Rare Disasters and Exchange Rates

罕见的灾难和汇率，提案编号0820517，作者是Emmanuel Farhi(哈佛大学和NBER)和Xavier Gabaix(纽约大学和NBER)。该提案包含一个新的汇率模型，它提供了远期保费难题的解决方案。这个谜题是因为投资于高利率货币(“套利交易”)的收益远远高于其与低利率货币之间的潜在风险差。这一解释结合了两个因素：罕见经济灾难的可能性，以及对汇率的资产观点。该模型是无摩擦的，有完整的市场，适用于任意数量的国家，并以封闭的形式推导出汇率、股票和债券的价值。在该模型中，罕见的世界性灾难可能会发生，并影响每个国家的生产力。根据均值回归过程，每个国家面临的灾害风险随着时间的推移而不同。高风险国家的风险溢价很高：它们的特点是汇率贬值，利率较高。随着他们的风险溢价均值恢复，他们的汇率也会升值。因此，高利率国家的货币平均升值。为了使灾难风险的概念更具可操作性，这些提案展示了期权价格如何在原则上揭示潜在的灾难风险，并帮助预测汇率走势。对模型的校准产生了汇率波动性的量化现实值、回归系数的先前意想不到的符号以及近乎随机游走的汇率动态。该项目具有以下鲜明特点。(I)它很容易产生数据的两个中心特征，即汇率的“过度波动”和“远期溢价之谜的解决方案”。(Ii)该模型具有一种新颖的分析结构，基于罕见灾害的思想，以及新开发的一类“线性生成过程”。这使得该模型非常易于处理：汇率、股票和债券价格可以在无摩擦设置下以精确的封闭形式从该模型中获得。该框架可以作为国际宏观经济学的一种新的多用途模型。(Iii)该模型做出了新的可检验的预测：崩盘溢价较高的货币随后应该会升值。此外，该模型还产生了一系列关于各国汇率以及债券、期权和股票价格的联合行为的预测。这项拟议的研究为理解盯住汇率的影响提供了一种方法。这一点尤其重要，因为很大一部分新兴国家(例如中国)确实盯住了本国货币。为了分析钉住汇率，人们需要一个在没有钉住汇率的情况下产生波动的模型，就像这里提供的模型一样。最后，项目理论描述了如何在资产价格中检测到重大灾难的潜在重要性。

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.