Results 1  10
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67
Optimal filtering of jump diffusions: extracting latent states from asset prices
, 2007
"... This paper provides a methodology for computing optimal filtering distributions in discretely observed continuoustime jumpdiffusion models. Although it has received little attention, the filtering distribution is useful for estimating latent states, forecasting volatility and returns, computing mo ..."
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Cited by 44 (8 self)
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This paper provides a methodology for computing optimal filtering distributions in discretely observed continuoustime jumpdiffusion models. Although it has received little attention, the filtering distribution is useful for estimating latent states, forecasting volatility and returns, computing model diagnostics such as likelihood ratios, and parameter estimation. Our approach combines timediscretization schemes with Monte Carlo methods to compute the optimal filtering distribution. Our approach is very general, applying in multivariate jumpdiffusion models with nonlinear characteristics and even nonanalytic observation equations, such as those that arise when option prices are available. We provide a detailed analysis of the performance of the filter, and analyze four applications: disentangling jumps from stochastic volatility, forecasting realized volatility, likelihood based model comparison, and filtering using both option prices and underlying returns.
2004): “Model specification and risk premiums: Evidence from futures options,” Working paper, Columbia University, forthcoming in Journal of Finance
"... There are two central issues in option pricing: selecting an appropriate model and quantifying the risk premiums of the various underlying factors. In this paper, we use the information in the crosssection of S&P futures options from 1987 to 2003 to examine these issues. We first test for the p ..."
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Cited by 38 (4 self)
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There are two central issues in option pricing: selecting an appropriate model and quantifying the risk premiums of the various underlying factors. In this paper, we use the information in the crosssection of S&P futures options from 1987 to 2003 to examine these issues. We first test for the presence of jumps in volatility by analyzing the higher moment behavior of option implied variance. The option data provides strong evidence supporting the presence of jumps in volatility. In conjunction with previous results, this implies that stochastic volatility, jumps in returns and jumps in volatility are all important components. Next, we find strong crosssectional evidence in support of jumps in returns, and modest evidence for jumps in volatility. We find evidence for reasonable jump risk premiums, but do not find any evidence for a diffusive volatility risk premium. We also find strong evidence for time variation in thejumpriskpremiums.
Inflation and earnings uncertainty and volatility forecasts: A structural form approach, Working Paper
, 2008
"... We propose a new structural form methodology for understanding the fluctuations and predictability of volatilities and covariances of asset returns. The methodology is applied to a model in which investors learn about the joint movements in inflation and real earnings through business cycles. The ec ..."
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Cited by 32 (2 self)
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We propose a new structural form methodology for understanding the fluctuations and predictability of volatilities and covariances of asset returns. The methodology is applied to a model in which investors learn about the joint movements in inflation and real earnings through business cycles. The econometrician extracts investors ’ beliefs about fundamentals from the prices and volatilities of stocks and bonds. The duration of episodes of enhanced investor uncertainty are forecastable and lead to forecasts of volatilities that are more precise than those obtained from a reduced form specification that includes lagged volatility and several macroeconomic variables. The model’s success stems largely from endogenous and timevarying weights that investors assign to news about real fundamental growth and discount rates.
Do bonds span volatility risk in the U.S. Treasury market? A speci test of ane term structure models, Working paper
, 2006
"... Further, we thank Mitch Haviv of GovPX for providing useful information on their data. Of course, all errors remain our sole responsibility. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Chicago, the Federal Reserve System, or the Nation ..."
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Cited by 22 (0 self)
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Further, we thank Mitch Haviv of GovPX for providing useful information on their data. Of course, all errors remain our sole responsibility. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Chicago, the Federal Reserve System, or the National
Term structure estimation without using latent factors
, 2004
"... The term structure is modeled as a function of observable and unobservable (latent) factors. I describe how to estimate the relation between the observed factors and the term structure without specifying or estimating latentfactor dynamics. Noarbitrage requirements are imposed in the estimation pr ..."
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Cited by 21 (0 self)
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The term structure is modeled as a function of observable and unobservable (latent) factors. I describe how to estimate the relation between the observed factors and the term structure without specifying or estimating latentfactor dynamics. Noarbitrage requirements are imposed in the estimation procedure. I apply the methodology to the joint dynamics of inflation and the term structure. As other research has noted, both shortterm and longterm bond yields adjust gradually to a change in inflation. I find that the dynamics of the price of interest rate risk needed to fit this pattern from 1983 through 2003 are implausible. An alternative interpretation is that investors were systematically surprised by the slow adjustment of shortterm yields to inflation.
Why Gaussian MacroFinance Term Structure Models are (Nearly) Unconstrained FactorVARs.” Discussion paper,
, 2011
"... ABSTRACT This article develops a new family of Gaussian macrodynamic term structure models (MTSMs) in which bond yields follow a lowdimensional factor structure and the historical distribution of bond yields and macroeconomic variables is characterized by a vectorautoregression with order p > 1 ..."
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Cited by 21 (7 self)
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ABSTRACT This article develops a new family of Gaussian macrodynamic term structure models (MTSMs) in which bond yields follow a lowdimensional factor structure and the historical distribution of bond yields and macroeconomic variables is characterized by a vectorautoregression with order p > 1. Most formulations of MTSMs with p > 1 are shown to imply a much higher dimensional factor structure for yields than what is called for by historical data. In contrast, our "asymmetric" arbitragefree MTSM gives modelers the flexibility to match historical lag distributions with p > 1 while maintaining a parsimonious factor representation of yields. Using our canonical family of MTSMs we revisit: (i) the impact of noarbitrage restrictions on the joint distribution of bond yields and macro risks, comparing models with and without the restriction that macro risks are spanned by yieldcurve information; and (ii) the identification of the policy parameters in Taylorstyle monetary policy rules within MTSMs with macro risk factors and lags. ( JEL: G12,E43, C58, E58) KEYWORDS: Macrofinance term structure model, Lags, Taylor Rule Identification Dynamic term structure models in which a subset of the pricing factors are macroeconomic variables (MTSMs) often have bond yields depending on lags of these factors. 1 As typically parameterized, such MTSMs imply that the crosssection
Risk and return on bond, currency and equity markets: A unified approach. Working paper
, 2007
"... George Tauchen, Adrien Verdelhan for their helpful comments and suggestions. The usual disclaimer applies. Risk and Return in Bond, Currency and Equity Markets We develop a general equilibrium longrun risks model that can simultaneously account for key asset price puzzles in bond, currency and equ ..."
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Cited by 19 (5 self)
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George Tauchen, Adrien Verdelhan for their helpful comments and suggestions. The usual disclaimer applies. Risk and Return in Bond, Currency and Equity Markets We develop a general equilibrium longrun risks model that can simultaneously account for key asset price puzzles in bond, currency and equity markets. Specifically, we show that the model can explain the predictability of returns and violations of the expectations hypothesis in bond and foreign exchange markets. It also accounts for the levels and volatilities of bond yields and exchange rates, and the wellknown risk premium and volatility puzzles in equity markets. The model matches the observed consumption and inflation dynamics. Using domestic and foreign consumption and asset markets data we provide robust empirical support for our models predictions. We argue that key economic channels featured in the longrun risks model — longrun growth fluctuations and timevarying uncertainty, along with a preference for early resolution of uncertainty — provide a coherent framework to simultaneously explain a rich array of asset market puzzles. 1
Discretetime dynamic term structure models with generalized market prices of risk
, 2006
"... This paper develops a rich class of discretetime, nonlinear dynamic term structure models (DTSMs). Under the riskneutral measure, the distribution of the state vector Xt resides within a family of discretetime affine processes that nests the exact discretetime counterparts of the entire class of ..."
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Cited by 17 (0 self)
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This paper develops a rich class of discretetime, nonlinear dynamic term structure models (DTSMs). Under the riskneutral measure, the distribution of the state vector Xt resides within a family of discretetime affine processes that nests the exact discretetime counterparts of the entire class of continuoustime models in Duffie and Kan (1996) and Dai and Singleton (2000). Moreover, we allow the market price of risk Λt, linking the riskneutral and historical distributions of X, to depend generally on the state Xt. The conditional likelihood functions for coupon bond yields for the resulting nonlinear models under the historical measure are known exactly in closed form. As an illustration of our approach, we estimate a three factor model with a cubic term in the drift of the stochastic volatility factor and compare it to a model with a linear drift. Our results show that inclusion of a cubic term in the drift significantly improves the models statistical fit as well as its outofsample forecasting performance.
DiscreteTime AffineQ Term Structure Models with Generalized Market Prices of Risk
 Review of Financial Studies
, 2010
"... This article develops a rich class of discretetime, nonlinear dynamic term structure models (DTSMs). Under the riskneutral measure, the distribution of the state vector Xt resides within a family of discretetime affine processes that nests the exact discretetime counterparts of the entire clas ..."
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Cited by 13 (6 self)
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This article develops a rich class of discretetime, nonlinear dynamic term structure models (DTSMs). Under the riskneutral measure, the distribution of the state vector Xt resides within a family of discretetime affine processes that nests the exact discretetime counterparts of the entire class of continuoustime models in Duffie and Kan (1996) and Dai and Singleton (2000). Under the historical distribution, our approach accommodates nonlinear (nonaffine) processes while leading to closedform expressions for the conditional likelihood functions for zerocoupon bond yields. As motivation for our framework, we show that it encompasses many of the equilibrium models with habitbased preferences or recursive preferences and longrun risks. We illustrate our methods by constructing maximum likelihood estimates of a nonlinear discretetime DTSM with habitbased preferences in which bond prices are known in closed form. We conclude that habitbased models, as typically parameterized in the literature, do not match key features of the conditional distribution of bond yields. (JEL G12, C50, E13, E21) 1.
What’s Real About the Business Cycle?
"... This paper argues that a linear statistical model with homoskedastic errors cannot capture the nineteenthcentury notion of a recurring cyclical pattern in key economic aggregates. A simple nonlinear alternative is proposed and used to illustrate that the dynamic behavior of unemployment seems to ch ..."
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Cited by 12 (1 self)
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This paper argues that a linear statistical model with homoskedastic errors cannot capture the nineteenthcentury notion of a recurring cyclical pattern in key economic aggregates. A simple nonlinear alternative is proposed and used to illustrate that the dynamic behavior of unemployment seems to change over the business cycle, with the unemployment rate rising more quickly than it falls. Furthermore, many but not all economic downturns are also accompanied by a dramatic change in the dynamic behavior of shortterm interest rates. It is suggested that these nonlinearities are most naturally interpreted as resulting from shortrun failures in the employment and credit markets and that understanding these shortrun failures is the key to understanding the nature of the business cycle.