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Variable Rare Disasters: An Exactly Solved Framework for
 Ten Puzzles in Macro Finance, Working Paper, NYU
, 2009
"... This article incorporates a timevarying severity of disasters into the hy ..."
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This article incorporates a timevarying severity of disasters into the hy
Rare Disasters and Exchange Rates: A Theory of the Forward Premium Puzzle,” October 2007. Working Paper Harvard University. 23 Frachot, Antoine, “A Reexamination of the Uncovered Interest Rate Parity Hypothesis
 Frankel, Jeffrey and Jumana Poonawala, “The Forward Market in Emerging Currencies: Less Biased than in Major Currencies,” 2007. Working paper NBER
"... We propose a new theory of the forward premium puzzle for exchange rates. Our explanation combines two ingredients: the possibility of rare economic disasters, and an asset view of the exchange rate. Our model is frictionless and has complete markets. In the model, rare worldwide disasters can occur ..."
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Cited by 13 (1 self)
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We propose a new theory of the forward premium puzzle for exchange rates. Our explanation combines two ingredients: the possibility of rare economic disasters, and an asset view of the exchange rate. Our model is frictionless and has complete markets. 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 meanreverting process. Risky countries command high risk premia: they feature a low exchange rate and a high interest rate. As their risk premium reverts to the mean, their exchange rate appreciates. Therefore, the currencies of high interest rate countries appreciate on average. This provides an explanation for the forward premium puzzle (a.k.a. uncovered interest rate parity puzzle). We then extend the framework to incorporate two factors: a slow moving productivity factor, and a fast meanreverting disaster risk factor. We calibrate the model and obtain quantitatively realistic values for the volatility of the exchange rate, the forward premium puzzle regression coefficients, and nearrandom walk exchange rate dynamics. Finally, we work out a model of the stock market, which allows us to make a series of predictions about the joint behavior of exchange rates, bonds, options and stocks across countries. (JEL: E43, E44, F31, G12, G15)
Rare Disasters and Exchange Rates
, 2008
"... We propose a new model of exchange rates, which yields a theory of the forward premium puzzle. Our explanation combines two ingredients: the possibility of rare economic disasters, and an asset view of the exchange rate. Our model is frictionless, has complete markets, and works for an arbitrary num ..."
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Cited by 10 (0 self)
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We propose a new model of exchange rates, which yields a theory of the forward premium puzzle. Our explanation combines two ingredients: the possibility of rare economic disasters, and an asset view of the exchange rate. Our model is frictionless, has complete markets, and works for an arbitrary number of countries. 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 meanreverting 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, we show how options prices might in principle uncover latent disaster risk, and help forecast exchange rate movements. We then extend the framework to incorporate two factors: a disaster risk factor, and a business cycle factor. We calibrate the model and obtain quantitatively realistic values for the volatility of the exchange rate, the forward premium puzzle regression coefficients, and nearrandom walk exchange rate dynamics. Finally, we solve a model of stock markets across countries, which yields a series of predictions about the joint behavior of exchange rates, bonds, options and stocks across countries. The evidence from the options market appears to be supportive of the
A MeanVariance Benchmark for Intertemporal Portfolio Theory
, 2008
"... By reinterpreting the symbols, oneperiod meanvariance portfolio theory can apply to dynamic intertemporal problems in incomplete markets, with nonmarketed income. Investors first hedge nontraded income and preference shocks. Then, their optimal payoffs are split between an indexed perpetuity and ..."
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Cited by 8 (3 self)
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By reinterpreting the symbols, oneperiod meanvariance portfolio theory can apply to dynamic intertemporal problems in incomplete markets, with nonmarketed income. Investors first hedge nontraded income and preference shocks. Then, their optimal payoffs are split between an indexed perpetuity and a “longrun meanvariance efficient” payoff, which avoids variation over time as well as variation across states of nature. In equilibrium, the market payoff and the average outsideincome hedge payoff span the longrun meanvariance frontier, and longrun expected returns are linear functions of longrun market and outsideincomehedge betas. State variables for investment opportunities and outside income are conveniently absent in these characterizations.
Timeseries predictability in the disaster model
 Finance Research Letters
, 2008
"... This paper studies whether the RietzBarro “disaster”model, extended for a timevarying probability of disaster, can match the empirical evidence on predictability of stock returns. It is shown that when utility is CRRA, the model cannot replicate these …ndings, regardless of parameter values. This ..."
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Cited by 8 (1 self)
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This paper studies whether the RietzBarro “disaster”model, extended for a timevarying probability of disaster, can match the empirical evidence on predictability of stock returns. It is shown that when utility is CRRA, the model cannot replicate these …ndings, regardless of parameter values. This motivates extending the disaster model to allow for EpsteinZin utility. Analytical results show that when the probability of disaster is iid, the model with EpsteinZin utility can match the evidence on predictability qualitatively if the elasticity of substitution is greater than unity. The case of a persistent probability of disaster is studied numerically, with partial success. 1
Affine models
 In R. Cont (Ed.), Encyclopedia of Quantitative Finance
, 2009
"... Abstract. Affine term structure models have gained a lot of attention in the finance literature, which is due to their analytic tractability and statistical flexibility. The aim of this article is to present both, theoretical foundations and empirical aspects. Starting from the first short rate mode ..."
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Cited by 7 (1 self)
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Abstract. Affine term structure models have gained a lot of attention in the finance literature, which is due to their analytic tractability and statistical flexibility. The aim of this article is to present both, theoretical foundations and empirical aspects. Starting from the first short rate models, namely the Vasiček and the CoxIngersollRoss ones, we then give an overview of some properties of affine processes and explain their relation to affine term structure models. Pricing and estimation techniques are eventually mentioned, showing how the analytic tractability of affine models can be exploited for practical purposes.
LinearityGenerating Processes, Unspanned Stochastic Volatility, and InterestRate Option Pricing
"... We propose to use the linearitygenerating framework to accommodate the evidence of unspanned stochastic volatility: Variations in implied volatilities on interestrate options such as caps and swaptions are independent of the variations on the interest rate term structure. Under this framework, bon ..."
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Cited by 5 (1 self)
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We propose to use the linearitygenerating framework to accommodate the evidence of unspanned stochastic volatility: Variations in implied volatilities on interestrate options such as caps and swaptions are independent of the variations on the interest rate term structure. Under this framework, bond valuation depends only on the transition dynamics of interestrate factors, but not on their volatilities. Thus, interestrate volatility is truly unspanned. Furthermore, this framework allows tractable pricing of options on any bond portfolios, including both caps and swaptions. This feat is not possible under existing exponentialaffine or quadratic frameworks. Finally, the framework allows sequential estimation of the interestrate term structure and the interestrate option implied volatility surface, thus facilitating joint empirical analysis. Within this framework, we perform specification analysis on interestrate factor transition dynamics and its relation to the interestrate term structure; we also analyze the interestrate volatility dynamics and its impact on interestrate option pricing. We estimate several specifications for the transition dynamics to ten years worth of U.S. dollar LIBOR and swap rates across 15 maturities. We also estimate several interestrate volatility dynamics specifications using ten years of swaption implied volatilities across a matrix of ten option maturities and seven swap tenors. The estimation results show
Disasterization: A Simple Way to Fix the Asset Pricing Properties of Macroeconomic Models
, 2010
"... A central difficulty in economics is to create a model economy that has both good business cycle properties and good asset pricing properties. Macro models have the former, fail in the latter. Finance models typically work with endowment economies, and are hard to integrate with macro. I show how to ..."
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A central difficulty in economics is to create a model economy that has both good business cycle properties and good asset pricing properties. Macro models have the former, fail in the latter. Finance models typically work with endowment economies, and are hard to integrate with macro. I show how to solve this difficulty by a simple, portable, modelling device, the “disasterization ” procedure. Take an economy with good business cycle properties, and create a new, “disasterized ” economy, which is essentially identical to the original one, except that, disasters can destroy part of the capital stock and productivity. In the disasterized economy, asset prices exhibit high and volatile risk premia, but investment, employment, the shortterm real interest rate remain the same as in the original economy. Hence, we have a tractable unified framework to think about both the macroeconomy and the financial side. As an application, I consider a longstanding difficulty in macrofinance, Tobin’s �. In the model, like in the real world, stock market valuations (�) are very volatile, negatively correlated with future stock returns, but uncorrelated with investment. I conclude by showing
Regularity Conditions to Ensure the Existence of LinearityGenerating Processes,” working paper
, 2008
"... “Linearitygenerating ” processes offer a tractable procedure to model cashflows and pricing kernels in a way that yields exact closed form expressions for bond and stock prices. Prices are simply affine (not exponentialaffine) in the factors. The linearitygenerating class operates in discrete an ..."
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“Linearitygenerating ” processes offer a tractable procedure to model cashflows and pricing kernels in a way that yields exact closed form expressions for bond and stock prices. Prices are simply affine (not exponentialaffine) in the factors. The linearitygenerating class operates in discrete and continuous time with an arbitrary number of factors. This paper presents novel and general regularity conditions which ensure that processes are welldefined. It illustrates them with a series of economic examples. (JEL: C65, E43, G12, G13)