Bank Testing Linear Factor Pricing Models with Large Cross-Sections: A Distribution-Free Approach

We develop a finite-sample procedure to test the beta-pricing representation of linear factor pricing models that is applicable even if the number of test assets is greater than the length of the time series. Our distribution-free framework leaves open the possibility of unknown forms of non-normalities, heteroskedasticity, time-varying correlations, and even outliers in the asset returns. The power of the proposed test procedure increases as the time-series lengthens and/or the cross-section becomes larger. This stands in sharp contrast to the usual tests that lose power or may not even be computable if the cross-section is too large. Finally, we revisit the CAPM and the Fama-French three factor model. Our results strongly support the mean-variance efficiency of the market portfolio.Econometric and statistical methods; Financial markets

Exact Tests of Equal Forecast Accuracy with an Application to the Term Structure of Interest Rates

The author proposes a class of exact tests of the null hypothesis of exchangeable forecast errors and, hence, of the hypothesis of no difference in the unconditional accuracy of two competing forecasts. The class includes analogues of the well-known Diebold and Mariano (1995) parametric and non-parametric test statistics. The forecast errors can be non-normal and contemporaneously correlated, and general forms of the loss function are admitted. The nonparametric distribution-free property of these new tests makes them robust to the presence of conditional heteroscedasticity, heavy tails, and outliers in the loss-differential series. These tests are used with a randomization or “Monte Carlo” resampling technique, which yields an exact and computationally inexpensive inference procedure. Simulations confirm the reliability of the new test procedure, and its power is found to be comparable with that of the size-corrected parametric Diebold-Mariano test. The test procedure is illustrated with an application to the term structure of interest rates. The application shows that exchangeable forecast errors can be found empirically even when comparing forecasts from estimated models.Econometric and statistical methods

Multiple testing of the forward rate unbiasedness hypothesis across currencies

We develop exact distribution-free test procedures for joint inference about the forward rate unbiasedness hypothesis (FRUH) across multiple currencies. The procedures can be applied with either levels or differences specifications. This unified approach proceeds with sign and signed rank tests for each currency and then uses Monte Carlo resampling to control the overall Type I error rate of either: (i) global FRUH tests obtained via combinations of the p-values; or (ii) individual FRUH tests using multiplicity adjusted p-values. Our framework allows for missing data and for the presence of time-varying conditional covariances between currencies. The usefulness of the new procedures is illustrated with a simulation study and with assessments of the FRUH across 13 currencies in an unbalanced panel. Multiplicity adjusted p-values reveal that the joint FRUH rejections are primarily driven by just a few of the more minor currencies

Multivariate tests of mean-variance efficiency and spanning with a large number of assets and time-varying covariances

We develop a finite-sample procedure to test the mean-variance efficiency and spanning hypotheses, without imposing any parametric assumptions on the distribution of model disturbances. In so doing, we provide an exact distribution-free method to test uniform linear restrictions in multivariate linear regression models. The framework allows for unknown forms of nonnormalities as well as time-varying conditional variances and covariances among the model disturbances. We derive exact bounds on the null distribution of joint F statistics to deal with the presence of nuisance parameters, and we show how to implement the resulting generalized nonparametric bounds tests with Monte Carlo resampling techniques. In sharp contrast to the usual tests that are not even computable when the number of test assets is too large, the power of the proposed test procedure potentially increases along both the time and cross-sectional dimensions

Unfolded GARCH models

A new GARCH-type model for autoregressive conditional volatility, skewness, and kurtosis is proposed. The approach decomposes returns into their signs and absolute values, and specifies the joint distribution by combining a multiplicative error model for the absolute values, a dynamic binary choice model for the signs, and a copula function for their interaction. The conditional volatility and kurtosis are determined by innovations following a folded (or absolute) Studentt distribution with time-varying degrees of freedom, and separate time variation in conditional return skewness is achieved by allowing the copula parameter to be dynamic. Model estimation is performed with Bayesian methods using an adaptive Markov chain Monte Carlo algorithm. An empirical application to the returns on four major international stock market indices illustrates the statistical and economic significance of the new model for conditional higher moments

Identication-robust moment-based tests for Markov switching in autoregressive models

This paper develops tests of the null hypothesis of linearity in the context of autoregressive models with Markov-switching means and variances. These tests are robust to the identi!cation failures that plague conventional likelihood-based inference methods. The approach exploits the moments of normal mixtures implied by the regime-switching process and uses Monte Carlo test techniques to deal with the presence of an autoregressive component in the model speci!cation. The proposed tests have very respectable power in comparison with the optimal tests for Markov-switching parameters of Carrasco et al. (2014), and they are also quite attractive owing to their computational simplicity. The new tests are illustrated with an empirical application to an autoregressive model of USA output growth

Empirical Assessment of an Intertemporal Option Pricing Model with Latent variables

This paper assesses the empirical performance of an intertemporal option pricing model with latent variables which generalizes the Hull-White stochastic volatility formula. Using this generalized formula in an ad-hoc fashion to extract two implicit parameters and forecast next day S&P 500 option prices, we obtain similar pricing errors than with implied volatility alone as in the Hull-White case. When we specialize this model to an equilibrium recursive utility model, we show through simulations that option prices are more informative than stock prices about the structural parameters of the model. We also show that a simple method of moments with a panel of option prices provides good estimates of the parameters of the model. This lays the ground for an empirical assessment of this equilibrium model with S&P 500 option prices in terms of pricing errors.On évalue dans cet article la performance empirique d’un modèle dynamique d’évaluation d’options qui fournit une formule de prix fondée sur des processus latents de variables d’état. Cette formule est une généralisation de la formule dite de Hull et White (1987) qui évalue une option européenne écrite sur un actif à volatilité stochastique. On propose dans un premier temps de fonder sur cette formule une procédure empirique ad hoc permettant l’évaluation d’une option à partir du calcul de deux paramètres implicites extraits sur les prix d’options observés la veille. Appliquée à la prévision des prix d’options sur l’indice S&P 500, cette procédure offre un gain de précision significatif par rapport à la pratique usuelle de prévision des prix à travers une volatilité implicite conformément à ce que suggère la formule de Hull et White. Dans un second temps, on propose de particulariser le modèle dans un contexte d’équilibre intertemporel avec utilité récursive. On fournit alors des résultats d’expériences de Monte Carlo montrant que les statistiques de prix d’options produisent des estimateurs des paramètres structurels de l’équilibre beaucoup plus précis que les données de prix de l’actif sous-jacent. Ceci suggère en retour que les paramètres structurels devraient jouer un rôle important dans l’évaluation d’options. Cette affirmation est validée empiriquement sur les données d’options sur l’indice S&P 500 en montrant que la formule de Hull et White est dominée, en termes de prévision des prix d’options hors-échantillon par une formule dépendant explicitement de paramètres de préférence, a fortiori si ceux-ci prennent en compte de façon non contrainte à la fois l’aversion pour le risque et l’élasticité de substitution intertemporelle

Asymmetric Smiles, Leverage Effects and Structural Parameters

In this paper, we characterize the asymmetries of the smile through multiple leverage effects in a stochastic dynamic asset pricing framework. The dependence between price movements and future volatility is introduced through a set of latent state variables. These latent variables can capture not only the volatility risk and the interest rate risk which potentially affect option prices, but also any kind of correlation risk and jump risk. The standard financial leverage effect is produced by a cross-correlation effect between the state variables which enter into the stochastic volatility process of the stock price and the stock price process itself. However, we provide a more general framework where asymmetric implied volatility curves result from any source of instantaneous correlation between the state variables and either the return on the stock or the stochastic discount factor. In order to draw the shapes of the implied volatility curves generated by a model with latent variables, we specify an equilibrium-based stochastic discount factor with time non-separable preferences. When we calibrate this model to empirically reasonable values of the parameters, we are able to reproduce the various types of implied volatility curves inferred from option market data.Dans cet article, nous caractérisons les asymétries observées dans les courbes de volatilités implicites par la présence d'effets de levier multiples dans un modèle dynamique stochastique d'évaluation des actifs financiers. La dépendance entre les mouvements de prix et la volatilité future est introduite par l'intermédiaire d'un ensemble de variables d'état latentes. Ces variables d'état sont susceptibles de capter non seulement le risque de volatilité et le risque de taux d'intérêt qui peuvent influer sur les prix d'options, mais encore les risques de corrélation et de saut. L'effet de levier financier traditionnel est produit quant à lui par une corrélation instantanée entre les variables d'état qui entrent dans le processus de volatilité stochastique du prix de l'action et le processus du prix de l'action proprement dit. Nous disposons toutefois d'un cadre plus général dans lequel l'asymétrie des courbes de volatilités implicites résulte de toute corrélation instantanée entre les variables d'état et soit le rendement de l'action soit le facteur d'actualisation stochastique. Dans le but de tracer les formes des courbes de volatilités implicites générées par un modèle avec variables latentes, nous spécifions un facteur d'actualisation stochastique fondé sur un modèle d'équilibre avec préférences non séparables dans le temps. Lorsque nous calibrons ce modèle avec des valeurs raisonnables des paramètres, nous reproduisons les diverses formes de courbes de volatilités implicites qui sont produites à partir des données de prix d'options observées sur le marché

The New Keynesian Phillips Curve: An empirical assessment

The recent works of Gali and Gertler (1999) and Gali, Gertler and Lopez-Salido (2001) provide evidence supporting the New Keynesian Phillips curve (NKPC). This model posits the dynamics of inflation as being forward-looking and related to real marginal costs. In this paper, we examine the empirical relevance of their results for the United States. Our approach addresses several important econometric issues with the standard approaches typically used for estimation and inference in NKPC models. Using the continously-updated GMM estimator proposed by Hansen, Heaton and Yaron (1996) and the 3-step GMM estimator developed by Bonnal and Renault (2003), the empirical evidence of the NKPC is rather mixed. Specifically, results are sensitive to the instruments sets, normalisation, estimators, the sample period and revisions of dataGMM, Phillips Curve, Inflation dynamics