Jinggang Huang

A Utility-Based Approach to Some Information Measures

We review a decision theoretic, i.e., utility-based, motivation for entropy and Kullback-Leibler relative entropy, the natural generalizations that follow, and various properties of thesegeneralized quantities. We then consider these generalized quantities in an easily interpreted spe-cial case. We show that the resulting quantities, share many of the properties of entropy andrelative entropy, such as the data processing inequality and the second law of thermodynamics.We formulate an important statistical learning problem – probability estimation – in terms of ageneralized relative entropy. The solution of this problem reflects general risk preferences via theutility function; moreover, the solution is optimal in a sense of robust absolute performance.

Modeling Multi-Period Corporate Default Probability When Hazard Ratios Decay

A number of researchers have used the Cox Proportional Hazard Model to estimate multi-period corporate default probabilities. By construction, models estimated in this manner have hazard ratios that are constant over time. We present evidence, drawn from historical data, indicating that empirical hazard ratios, in fact, exhibit pronounced decay over time, contrary to the assumptions of the Cox Proportional Hazard Model. We provide a possible explanation for this phenomenon, in terms of the evolution, posited by other authors, of the explanatory variables. We propose a hazard rate model with time varying coefficients, which incorporates the decaying hazard ratio property. Our model outperforms the standard Cox regression on an out-of-sample/time experiment.

Joint and Conditional Transformed T−Mixture Models with Applications to Financial and Economic Data

We estimate joint and conditional probability densities via a new hybrid approach that incorporates ideas from copula modeling and makes use of known analytic results involving the conditional distributions of multivariate random variables that have joint (usual) multivariate t or t−mixture distributions. Our method amounts to the application of t or t−mixture modeling in a special “working space” that is used in copula modeling. We also provide new simulation algorithms and describe numerical experiments, performed on accounting data, stock return data, and housing price data, in which we compare the performance of our method with a number of benchmark approaches.

Finding Stress Scenarios that Get the Job Done, with a Credit Risk Application

We introduce new methods to generate finite representative collections of plausible yet severe scenarios. We apply these methods to generate single- obligor credit risk scenarios and demonstrate, via numerical experiments, that with respect to certain performance measures, our method is better able to discover (ex ante) scenarios “close” to those that occurred (as determined ex post), than previously described methods. Moreover, our methods discover these scenarios at substantially lower computational cost.

Most Entropic Copulas: General Form, and Calibration to High-Dimensional Data in an Important Special Case

We present some general results pertaining to Most Entropic Copulas (MECs), and describe the connection between MECs and a special type of Markov random field model. We also describe a fundamental, new, MEC, the Spearman Copula, which is, in some sense, the simplest nontrivial MEC, and present an efficient numerical method that can be applied to calibrate high-dimensional homogeneous Spearman Copulas. We benchmark Spearman Copula performance against that of other common copulas, on data from the joint distance-to-default movement of companies in the Dow Jones CDX IG Index, a standard portfolio of 125 investment grade entities in North America.

Missing value imputation via copula and transformation methods, with applications to financial and economic data

We present new, tractable methods to impute missing values based on conditional probability density functions that we estimate via copula and mixture models. Our methods exploit known analytical results concerning conditional distributions for the Arellano-Valle and Bolfarines generalised t-distribution and fast, accurate quadrature methods. We also benchmark our approach on three financial/economic datasets (two of which are publicly available) and show that our methods outperform benchmark approaches on these data.

ESTIMATING UNIVARIATE DISTRIBUTIONS VIA RELATIVE ENTROPY MINIMIZATION: CASE STUDIES ON FINANCIAL AND ECONOMIC DATA

We use minimum relative entropy (MRE) methods to estimate univariate probability density functions for a varied set of financial and economic variables, including S&P500 index returns, individual stock returns, power price returns and a number of housing-related economic variables. Some variables have fat tail distributions, others have finite support. Some variables have point masses in their distributions and others have multimodal distributions. We indicate specifically how the MRE approach can be tailored to the stylized facts of the variables that we consider and benchmark the MRE approach against alternative approaches. We find, for a number of variables, that the MRE approach outperforms the benchmark methods.

How Much is a Model Upgrade Worth

In order to shed light on cost/benefit tradeoffs faced by financial model builders and purchasers, we construct a monetary measure of the differential performance between probabilistic models. To this end, we adopt the point of view of an investor who maximizes his expected utility under the model he believes. We explore general properties of the monetary value of a model upgrade and investigate a variety of important special cases. We develop explicit formulas that can be applied in realistic settings by practitioners, for example, to default probability models, and provide a case study in this context.

Imputation Via Copula and Transformation Methods, With Applications to Financial and Economic Data

We present new, tractable methods to impute missing values based on conditional probability density functions that we estimate via copula and mixture models. Our methods exploit known analytical results concerning conditional distributions for the Arellano-Valle and Bolfarine’s generalized t-distribution and fast, accurate quadrature methods. We also benchmark our approach on three financial/economic data sets (two of which are publicly available) and show that our methods outperform benchmark approaches on these data.

A Partially Isotropic Reduced Pca Model for Large Equity Portfolios

We estimate joint stock return probability distributions for large portfolios of stocks via a method that can accommodate fat-tailed, dependent, covariates with an ill-conditioned covariance matrix. Our method strikes a balance between fidelity to the training data and regularization, with the goal of producing a model that generalizes well out-of-sample. We benchmark our approach against other methods.