A Large Trader in Bubbles and Crashes: An Application to Currency Attacks

Abreu and Brunnermeier (2003) study stock market bubbles and crashes in a dynamic model with a continuum of rational small traders. We introduce a large trader into their model and apply it to currency attacks. In an attack against a fixed exchange rate regime with a gradually overvaluing currency, traders lack common knowledge about the time when the overvaluation starts. Meanwhile, they need to coordinate to break a peg. In such a setup, both the inability of traders to synchronize their attack and their incentive to time the collapse of the regime lead to the persistent overvaluation of the currency. We find that the presence of a large trader with perfect information will accelerate the collapse of the regime and alleviate currency overvaluation. However, if a large trader has incomplete information, the presence of a large trader may accelerate or delay the collapse of the regime ex post, depending on the size of his wealth and the precision of his information. More specifically, we find that a large trader with both a large amount of wealth and very noisy information can greatly delay the collapse of the regime ex post. Moreover, we find that the presence of a large trader with incomplete information can greatly increase the unpredictability about the time when the regime collapses, implying the difficulty for traders to time the collapse.