This paper provides closed-form likelihood approximations for multivariate jump-diffusion processes widely used in finance. For a fixed order of approximation, the maximum-likelihood estimator (MLE) computed from this approximate likelihood achieves the asymptotic efficiency of the true yet uncomputable MLE as the sampling interval shrinks. This method is used to uncover the realignment probabi...

In this paper, we describe a general method for constructing the posterior distribution of an option price. Our framework takes as inputs the prior distributions of the parameters of the stochastic process followed by the underlying, as well as the likelihood function implied by the observed price history for the underlying. Our work extends that of Karolyi (1993) and Darsinos and Satchell (200...

The Basel II Accord requires banks to establish rigorous statistical procedures for the estimation and validation of default and ratings transition probabilities. This raises great technical challenges when sufficient default data are not available, as is the case for low default portfolios. We develop a new model that describes the typical internal credit rating process used by banks. The mode...

Reduced rank regression analysis provides maximum likelihood estimators of a matrix of regression coefficients of specified rank and of corresponding linear restrictions on such matrices. These estimators depend on the eigenvectors of an ‘‘effect’’ matrix in the metric of an error covariance matrix. In this paper it is shown that the maximum likelihood estimator of the restrictions can be appro...

In this paper we consider the estimation of Markov models where the transition density is unknown. The approach we propose is the empirical characteristic function (ECF) estimation procedure with an approximate optimal weight function. The approximate optimal weight function is obtained through an Edgeworth/Gram-Charlier expansion of the logarithmic transition density of the Markov process. Bas...

Missing data is one of the most common challenges facing empirical researchers. This paper presents a general GMM framework for dealing with missing data on explanatory variables or instrumental variables. For a linear-regression model with missing covariate data, an efficient GMM estimator under minimal assumptions on missingness is proposed. The estimator, which also allows for a specificatio...

This paper introduces a novel approach to investigate the dynamics of state distributions, which accommodate both cross-sectional distributions of repeated panels and intra-period distributions of a time series observed at high frequency. In our approach, densities of the state distributions are regarded as functional elements in a Hilbert space, and are assumed to follow a functional autoregre...

The generalized method of moments estimator may be substantially biased in finite samples, especially so when there are large numbers of unconditional moment conditions. This paper develops a class of first order equivalent semi-parametric efficient estimators and tests for conditional moment restrictions models based on a local or kernel-weighted version of the Cressie-Read power divergence fa...

A Note on Parametric and Nonparametric Regression in the Presence of Endogenous Control Variables This note argues that nonparametric regression not only relaxes functional form assumptions vis-a-vis parametric regression, but that it also permits endogenous control variables. To control for selection bias or to make an exclusion restriction in instrumental variables regression valid, additiona...

Decomposing the Composition Effect This paper proposes a decomposition of the composition effect, i.e. the part of the observed between-group difference in the distribution of some economic outcome that can be explained by differences in the distribution of covariates. Our decomposition contains three types of components: (i) the “direct contributions” of each covariate due to between-group dif...