Rare Disasters and Exchange Rates

罕见灾害与汇率，提案号0820517，作者：Emmanuel Farhi（哈佛大学和国家经济研究局）和Xavier Gabaix（纽约大学和国家经济研究局）。该提案包含了一个新的汇率模型，为远期溢价之谜提供了一个解决方案。这个谜题是由于投资高利率货币（“套息交易”）的收益远远超过了与低利率货币的潜在风险差的保证。这种解释结合了两个因素：罕见的经济灾难的可能性，以及对汇率的资产观点。这个模型是无摩擦的，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，罕见的世界性灾害可能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时间而变化。高风险国家的风险溢价高：它们的特点是汇率贬值和利率高。随着它们的风险溢价均值回归，它们的汇率就会升值。因此，高利率国家的货币平均升值。为了使灾害风险的概念更具可操作性，这些建议显示了期权价格在原则上如何揭示潜在的灾害风险，并帮助预测汇率变动。模型的校准产生了汇率波动性的定量现实值，回归系数的先前意想不到的符号，以及近乎随机行走的汇率动态。本项目具有以下特点：(i)它很容易产生数据的两个中心特征，即汇率的“过度波动”，以及“远期溢价之谜”的（解决方案）。（ii）该模型基于罕见灾害的思想和新发展的一类“线性生成过程”，具有新的分析结构。这使得该模型非常容易处理：汇率、股票和债券价格可以在无摩擦的设置中以精确的封闭形式从中获得。该框架可以为国际宏观经济学提供一个新的多用途模型。（三）模型作出新的可检验的预测：崩盘溢价高的货币随后应升值。此外，该模型还对各国的汇率、债券、期权和股票价格的共同行为做出了一系列预测。拟议的研究为理解汇率挂钩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（如中国）都实行钉住汇率。要分析挂钩制度，我们需要一个模型，在没有像本文所提供的模型那样的挂钩制度的情况下，产生不稳定的汇率。最后，项目理论描述了如何在资产价格中发现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.