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Abstract This paper shows that the probability of extreme default losses on portfolios of U.S. corporate debt is much greater than would be estimated under the standard assumption that default correlation arises only from exposure to observable risk factors. At the high confidence levels at which bank loan portfolio and CDO default losses are typically measured for economic-capital and rating purposes, our empirical results indicate that conventionally based estimates are downward biased by a full order of magnitude on test portfolios. Our estimates are based on U.S. public non-financial firms existing between 1979 and 2004. We find strong evidence for the presence of common latent factors, even when controlling for observable factors that provide the most accurate available model of firm-by-firm default probabilities.

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and the 2004 Institute of Mathematical Statistics Annual Meeting/6th Bernoulli World Congress for helpful comments. We are responsible for any remaining errors. A Bayesian Analysis of Return Dynamics with Stochastic Volatility and Lévy Jumps We develop Bayesian Markov chain Monte Carlo methods for inferences of continuous-time models with stochastic volatility and infinite-activity Lévy jumps using discretely sampled data. Simulation studies show that (i) our methods provide accurate joint identification of diffusion, stochastic volatility, and Lévy jumps, and (ii) affine jump-diffusion models fail to adequately approximate the behavior of infinite-activity jumps. In particular, the affine jump-diffusion models fail to capture the “infinitely many ” small LévyjumpswhicharetoobigforBrownianmotiontomodelandtoosmall for compound Poisson process to capture. Empirical studies show that infinite-activity Lévy jumps are essential for modeling the S&P 500 index returns. The continuous-time finance literature in the past few decades has mainly relied on Brownian motion and compound Poisson process as basic model building blocks. Sophisticated models based solely on Brownian motion and compound Poisson process have been developed to capture important

Standard practice for the estimation of dynamic stochastic general equilibrium (DSGE) models maintains the assumption that economic variables are properly measured by a single indicator, and that all relevant information for the estimation is summarized by a small number of data series. However, recent empirical research on factor models has shown that information contained in large data sets is relevant for the evolution of important macroeconomic series. This suggests that conventional model estimates and inference based on estimated DSGE models are likely to be distorted. In this paper, we propose an empirical framework for the estimation of DSGE models that exploits the relevant information from a data-rich environment. This framework provides an interpretation of all information contained in a large data set, and in particular of the latent factors, through the lenses of a DSGE model. The estimation involves Bayesian Markov-Chain Monte-Carlo (MCMC) methods extended so that the estimates can, in some cases, inherit the properties of classical maximum likelihood estimation. We apply this estimation approach to a state-of-the-art DSGE monetary model. Treating theoretical concepts of the model – such as output, inflation and employment – as partially observed, we show that the information from a large set of macroeconomic indicators is important for accurate estimation of the model. It also allows us to improve the forecasts of important economic variables.

We propose a simulated maximum likelihood estimator (SMLE) for general stochastic dynamic models based on nonparametric kernel methods. The method requires that, while the actual likelihood function cannot be written down, we can still simulate observations from the model. From the simulated observations, we estimate the unknown density of the model nonparametrically by kernel methods, and then obtain the SMLEs of the model parameters. Our method avoids the issue of non-identification arising from poor choice of auxiliary models in simulated methods of moments (SMM) or indirect inference. More importantly, our SMLEs achieve higher efficiency under weak regularity conditions. Finally, our method allows for potentially nonstationary processes, including time-inhomogeneous dynamics.

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stochastic volatility, predictability We especially thank John Cochrane, as portions of this manuscript originated from extensive conversations between John and the authors. We also thank Joe Chen, Chris Jones, Greg Willard, and seminar

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We survey asset allocation in finance from a Bayesian decision-theoretic perspective. We study an investor who wishes to maximize the expected long-run growth of the market. With the aid of Stein’s lemma we derive the Kelly criteria for optimal bet size and Merton’s allocation rule for risky stocks. We therefore provide an equivalence between these two criteria. Bayesian inference naturally determines the inputs for this analysis, namely, the expected excess return and volatility of the risky asset. Extensions to exchangeable returns where the investor learns about the probability of success illustrate the feature that risk-averse investors are still willing to hold a small proportion of a risky asset even though the odds are unfavorable at the current time. The option value of future learning leads one to a positive allocation. We conclude with directions for future research.