Investigating nonlinearities in real exchange rate adjustment: Threshold cointegration and the dynamics of exchange rates and relative prices

Motivated by growing evidence of nonlinear mean-reverting behavior in real exchange rates, this paper investigates the underlying dynamics in the context of a threshold vector error correction model (TVECM) of nominal exchange rate and relative prices. Unlike univariate models, our nonlinear multivariate framework takes into explicit account the joint behavior and individual dynamics of the nominal exchange rate and relative prices when these two key variables are threshold cointegrated. Our empirical application unravels their relative contribution to mean reversion and underscores the importance of capturing their interactions in investigating the nonlinear adjustment toward purchasing power parity.     

Bivariate FIGARCH and fractional cointegration

We consider the modelling of volatility on closely related markets. Univariate fractional volatility (FIGARCH) models are now standard, as are multivariate GARCH models. In this paper, we adopt a combination of the two methodologies. There is as yet little consensus on the methodology for testing for fractional cointegration. The contribution of this paper is to demonstrate the feasibility of estimating and testing cointegrated bivariate FIGARCH models. We apply these methods to volatility on the NYMEX and IPE crude oil markets. We find a common order of fractional integration for the two volatility processes and confirm that they are fractionally cointegrated. An estimated error correction FIGARCH model indicates that the preponderant adjustment is of the IPE towards NYMEX.     

Output Gap Estimation and Monetary Policy in China

Using the Bayesian multivariate Beveridge-Nelson decomposition method, this paper estimates China's output gap based on a multivariate dynamic model featuring distinct interactions among real output, inflation, money, and the exchange rate in China during the period 1980-2010. The authors compare the statistical nature and potential forecasting effects of the resulting multivariate gap measure on monetary policy with those of the output gap measures based on univariate models. The empirical results show that only the measure based on the multivariate system significantly predicts monetary policy, which indicates that the output gap estimated by the multivariate system contains more information than the traditional measures for macroeconomic policy adjustments do.     

Multivariate Models of Equity Returns for Investment Guarantees Valuation

Abstract

In this paper we investigate the valuation of investment guarantees in a multivariate (discrete-time) framework. We present how to build multivariate models in general, and we survey the most important multivariate GARCH models. A direct multivariate application of regime-switching models is also discussed, as is the estimation of these models using maximum likelihood and their comparison in a multivariate setting. The computation of the CTE provision is further presented. We have estimated the models with a multivariate dataset (Canada, United States, United Kingdom, and Japan), and we compared the quality of their fit using multiple criteria and tests. We observe that multivariate GARCH models provide a better overall fit than regime-switching models. However, regime-switching models appropriately represent the fat tails of the returns distribution, which is where most GARCH models fail. This leads to significant differences in the value of the CTE provisions, and, in general, provisions computed with regime-switching models are higher. Thus, the results from this multivariate analysis are in line with what was obtained in the literature of univariate models.     

Unbiasedness of the Forward Exchange Rates

This paper derives an error correction model under the assumption that the spot and the forward rates are cointegrated, the first difference of forward rates is stationary, and the first order autocorrelation in the forecast error is allowed. When tests of the unbiasedness hypothesis are conducted with an error correction model using generalized methods of moments [GMM], the unbiasedness hypothesis cannot be rejected. Furthermore, the multivariate GMM estimation supports the hypothesis of unbiasedness of the forward exchange rates and the absence of a risk premium in the foreign exchange markets.     

The farmers home administration and farm debt failure prediction

From its creation in 1935, the Farmers Home Administration (FmHA) has evaluated loan applications on the basis of projected repayment ability. Because of sharply increasing farm debt failures as well as criticisms on the part of the US General Accounting Office (GAO) of the agency's credit screening process, the FmHA in the late 1980s developed a credit scoring system with four univariate input factors (GAO, 1989, p. 38). In the end, the FmHA was not satisfied with its new credit screening model and retained Price Waterhouse (PW) to design a more discriminating one. The PW model, too, however, uses a combination of univariate scores (PW, 1991, p. ES-1). Our study, which incorporates actual Farm and Home Plan (FHP) data, develops and compares three multivariate models including an ordinary least squares (OLS) model, a logistic regression (logit) model, and a genetic-algorithm-derived neural network model (NNM). Each multivariate model outperforms the FmHA and PW models in predicting farm debt failure. The NNM outperforms both the OLS and logit models based on error rates. In addition, the NNM proves superior to the other multivariate models from a public policy point of view in that it spreads the cutoff point between errors (making the cutoff less arbitrary) and allows improvement in the tradeoff between Type I and Type II errors. The study demonstrates that the accounting data contained in the FHP are useful for predicting farm debt failure.     

Mean–variance and mean–semivariance portfolio selection: a multivariate nonparametric approach

While univariate nonparametric estimation methods have been developed for estimating returns in mean-downside risk portfolio optimization, the problem of handling possible cross-correlations in a vector of asset returns has not been addressed in portfolio selection. We present a novel multivariate nonparametric portfolio optimization procedure using kernel-based estimators of the conditional mean and the conditional median. The method accounts for the covariance structure information from the full set of returns. We also provide two computational algorithms to implement the estimators. Via the analysis of 24 French stock market returns, we evaluate the in-sample and out-of-sample performance of both portfolio selection algorithms against optimal portfolios selected by classical and univariate nonparametric methods for three highly different time periods and different levels of expected return. By allowing for cross-correlations among returns, our results suggest that the proposed multivariate nonparametric method is a useful extension of standard univariate nonparametric portfolio selection approaches.     

Corrections for Trading Frictions in Multivariate Returns

When observed stock returns are obtained from trades subject to friction, it is known that an individual stock's beta and covariance are measured with error. Univariate models of additive error adjustment are available and are often applied simultaneously to more than one stock. Unfortunately, these multivariate adjustments produce non-positive definite covariance and correlation matrices, unless the return sample sizes are very large. To prevent this, restrictions on the adjustment matrix are developed and a correction is proposed, which dominates the uncorrected estimator. The estimators are illustrated with asset opportunity set estimates where daily returns have trading frictions.     

Common Stochastic Trends in a System of Exchange Rates

Univariate tests reveal strong evidence for the presence of a unit root in the univariate time-series representation for seven daily spot and forward exchange rate series. Furthermore, all seven spot and forward rates appear to be cointegrated; that is, the forward premiums are stationary, and one common unit root, or stochastic trend, is detectable in the multivariate time-series models for the seven spot and forward rates, respectively. This is consistent with the hypothesis that the seven exchange rates possess one long-run relationship and that the disequilibrium error around that relationship partly accounts for subsequent movements in the exchange rates.     

Multivariate asset return prediction with mixture models

The use of mixture distributions for modeling asset returns has a long history in finance. New methods of demonstrating support for the presence of mixtures in the multivariate case are provided. The use of a two-component multivariate normal mixture distribution, coupled with shrinkage via a quasi-Bayesian prior, is motivated, and shown to be numerically simple and reliable to estimate, unlike the majority of multivariate GARCH models in existence. Equally important, it provides a clear improvement over use of GARCH models feasible for use with a large number of assets, such as constant conditional correlation, dynamic conditional correlation, and their extensions, with respect to out-of-sample density forecasting. A generalization to a mixture of multivariate Laplace distributions is motivated via univariate and multivariate analysis of the data, and an expectation–maximization algorithm is developed for its estimation in conjunction with a quasi-Bayesian prior. It is shown to deliver significantly better forecasts than the mixed normal, with fast and numerically reliable estimation. Crucially, the distribution theory required for portfolio theory and risk assessment is developed.     

Local Office Rent Dynamics

This study applies rent adjustment models for ten major European office markets. We capture long-run equilibrium relationships of demand and supply variables and their short-term corrections in a two equation error correction model. We test whether the local nature of office markets makes a model based on national economics inaccurate if local and national markets do not move in tandem. For this we employ a unique dataset, which includes both disaggregated and national variables to model changes in real prime rents for a group of premier and second tier office market cities across Europe for the period 1990–2006. We explicitly compare results that are derived from models that include different levels of geographic aggregation. Results of the two stage error correction model indicate that international office rents adjust to short-run changes in office related economic activity, lagged rent changes, and to the deviation of rents from their long-run values. At the same time our results offer no proof that error correction mechanism models for office rents improve significantly by specifying economic growth figures beyond the national aggregated level for the cities included in our analysis.     

The αVG model for multivariate asset pricing: calibration and extension

Luciano and Semeraro proposed a class of multivariate asset pricing models where the asset log-returns are modeled by a multivariate Brownian motion time-changed by a multivariate subordinator which consists of the weighted sum of a common and an idiosyncratic subordinator. In the original setting, Luciano and Semeraro imposed some constraints on the subordinator parameters such that the multivariate subordinator is of the same subordinator sub-class as its components, leading to asset log-returns of a particular Lévy type. This restriction leads to marginal characteristic functions which are independent on the common subordinator setting. In this paper, we propose to extend the original model by relaxing the constraints on the subordinator parameters, leading to marginal characteristic functions which become a function of the whole parameter set. Under this generalized version, the volatility of the log-returns depends on both the common and idiosyncratic subordinator settings, and not only on the idiosyncratic one, which makes the generalized model more in line with the empirical evidence of the presence of both an idiosyncratic and a common component in the business clock. For the numerical study, we compare the calibration fit of both univariate option surfaces and market implied correlations for a period extending from the 2nd of June 2008 until the 30th of October 2009 under the two model settings and assess the calibration risk arising from different calibration procedures by pricing traditional multivariate exotic options. In particular we show that the decoupling calibration procedure fails to accurately replicate the market dependence structure under the original model for highly correlated asset returns and we propose an alternative methodology which rests on a joint calibration of the univariate and the dependence structure and which leads to an accurate fit of the market reality under both the generalized and original models.     

Correlation Risk and Optimal Portfolio Choice

We develop a new framework for multivariate intertemporal portfolio choice that allows us to derive optimal portfolio implications for economies in which the degree of correlation across industries, countries, or asset classes is stochastic. Optimal portfolios include distinct hedging components against both stochastic volatility and correlation risk. We find that the hedging demand is typically larger than in univariate models, and it includes an economically significant covariance hedging component, which tends to increase with the persistence of variance–covariance shocks, the strength of leverage effects, the dimension of the investment opportunity set, and the presence of portfolio constraints.     

Prediction Error of the Multivariate Chain Ladder Reserving Method

Abstract

In this paper we consider the claims reserving problem in a multivariate context: that is, we study the multivariate chain-ladder (CL) method for a portfolio of N correlated runoff triangles based on multivariate age-to-age factors. This method allows for a simultaneous study of individual runoff subportfolios and facilitates the derivation of an estimator for the mean square error of prediction (MSEP) for the CL predictor of the ultimate claim of the total portfolio. However, unlike the already existing approaches we replace the univariate CL predictors with multivariate ones. These multivariate CL predictors reflect the correlation structure between the subportfolios and are optimal in terms of a classical optimality criterion, which leads to an improvement of the estimator for the MSEP. Moreover, all formulas are easy to implement on a spreadsheet because they are in matrix notation. We illustrate the results by means of an example.     

Marginal consistent dependence modelling using weak subordination for Brownian motions

We present an approach for modelling dependencies in exponential Lévy market models with arbitrary margins originated from time changed Brownian motions. Using weak subordination of Buchmann et al. [Bernoulli, 2017], we face a new layer of dependencies, superior to traditional approaches based on pathwise subordination, since weakly subordinated processes are not required to have independent components considering multivariate stochastic time changes. We apply a subordinator being able to incorporate any joint or idiosyncratic information arrivals. We emphasize multivariate variance gamma and normal inverse Gaussian processes and state explicit formulae for the Lévy characteristics. Using maximum likelihood, we estimate multivariate variance gamma models on various market data and show that these models are highly preferable to traditional approaches. Consistent values of basket-options under given marginal pricing models are achieved using the Esscher transform, generating a non-flat implied correlation surface.     

35 years of studies on business failure: an overview of the classic statistical methodologies and their related problems

Over the last 35 years, business failure prediction has become a major research domain within corporate finance. Numerous corporate failure prediction models have been developed, based on various modelling techniques. The most popular are the classic cross-sectional statistical methods, which have resulted in various ‘single-period’ or static models, especially multivariate discriminant models and logit models. To date, there has been no clear overview and discussion of the application of classic statistical methods to business failure prediction. Therefore, this paper extensively elaborates on the application of (1) univariate analysis, (2) risk index models, (3) multivariate discriminant analysis, and (4) conditional probability models in corporate failure prediction. In addition, because there is no clear and comprehensive analysis in the existing literature of the diverse problems related to the application of these methods to the topic of corporate failure prediction, this paper brings together all problem issues and enlarges upon each of them. It discusses all problems related to: (1) the classical paradigm (i.e. the arbitrary definition of failure, non-stationarity and data instability, sampling selectivity, and the choice of the optimisation criteria); (2) the neglect of the time dimension of failure; and (3) the application focus in failure prediction modelling. Further, the paper elaborates on a number of other problems related to the use of a linear classification rule, the use of annual account information, and neglect of the multidimensional nature of failure. This paper contributes towards a thorough understanding of the features of the classic statistical business failure prediction models and their related problems.     

Simple Forecasts and Paradigm Shifts

We study the asset pricing implications of learning in an environment in which the true model of the world is a multivariate one, but agents update only over the class of simple univariate models. Thus, if a particular simple model does a poor job of forecasting over a period of time, it is discarded in favor of an alternative simple model. The theory yields a number of distinctive predictions for stock returns, generating forecastable variation in the magnitude of the value‐glamour return differential, in volatility, and in the skewness of returns. We validate several of these predictions empirically.     

Structural Error Correction Models: A System Method for Linear Rational Expectations Models and an Application to an Exchange Rate Model

This paper develops a system instrumental variable method to estimate the speed of adjustment coefficient in the long-run equilibrium of structural error correction models for a class of linear rational expectations models. This method is applied to an exchange rate model with sticky prices, in which the speed of adjustment coefficient governs the half-life of the real exchange rate. Compared to single equation methods, the system method gives smaller half-life estimates with sharper standard errors.     

The effect of EDGAR on the market reaction to 10-K filings

This paper examines the impact of making accounting information available on the Internet simultaneously and almost costlessly to all market participants. More specifically, we examine if filing form 10-K on EDGAR has any effect on the information dissemination process when compared to the traditional method of filing. We examine a random sample of firms that file on EDGAR for the first time and compare the market response to their 10-K filing to that of the previous year's filing which was not on EDGAR. Consistent with the preexisting literature, we do not find a market reaction to the pre-EDGAR filing. In contrast, we find both a price and volume reaction to 10-K's filed on EDGAR. We perform a variety of univariate and multivariate tests to ensure that our results are not driven by other factors, i.e., firm characteristics and timing of 10-K filings. Overall, we find evidence that the market reacts more significantly to 10-K's filed on EDGAR. In our multivariate tests we also examine whether the EDGAR effect is more important for certain types of firms. Consistent with our expectations, we find the EDGAR effect is smaller for faster growing firms for which we believe there are more non-EDGAR sources of information. Finally, we document that, on average, 10-K's filed on EDGAR are filed earlier than 10-K's filed under traditional methods.     

Nonlinear Cointegration Relationships Between Non-Life Insurance Premiums and Financial Markets

The aim of this article is to study the adjustment dynamics of the non-life insurance premium (NLIP) and test its dependence to the financial markets in five countries (Canada, France, Japan, the United Kingdom, and the United States). First, we justify the linkage between the insurance and the financial markets by the underwriting cycle theory and financial models of insurance pricing. Second, we examine the relationship between the NLIP, the interest rate, and the stock price using the recent developments of nonlinear econometrics. We use threshold cointegration models: the switching transition error correction models (STECM). We show that STECM perform better than a linear error correction model (LECM) to reproduce the NLIP dynamics. Our empirical results show that the adjustment of the NLIP in France, Japan, and the United States is rather discontinuous, asymmetrical, and nonlinear. Moreover, we suggest a strong evidence of significant linkages between insurance and financial markets, show two regimes for the NLIP, and find that the NLIP adjustment toward equilibrium is time varying with a convergence speed that varies according to the insurance disequilibrium size.