Rare Disasters and Exchange Rates

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Rare Disasters and Exchange Rates, Proposal Number 0820517by Emmanuel Farhi (Harvard and NBER) and Xavier Gabaix (NYU and NBER) This proposal contains a new model of exchange rates which offers a solution of the forward premium puzzle. The puzzle is due to investing in high interest rate currencies (the "carry trade") yielding much more than warranted by the underlying risk differential with low-interest currencies. The explanation combines two ingredients: the possibility of rare economic disasters, and an asset view of the exchange rate. The model is frictionless, has complete markets, works for an arbitrary number of countries, and derives in closed form the values of exchange rates, stocks, and bonds. In the model, rare worldwide disasters can occur and affect each country's productivity. Each country's exposure to disaster risk varies over time according to a mean-reverting process. Risky countries command high risk premia: they feature a depreciated exchange rate and a high interest rate. As their risk premium mean reverts, their exchange rate appreciates. Therefore, currencies of high interest rate countries appreciate on average. To make the notion of disaster risk more implementable, the proposals shows how options prices can in principle uncover latent disaster risk, and help forecast exchange rate movements. Calibration of the model yields quantitatively realistic values for the volatility of the exchange rate, the formerly unexpected sign of the regression coefficients, and near-random walk exchange rate dynamics. The project has the following distinctive features. (i) It generates easily two central features of the data, namely "excess volatility" of exchange rates, and the (solution to the) "forward premium puzzle." (ii) The model has a novel analytical structure, based on the ideas of rare disasters, and the newly-developed class of "linearity-generating processes." This makes the model very tractable: Exchange rates, stocks and bonds prices can be obtained from it in exact closed forms in a frictionless setup. The framework can serve as a new multi-purpose model for international macroeconomics. (iii) The model makes new testable predictions: Currencies with high crash premiums should subsequently appreciate. In addition, the model yields a series of predictions about the joint behavior of exchange rates and the prices of bonds, options and stocks across countries. The proposed research offers a way to understand the impact of exchange rate pegging. This is particularly relevant, as a large fraction of emerging countries (e.g., China) do peg their currency. To analyze pegs, one needs a model that generates a volatile exchange rate in absence of a peg like the model here provided.Last not least, the projects theory delineates how the latent importance of large disasters can be detected in asset prices.