterogeneous trading explain the exchange rate conundrum? Res Int Bus Finance 46:313–323CrossRefGoogle Scholar
  14. de Grauwe P, Grimaldi M (2006) The exchange rate in a behavioral finance framework. Princeton University Press, PrincetonGoogle Scholar
  15. Dornbusch R (1976) Expectations and exchange rate dynamics. J Polit Econ 84(6):1161–1176CrossRefGoogle Scholar
  16. Du W, Tepper A, Verdelhan A (2018) Deviations from covered interest rate parity. J Finance 73(3):915–957CrossRefGoogle Scholar
  17. Fama EF (1970) Efficient capital markets: a review of theory and empirical work. J Finance 25(2):383–417CrossRefGoogle Scholar
  18. Flaschel P (2009) The macrodynamics of capitalism: elements for a synthesis of marx, keynes and schumpeter, second revised and enlarged edn. Springer, BerlinGoogle Scholar
  19. Fong W-M, Valente G, Fung JK (2010) Covered interest arbitrage profits: the role of liquidity and credit risk. J Bank Finance 34(5):1098–1107CrossRefGoogle Scholar
  20. Frankel J, Froot K (1986) Understanding the US dollar in the eighties: the expectations of chartists and fundamentalists. Econ Rec (Special Issue):24–38Google Scholar
  21. Gabaix X, Maggiori M (2015) International liquidity and exchange rate dynamics. Q J Econ 130(3):1369–1420CrossRefGoogle Scholar
  22. Griffioli TM, Ranaldo A (2010) Limits to arbitrage during the crisis: funding liquidity constraints and covered interest parity. Technical report, Swiss National BankGoogle Scholar
  23. Gromb D, Vayanos D (2002) Equilibrium and welfare in markets with financially constrained arbitrageurs. J Financ Econ 66(2):361–407CrossRefGoogle Scholar
  24. Gromb D, Vayanos D (2016) Arbitrage and its limits. Palgrave Macmillan, London, pp 1–3Google Scholar
  25. He X-Z, Li K (2012) Heterogeneous beliefs and adaptive behaviour in a continuous-time asset price model. J Econ Dyn Control 36:973–987CrossRefGoogle Scholar
  26. Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  27. Hommes CH (2006) Chapter 23: heterogeneous agent models in economics and finance. Handbook of computational economics, vol 2. Elsevier, New York, pp 1109–1186Google Scholar
  28. Kuznetsov YA (1997) Elements of applied bifurcation theory. Applied mathematical sciences, vol 112, 2nd edn. Springer, New YorkGoogle Scholar
  29. Kyle AS, Xiong W (2002) Contagion as a wealth effect. J Finance 56(4):1401–1440CrossRefGoogle Scholar
  30. Ljungqvist A, Qian W (2016) How constraining are limits to arbitrage? Rev Financ Stud 29(8):1975–2028CrossRefGoogle Scholar
  31. Lyons R (2001) The microstructure approach to exchange rates. applied mathematical sciences. MIT Press, CambridgeCrossRefGoogle Scholar
  32. Meese R, Rogoff K (1983) Empirical exchange rate models of the seventies: do they fit out of sample? J Int Econ 14(1–2):3–24CrossRefGoogle Scholar
  33. Porras Prado M, Saffi PAC, Sturgess J (2016) Ownership structure, limits to arbitrage, and stock returns: evidence from equity lending markets. Rev Financ Stud 29(12):3211–3244CrossRefGoogle Scholar
  34. Rime D, Schrimpf A, Syrstad O (2017) Segmented money markets and covered interest parity arbitrage. Technical report, Norges BankGoogle Scholar
  35. Sager MJ, Taylor MP (2006) Under the microscope: the structure of the foreign exchange market. Int J Finance Econ 11(1):81–95CrossRefGoogle Scholar
  36. Shleifer A, Vishny RW (1997) The limits of arbitrage. J Finance LI I(1):35–55CrossRefGoogle Scholar
  37. Westerhoff F (2003) Expectations driven distortions in foreign exchange market. J Econ Behav Organ 51(3):389–412CrossRefGoogle Scholar
  38. Westerhoff F, Reitz S (2003) Nonlinearities and cyclical behavior: the role of chartists and fundamentalists. Stud Nonlinear Dyn Econ 7(4):1558–3708.

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of EconomicsSouth Asian UniversityNew DelhiIndia

Personalised recommendations