Sources of time varying return comovements during different economic regimes: evidence from the emerging Indian equity market

We study the economic and non-economic sources of stock return comovements of the emerging Indian equity market and the developed equity markets of the US, UK, Germany, France, Canada and Japan. Our findings show that the probability of extreme comovements in the economic contraction regime is relatively higher than in the economic expansion regime. We show that international interest rates, inflation uncertainty and dividend yields are the main drivers of the asymmetric return comovements. Findings reported in the paper imply that the impact of interest rates and inflation on return comovements could be used for anticipating financial contagion and/or spillover effects. This is particularly critical since during extreme market conditions, the tail return comovements can potentially reveal critical information for active portfolio management

On Graphical Models via Univariate Exponential Family Distributions

Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly for non-Gaussian and non-categorical data. In this paper, we consider a general sub-class of graphical models where the node-wise conditional distributions arise from exponential families. This allows us to derive multivariate graphical model distributions from univariate exponential family distributions, such as the Poisson, negative binomial, and exponential distributions. Our key contributions include a class of M-estimators to fit these graphical model distributions; and rigorous statistical analysis showing that these M-estimators recover the true graphical model structure exactly, with high probability. We provide examples of genomic and proteomic networks learned via instances of our class of graphical models derived from Poisson and exponential distributions.Comment: Journal of Machine Learning Researc

Bootstrapping vs. Asymptotic Theory in Property and Casualty Loss Reserving

One of the key functions of a property and casualty (P&C) insurance company is loss reserving, which calculates how much money the company should retain in order to pay out future claims. Most P&C insurance companies use non-stochastic (non-random) methods to estimate these future liabilities. However, future loss data can also be projected using generalized linear models (GLMs) and stochastic simulation. Two simulation methods that will be the focus of this project are: bootstrapping methodology, which resamples the original loss data (creating pseudo-data in the process) and fits the GLM parameters based on the new data to estimate the sampling distribution of the reserve estimates; and asymptotic theory, which resamples only the GLM parameters (fitted from an original set of data) from a multivariate normal distribution to estimate the sampling distribution of the reserve estimates. Using Excel, R, and SAS software, the copulas of the GLM parameter estimates from the stochastic methods will be compared to the copula from a multivariate normal distribution. Ultimately, the Value at Risk (VaR) and Tail Value at Risk (TVaR) results from each method’s sampling distribution will be compared to each other, with the goal of showing that the two methods produce significantly different reserve estimates and risk capital estimates at the low end of the reserve distribution. This would answer the question as to whether the asymptotic theory procedure sufficiently approximates real-world scenarios

Copula Theory and Regression Analysis

Researchers are often interested to study in the relationships between one variable and several other variables. Regression analysis is the statistical method for investigating such relationship and it is one of the most commonly used statistical Methods in many scientific fields such as financial data analysis, medicine, biology, agriculture, economics, engineering, sociology, geology, etc. But basic form of the regression analysis, ordinary least squares is not suitable for actuarial applications because the relationships are often nonlinear and the probability distribution of the response variable may be non-Gaussian distribution. One of the method that has been successful in overcoming these challenges is the generalized linear model (GLM), which requires that the response variable have a distribution from the exponential family. In this research work, we study copula regression as an alternative method to OLS and GLM. The major advantage of a copula regression is that there are no restrictions on the probability distributions that can be used. First part of this study, we will briefly discuss about copula regression by using several variety of marginal copula functions and copula regression is the most appropriate method in non Gaussian variable(violated normality assumption) regression model fitting. Also we validated our results by using real world example data and random generated (50000 observations) data. Second part of this study, we discussed about multiple regression model based on copula theory, and also we derived multiple regression line equation for Multivariate Non-Exchangeable Generalized Farlie-Gumbel-Morgenstern (FGM) copula function