Abstract
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.
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Notes
However, Ljungqvist and Qian (2016) discussed the possibilities of arbitrageurs circumventing limits of arbitrage by publicly revealing the information that they possess about the fundamentals.
According to Gabaix and Maggiori (2015, p. 1370, Section 1),
“these institutions range from the (former) proprietary desks and investment management arms of global investment banks, such as Goldman Sachs and JP Morgan, to macro and currency hedge funds such as Soros Fund Management to active investment managers and pension funds such as PIMCO and BlackRock.”
See, for instance, de Grauwe and Grimaldi (2006).
The sufficient condition will also be necessary condition, provided \( \bar{w}_2 \ge \min \left[ \dfrac{1}{\beta _s} + \dfrac{\beta _r + \beta _f}{\beta _s \beta _c} , 1 \right] \) .
I am grateful to the referee for pointing this out.
There are two other steady states; however these are complex conjugates containing an imaginary component.
In the context of actual forex markets, for instance, we can think of large financial institutions, forex dealers and market makers in interbank markets as professional arbitrageurs, who would conduct arbitrage as long as not faced with limits of arbitrage. As Gabaix and Maggiori (2015) argued, this section of the market frequently faces financial constraints due to limits of arbitrage of the kind described by Shleifer and Vishny (1997). Rest of the market, however, will not attempt arbitrage because, given the size of forex market, they do not hope to have adequate influence for a successful arbitrage attempt.
There are two other steady states; however these are complex conjugates containing an imaginary component.
We should note here that if we use \(\bar{w}\) as a bifurcation parameter, then changing this parameter will also involve change in the steady state value of w. All the other variables, however, do not depend on \(\bar{w}\).
However, this is true only for the current set of numerical values of parameters, since \(\beta _w\) appears as a coefficient to positive terms in the expression of characteristic roots. This might possibly not hold true for alternative numerical configuration of parameters.
There are two other steady states; however, like (24) these are complex conjugates containing an imaginary component.
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This paper is dedicated to the memory of Prof. Carl Chiarella who passed away in June 2016. Some of preliminary results from this paper were presented at \(22{\mathrm{nd}}\) Annual Workshop on Economic Science with Heterogeneous Interacting Agents in June 2017 and Asia Pacific Economic Conference in November 2017. The author is grateful to the participants of these conferences for their comments. The paper also benefited from the useful suggestions of two referees on the earlier versions of this paper. The usual disclaimer applies.
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Datta, S. Exchange rate dynamics under limits of arbitrage and heterogeneous expectations. J Econ Interact Coord 14, 521–550 (2019). https://doi.org/10.1007/s11403-019-00237-6
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DOI: https://doi.org/10.1007/s11403-019-00237-6