MULTIFRACTIONAL STOCHASTIC VOLATILITY MODELS

The aim of this work is to advocate the use of multifractional Brownian motion (mBm) as a relevant model in financial mathematics. mBm is an extension of fractional Brownian motion where the Hurst parameter is allowed to vary in time. This enables the possibility to accommodate for varying local regularity, and to decouple it from long‐range dependence properties. While we believe that mBm is potentially useful in a variety of applications in finance, we focus here on a multifractional stochastic volatility Hull & White model that is an extension of the model studied in Comte and Renault. Using the stochastic calculus with respect to mBm developed in Lebovits and Lévy Véhel, we solve the corresponding stochastic differential equations. Since the solutions are of course not explicit, we take advantage of recently developed numerical techniques, namely functional quantization‐based cubature methods, to get accurate approximations. This allows us to test the behavior of our model (as well as the one in Comte and Renault) with respect to its parameters, and in particular its ability to explain some features of the implied volatility surface. An advantage of our model is that it is able both to fit smiles at different maturities, and to take volatility persistence into account in a more precise way than Comte and Renault.     

Preface

The paper examines the main issues surrounding distributional effects in the domains of natural resource management and land policies, agricultural technology and research policies, agricultural market and trade policies, and consumer‐oriented policies, including standards, subsidies, and labeling. Agriculture is drifting into an ever more drastic bifurcation at a global level and within many countries. Correcting that bifurcation will require large investments in rural areas and rural people, in institutions, and in information and biological technologies accessible by the poor in the world's smallholder sector. Large and growing national and international inequalities related to agriculture and rural areas threaten peace, growth, and sustainable development.     

Aid to Agriculture, Growth and Poverty Reduction

Agriculture and rural growth promotion show a recent 'comeback' in development cooperation, but action on the ground so far is not sufficient. After years of neglect, policy makers have recognized that poverty reduction in many low income countries can only be achieved if development efforts are clearly focused on the sector which employs most of the poor, and the space where most of the poor live. The importance of agricultural growth was amply demonstrated during the economic transformation of Asia. Forty years ago, Asia was a continent of widespread poverty. Today, most Asian countries are experiencing significant growth and poverty reduction. Rapid growth in productivity in the small-farm sector helped drive this process. Sub-Saharan Africa, however, failed to achieve rapid agricultural growth and remains mired in poverty and hunger. If Africa is to halve poverty by 2015 in accordance with the Millennium Development Goals (MDG), agriculture will need to maintain an annual growth rate of 6 per cent between 2000 and 2015. China's experience from 1978 to 1984 shows such growth is possible. Achieving the desired rapid rates of growth in Africa will require coherent policies by governments and donors, a substantial investment of public resources in rural infrastructure and access to agricultural technology, and significant improvement in national governance.     

Extracting cover sets from free fuzzy sorting data

Assignment of items to multiple categories requires suitable statistical methods. The present paper provides a new approach to solve this task. The concept of fuzzy sets is extended to cover sets (sets of overlapping clusters) in a simple manner introducing a vector of item membership sums. The application of the new concept is exemplified by modifying the fuzzy cluster analysis algorithm of Kaufman and Rousseeuw (Finding groups in data: an introduction to cluster analysis, 1990) to cover set cluster analysis appropriately. Wide equivalence of the numerical problems is demonstrated from Lagrange multipliers and Karush-Kuhn-Tucker conditions. Additionally, some extensions are introduced to the algorithm to improve its behavior for suboptimal large or small numbers of clusters. The adapted algorithm in most cases reproduces single sortings for correct numbers of clusters. Two applications to empirical free fuzzy sorting data sets are provided. Limitations of the algorithm are discussed.     

Who is Who

Praxis / MagazinNews

Who is Who     

Estimation of demand and supply functions from univariate sample with known separation

It is shown that the joint unconditional density function of demand and supply is a computable function of parameters of the conditional density function of the observed quantity. Propositions of formulating unconditional and conditional disequilibrium measures are suggested.     

Imputed Rent and Income Inequality: A Decomposition Analysis for Great Britain, West Germany and the U.S.

This article deals with income advantages derived from owner-occupied housing and their impact on the personal income distribution. Using micro-data from the British Household Panel Study (BHPS), the German Socio-Economic Panel (SOEP), and the U.S. Panel Study of Income Dynamics (PSID) we find distinct cross-national differences in terms of the prevalence and extent of imputed rent. Results from inequality decomposition analyses show this overall impact to be the net effect of two conflicting changes: On the one hand there is increasing income inequality between the groups of owneroccupiers and renters, respectively, and, on the other hand, we find inequality to be decreasing within the group of those owner-occupiers who own outright. When focussing on imputed rent as a means of old-age provision, our results for all three countries show an income advantage for, as well as a poverty reducing effect among the elderly. The empirical findings support the claim for the need of an improved harmonization of this non-cash income component especially for the purpose of cross-national comparative research.     

Heteroskedasticity and Neglected Parameter Heterogeneity

The paper studies the consequences of neglecting parameter heterogeneity for the linear regression model and cross-sectional data. Monte-Carlo experiments are used to illustrate that neglected parameter heterogeneity typically leads to (a) regression coefficients that are economically meaningless and (b)significant test statistics for heteroskedasticity and, possibly non-normality. The paper concludes that evidence for heteroskedasticity should not routinely lead to the use of White's well-known heteroskedasticity-consistent variance covariance matrix estimator. If heteroskedasticity is caused by neglected parameter heterogeneity or other causes of heteroskedasticity, such as wrong functional form, White's estimator will not serve any useful purpose.     

An efficient algorithm for Lindner’s test (configural frequency analysis)

Quality &; Quantity - Lindner’s (Psychologische Beiträge 26:393–415, 1984) test is a generalisation of Fisher’s exact test for 2 × 2 contingency tables to 2 k...