Local volatility changes in the black-scholes model

In this paper we address a problem arising in risk management; namely the study of price variations of different contingent claims in the Black-Scholes model due to anticipating future events. The method we propose to use is an extension of the classical Vega index, i.e. the price derivative with respect to the constant volatility, in thesense that we perturb the volatility in different directions. Thisdirectional derivative, which we denote the local Vega index, will serve as the main object in the paper and one of the purposes is to relate it to the classical Vega index. We show that for all contingent claims studied in this paper the local Vega index can be expressed as a weighted average of the perturbation in volatility. In the particular case where the interest rate and the volatility are constant and the perturbation is deterministic, the local Vega index is an average of this perturbation multiplied by the classical Vega index. We also study the well-known goal problem of maximizing the probability of a perfect hedge and show that the speed of convergence is in fact dependent of the local Vega index.

World population growth and fertility patterns, 1960-2000. A simple model explaining the evolution of world's fertility during the second half of the 20th Century

In this paper we attempt to describe the general reasons behind the world populationexplosion in the 20th century. The size of the population at the end of the century inquestion, deemed excessive by some, was a consequence of a dramatic improvementin life expectancies, attributable, in turn, to scientific innovation, the circulation ofinformation and economic growth. Nevertheless, fertility is a variable that plays acrucial role in differences in demographic growth. We identify infant mortality, femaleeducation levels and racial identity as important exogenous variables affecting fertility.It is estimated that in poor countries one additional year of primary schooling forwomen leads to 0.614 child less per couple on average (worldwide). While it may bepossible to identify a global tendency towards convergence in demographic trends,particular attention should be paid to the case of Africa, not only due to its differentdemographic patterns, but also because much of the continent's population has yet toexperience improvement in quality of life generally enjoyed across the rest of theplanet.

ClubMed? Cyclical fluctuations in the Mediterranean basin

We investigate macroeconomic fluctuations in the Mediterranean basin, their similarities and convergence. A model with four indicators, roughly covering theWest, the East and the Middle East and the North Africa portions of theMediterranean, characterizes well the historical experience since the early 1980.Idiosyncratic causes still dominate domestic cyclical fluctuations in many countries. Convergence and divergence coexist are local and transitory. The cyclicaloutlook for the next few years is rosier for the East than for the West.

Capital formation in machinery in Latin America, 1890-1930

Investment in machinery is a key aspect in the analysis of long-term economic growth during the era of the spread of industrialisation. But, historiography has only revealed what the pace of capital accumulation was in a few Latin American economies. This article offers continuous (annual) and consistent series on the magnitude of this investment in all of the Latin American countries for the period at the height of the first globalisation, 1890-1930. The paper gives special attention to comparative analysis, showing the differences that exist at the heart of the Latin American community, in the levels of capital formation in machinery as well as in the national development of this over time. The differences in the levels appear very indicative of the unequal degree of development reached by these economies. This article puts to test the hypothesis of intraregional divergence, obtaining the tentative result that there was divergence until 1913, but that there was convergence from 1914-1930.

Rational reasoning or adaptive behavior? Evidence from two-person beauty contest games

Many experiments have shown that human subjects do not necessarily behave in line with game theoretic assumptions and solution concepts. The reasons for this non-conformity are multiple. In this paper we study the argument whether a deviation from game theory is because subjects are rational, but doubt that others are rational as well, compared to the argument that subjects, in general, are boundedly rational themselves. To distinguish these two hypotheses, we study behavior in repeated 2-person and many-person Beauty-Contest-Games which are strategically different from one another. We analyze four different treatments and observe that convergence toward equilibrium is driven by learning through the information about the other player s choice and adaptation rather than self-initiated rational reasoning.

Credible redistributive policies and migration across US States

Does worker mobility undermine governments ability to redistribute income? Thispaper analyzes the experience of US states in the recent decades. We build a tractablemodel where both migration decisions and redistribution policies are endogenous. Wecalibrate the model to match skill premium and worker productivity at the state level,as well as the size and skill composition of migration flows. The calibrated modelis able to reproduce the large changes in skill composition as well as key qualitativerelationships of labor flows and redistribution policies observed in the data. Our resultssuggest that regional di¤erences in labor productivity are an important determinantof interstate migration. We use the calibrated model to compare the cross-section ofredistributive policies with and without worker mobility. The main result of the paperis that interstate migration has induced substantial convergence in tax rates acrossUS states, but no race to the bottom. Skill-biased in-migration has reduced the skillpremium and the need for tax-based redistribution in the states that would have hadthe highest tax rates in the absence of mobility.

Stabilization versus insurance: Welfare effects of procyclical taxation under incomplete markets

We construct and calibrate a general equilibrium business cycle model with unemployment and precautionary saving. We compute the cost of business cycles and locate the optimum in a set of simple cyclical fiscal policies. Our economy exhibits productivity shocks, giving firms an incentive to hire more when productivity is high. However, business cycles make workers' income riskier, both by increasing the unconditional probability of unusuallylong unemployment spells, and by making wages more variable, and therefore they decrease social welfare by around one-fourth or one-third of 1% of consumption. Optimal fiscal policy offsets the cycle, holding unemployment benefits constant but varying the tax rate procyclically to smooth hiring. By running a deficit of 4% to 5% of output in recessions, the government eliminates half the variation in the unemployment rate, most of the variation in workers'aggregate consumption, and most of the welfare cost of business cycles.

Separated by a common currency? Evidence from the Euro changeover

We study the price convergence of goods and services in the euro area in 2001-2002. To measure the degree of convergence, we compare the prices of around 220 items in 32 European cities. The width of the border is the price di¤erence attributed to the fact that the two cities are in different countries. We find that the 2001 European borders are negative, which suggests that the markets were very integrated before the euro changeover. Moreover, we do not identify an integration effect attributable to the introduction of the euro. We then explore the determinants of the European borders. We find that different languages, wealth and population differences tend to split the markets. Historical inflation, though, tends to lead to price convergence.

Adaptive model selection using empirical complexities

Given $n$ independent replicates of a jointly distributed pair $(X,Y)\in {\cal R}^d \times {\cal R}$, we wish to select from a fixed sequence of model classes ${\cal F}_1, {\cal F}_2, \ldots$ a deterministic prediction rule $f: {\cal R}^d \to {\cal R}$ whose risk is small. We investigate the possibility of empirically assessingthe {\em complexity} of each model class, that is, the actual difficulty of the estimation problem within each class. The estimated complexities are in turn used to define an adaptive model selection procedure, which is based on complexity penalized empirical risk.The available data are divided into two parts. The first is used to form an empirical cover of each model class, and the second is used to select a candidate rule from each cover based on empirical risk. The covering radii are determined empirically to optimize a tight upper bound on the estimation error. An estimate is chosen from the list of candidates in order to minimize the sum of class complexity and empirical risk. A distinguishing feature of the approach is that the complexity of each model class is assessed empirically, based on the size of its empirical cover.Finite sample performance bounds are established for the estimates, and these bounds are applied to several non-parametric estimation problems. The estimates are shown to achieve a favorable tradeoff between approximation and estimation error, and to perform as well as if the distribution-dependent complexities of the model classes were known beforehand. In addition, it is shown that the estimate can be consistent,and even possess near optimal rates of convergence, when each model class has an infinite VC or pseudo dimension.For regression estimation with squared loss we modify our estimate to achieve a faster rate of convergence.

Minimum price variations, time priority and quotes dynamics

We analyze the impact of a minimum price variation (tick) and timepriority on the dynamics of quotes and the trading costs when competitionfor the order flow is dynamic. We find that convergence to competitiveoutcomes can take time and that the speed of convergence is influencedby the tick size, the priority rule and the characteristics of the orderarrival process. We show also that a zero minimum price variation is neveroptimal when competition for the order flow is dynamic. We compare thetrading outcomes with and without time priority. Time priority is shownto guarantee that uncompetitive spreads cannot be sustained over time.However it can sometimes result in higher trading costs. Empiricalimplications are proposed. In particular, we relate the size of thetrading costs to the frequency of new offers and the dynamics of theinside spread to the state of the book.

Do institutional changes affect business cycles? Evidence from Europe

We study the effects that the Maastricht treaty, the creation of the ECB, andthe Euro changeover had on the dynamics of European business cycles using a panelVAR and data from ten European countries - seven from the Euro area and threeoutside of it. There are changes in the features of European business cycles and in thetransmission of shocks. They precede the three events of interest and are more linkedto a general process of European convergence and synchronization.

On the sources of the Great Moderation

The remarkable decline in macroeconomic volatility experienced by the U.S. economy since the mid-80s (the so-called Great Moderation) has been accompanied by large changes in the patterns of comovements among output, hours and labor productivity. Those changes are reflected in both conditional and unconditional second moments as well as in the impulse responses to identified shocks. That evidencepoints to structural change, as opposed to just good luck, as an explanation for the Great Moderation. We use a simple macro model to suggest some of the immediate sources which are likely to be behindthe observed changes.

Almost sure testability of classes of densities

Let a class $\F$ of densities be given. We draw an i.i.d.\ sample from a density $f$ which may or may not be in $\F$. After every $n$, one must make a guess whether $f \in \F$ or not. A class is almost surely testable if there exists such a testing sequence such that for any $f$, we make finitely many errors almost surely. In this paper, several results are given that allowone to decide whether a class is almost surely testable. For example, continuity and square integrability are not testable, but unimodality, log-concavity, and boundedness by a given constant are.

Inequalities for a new data-based method for selecting nonparametric density estimates

We continue the development of a method for the selection of a bandwidth or a number of design parameters in density estimation. We provideexplicit non-asymptotic density-free inequalities that relate the $L_1$ error of the selected estimate with that of the best possible estimate,and study in particular the connection between the richness of the classof density estimates and the performance bound. For example, our methodallows one to pick the bandwidth and kernel order in the kernel estimatesimultaneously and still assure that for {\it all densities}, the $L_1$error of the corresponding kernel estimate is not larger than aboutthree times the error of the estimate with the optimal smoothing factor and kernel plus a constant times $\sqrt{\log n/n}$, where $n$ is the sample size, and the constant only depends on the complexity of the family of kernels used in the estimate. Further applications include multivariate kernel estimates, transformed kernel estimates, and variablekernel estimates.

Duality in mean-variance frontiers with conditioning information

Portfolio and stochastic discount factor (SDF) frontiers are usually regarded as dual objects, and researchers sometimes use one to answer questions about the other. However, the introduction of conditioning information and active portfolio strategies alters this relationship. For instance, the unconditional portfolio frontier in Hansen and Richard (1987) is not dual to the unconditional SDF frontier in Gallant, Hansen and Tauchen (1990). We characterise the dual objects to those frontiers, and relate them to the frontiers generated with managed portfolios, which are commonly used in empirical work. We also study the implications of a safe asset and other special cases.