On the impact of fundamentals, liquidity and coordination on market stability

We develop a coordination game to model interactions betweenfundamentals and liquidity during unstable periods in financial markets.We then propose a flexible econometric framework for estimationof the model and analysis of its quantitative implications. The specificempirical application is carry trades in the yen dollar market, includingthe turmoil of 1998. We find a generally very deep market, withlow information disparities amongst agents. We observe occasionallyepisodes of market fragility, or turmoil with up by the escalator, downby the elevator patterns in prices. The key role of strategic behaviorin the econometric model is also confirmed.

Contribution biplots

In order to interpret the biplot it is necessary to know which points usually variables are the ones that are important contributors to the solution, and this information is available separately as part of the biplot s numerical results. We propose a new scaling of the display, called the contribution biplot, which incorporates this diagnostic directly into the graphical display, showing visually the important contributors and thus facilitating the biplot interpretation and often simplifying the graphical representation considerably. The contribution biplot can be applied to a wide variety of analyses such as correspondence analysis, principal component analysis, log-ratio analysis and the graphical results of a discriminant analysis/MANOVA, in fact to any method based on the singular-value decomposition. In the contribution biplot one set of points, usually the rows of the data matrix, optimally represent the spatial positions of the cases or sample units, according to some distance measure that usually incorporates some form of standardization unless all data are comparable in scale. The other set of points, usually the columns, is represented by vectors that are related to their contributions to the low-dimensional solution. A fringe benefit is that usually only one common scale for row and column points is needed on the principal axes, thus avoiding the problem of enlarging or contracting the scale of one set of points to make the biplot legible. Furthermore, this version of the biplot also solves the problem in correspondence analysis of low-frequency categories that are located on the periphery of the map, giving the false impression that they are important, when they are in fact contributing minimally to the solution.

Some hypothesis tests for the covariance matrix when the dimension is large compared to the sample size

This paper analyzes whether standard covariance matrix tests work whendimensionality is large, and in particular larger than sample size. Inthe latter case, the singularity of the sample covariance matrix makeslikelihood ratio tests degenerate, but other tests based on quadraticforms of sample covariance matrix eigenvalues remain well-defined. Westudy the consistency property and limiting distribution of these testsas dimensionality and sample size go to infinity together, with theirratio converging to a finite non-zero limit. We find that the existingtest for sphericity is robust against high dimensionality, but not thetest for equality of the covariance matrix to a given matrix. For thelatter test, we develop a new correction to the existing test statisticthat makes it robust against high dimensionality.

Dynamic perceptual mapping

Perceptual maps have been used for decades by market researchers to illuminatethem about the similarity between brands in terms of a set of attributes, to position consumersrelative to brands in terms of their preferences, or to study how demographic and psychometricvariables relate to consumer choice. Invariably these maps are two-dimensional and static. Aswe enter the era of electronic publishing, the possibilities for dynamic graphics are opening up.We demonstrate the usefulness of introducing motion into perceptual maps through fourexamples. The first example shows how a perceptual map can be viewed in three dimensions,and the second one moves between two analyses of the data that were collected according todifferent protocols. In a third example we move from the best view of the data at the individuallevel to one which focuses on between-group differences in aggregated data. A final exampleconsiders the case when several demographic variables or market segments are available foreach respondent, showing an animation with increasingly detailed demographic comparisons.These examples of dynamic maps use several data sets from marketing and social scienceresearch.

Performance assessment and league tables. Comparing like with like

We formulate performance assessment as a problem of causal analysis and outline an approach based on the missing data principle for its solution. It is particularly relevant in the context of so-called league tables for educational, health-care and other public-service institutions. The proposed solution avoids comparisons of institutions that have substantially different clientele (intake).

Constant coefficient tests for random coefficient regression

Random coefficient regression models have been applied in differentfields and they constitute a unifying setup for many statisticalproblems. The nonparametric study of this model started with Beranand Hall (1992) and it has become a fruitful framework. In thispaper we propose and study statistics for testing a basic hypothesisconcerning this model: the constancy of coefficients. The asymptoticbehavior of the statistics is investigated and bootstrapapproximations are used in order to determine the critical values ofthe test statistics. A simulation study illustrates the performanceof the proposals.

Approximation of quadratic irrationals and their pierce expansions

In this article two aims are pursued: on the one hand, to present arapidly converging algorithm for the approximation of square roots; on theother hand and based on the previous algorithm, to find the Pierce expansionsof a certain class of quadratic irrationals as an alternative way to themethod presented in 1984 by J.O. Shallit; we extend the method to findalso the Pierce expansions of quadratic irrationals of the form $2 (p-1)(p - \sqrt{p^2 - 1})$ which are not covered in Shallit's work.

Why ethnic fractionalization? Polarization, ethnic conflict and growth

This paper ia an attempt to clarify the relationship between fractionalization,polarization and conflict. The literature on the measurement of ethnic diversityhas taken as given that the proper measure for heterogeneity can be calculatedby using the fractionalization index. This index is widely used in industrialeconomics and, for empirical purposes, the ethnolinguistic fragmentation isready available for regression exercises. Nevertheless the adequacy of asynthetic index of hetergeneity depends on the intrinsic characteristicsof the heterogeneous dimension to be measured. In the case of ethnicdiversity there is a very strong conflictive dimension. For this reasonwe argue that the measure of heterogeneity should be one of the class ofpolarization measures. In fact the intuition of the relationship betweenconflict and fractionalization do not hold for more than two groups. Incontrast with the usual problem of polarization indices, which are ofdifficult empirical implementation without making some arbitrary choiceof parameters, we show that the RQ index, proposed by Reynal-Querol (2002),is the only discrete polarization measure that satisfies the basic propertiesof polarization. Additionally we present a derivation of the RQ index froma simple rent seeking model. In the empirical section we show that whileethnic polarization has a positive effect on civil wars and, indirectly ongrowth, this effect is not present when we use ethnic fractionalization.

The effects of uncertainty avoidance on brand performance: Marketing creativity, product innovation and the brand duration

This paper investigates the link between brand performance and cultural primes in high-risk,innovation-based sectors. In theory section, we propose that the level of cultural uncertaintyavoidance embedded in a firm determine its marketing creativity by increasing the complexityand the broadness of a brand. It determines also the rate of firm product innovations.Marketing creativity and product innovation influence finally the firm marketingperformance. Empirically, we study trademarked promotion in the Software Security Industry(SSI). Our sample consists of 87 firms that are active in SSI from 11 countries in the period1993-2000. We use the data coming from SSI-related trademarks registered by these firms,ending up with 2,911 SSI-related trademarks and a panel of 18,213 observations. We estimatea two stage model in which first we predict the complexity and the broadness of a trademarkas a measure of marketing creativity and the rate of product innovations. Among severalcontrol variables, our variable of theoretical interest is the Hofstede s uncertainty avoidancecultural index. Then, we estimate the trademark duration with a hazard model using thepredicted complexity and broadness as well as the rate of product innovations, along with thesame control variables. Our evidence confirms that the cultural avoidance affects the durationof the trademarks through the firm marketing creativity and product innovation.

Asymptotic behaviour of the density in a parabolic SPDE

Consider the density of the solution $X(t,x)$ of a stochastic heat equation with small noise at a fixed $t\in [0,T]$, $x \in [0,1]$.In the paper we study the asymptotics of this density as the noise is vanishing. A kind of Taylor expansion in powers of the noiseparameter is obtained. The coefficients and the residue of the expansion are explicitly calculated.In order to obtain this result some type of exponential estimates of tail probabilities of the difference between the approximatingprocess and the limit one is proved. Also a suitable local integration by parts formula is developped.

On a problem of Alfréd Rényi

Alfréd Rényi, in a paper of 1962, A new approach to the theory ofEngel's series, proposed a problem related to the growth of theelements of an Engel's series. In this paper, we reformulate andsolve Rényi's problem for both, Engel's series and Pierceexpansions.

A general decomposition formula for derivative prices in stochastic volatility models

We see that the price of an european call option in a stochastic volatilityframework can be decomposed in the sum of four terms, which identifythe main features of the market that affect to option prices: the expectedfuture volatility, the correlation between the volatility and the noisedriving the stock prices, the market price of volatility risk and thedifference of the expected future volatility at different times. We alsostudy some applications of this decomposition.

Existence of sparsely supported correlated equilibria

We show that every finite N-player normal form game possesses a correlated equilibrium with a precise lower bound on the number of outcomes to which it assigns zero probability. In particular, the largest games with a unique fully supported correlated equilibrium are two-player games; moreover, the lower bound grows exponentially in the number of players N.

A total order in [0,1] defined through a 'next' operator

A `next' operator, s, is built on the set R1=(0,1]-{ 1-1/e} defining a partial order that, with the help of the axiom of choice, can be extended to a total order in R1. Besides, the orbits {sn(a)}nare all dense in R1 and are constituted by elements of the samearithmetical character: if a is an algebraic irrational of degreek all the elements in a's orbit are algebraic of degree k; if a istranscendental, all are transcendental. Moreover, the asymptoticdistribution function of the sequence formed by the elements in anyof the half-orbits is a continuous, strictly increasing, singularfunction very similar to the well-known Minkowski's ?(×) function.

A generalization of Hull and White formula and applications to option pricing approximation

By means of Malliavin Calculus we see that the classical Hull and White formulafor option pricing can be extended to the case where the noise driving thevolatility process is correlated with the noise driving the stock prices. Thisextension will allow us to construct option pricing approximation formulas.Numerical examples are presented.