Exchange rate dynamics under limits of arbitrage and heterogeneous expectations

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.