Option pricing under stochastic volatility and stochastic interest rate in the Spanish case

Among the underlying assumptions of the Black-Scholes option pricingmodel, those of a fixed volatility of the underlying asset and of aconstantshort-term riskless interest rate, cause the largest empirical biases. Onlyrecently has attention been paid to the simultaneous effects of thestochasticnature of both variables on the pricing of options. This paper has tried toestimate the effects of a stochastic volatility and a stochastic interestrate inthe Spanish option market. A discrete approach was used. Symmetricand asymmetricGARCH models were tried. The presence of in-the-mean and seasonalityeffectswas allowed. The stochastic processes of the MIBOR90, a Spanishshort-terminterest rate, from March 19, 1990 to May 31, 1994 and of the volatilityofthe returns of the most important Spanish stock index (IBEX-35) fromOctober1, 1987 to January 20, 1994, were estimated. These estimators wereused onpricing Call options on the stock index, from November 30, 1993 to May30, 1994.Hull-White and Amin-Ng pricing formulas were used. These prices werecomparedwith actual prices and with those derived from the Black-Scholesformula,trying to detect the biases reported previously in the literature. Whereasthe conditional variance of the MIBOR90 interest rate seemed to be freeofARCH effects, an asymmetric GARCH with in-the-mean and seasonalityeffectsand some evidence of persistence in variance (IEGARCH(1,2)-M-S) wasfoundto be the model that best represent the behavior of the stochasticvolatilityof the IBEX-35 stock returns. All the biases reported previously in theliterature were found. All the formulas overpriced the options inNear-the-Moneycase and underpriced the options otherwise. Furthermore, in most optiontrading, Black-Scholes overpriced the options and, because of thetime-to-maturityeffect, implied volatility computed from the Black-Scholes formula,underestimatedthe actual volatility.

Shrews in suburbia: an application of Goodman's extinction model

An equation is applied for calculating the expected persistence time of an unstructured population of the white-toothed shrew Crocidura russula from Preverenges, a suburban area in western Switzerland. Population abundance data from March and November between 1977 and 1988 were fit to the logistic density dependence model to estimate mean population growth rate as a function of population density. The variance in mean growth rate was approximated with two different models. The largest estimated persistence time was less than a few decades, the smallest less than 10 years. The results are sensitive to the magnitude of variance in population growth rate. Deviations from the logistic density dependence model in November are quite well explained by weather variables but those in March are uncorrelated with weather variables. Variability in population growth rates measured in winter months may be better explained by behavioural mechanisms. Environmental variability, dispersal of juveniles and refugia within the range of the population may contribute to its long-term survival.

25-hydroxyvitamin D concentration is inversely associated with serum MMP-9 in a cross-sectional study of African American ESRD patients.

BACKGROUND: Circulating 25-hydroxyvitamin D [25(OH)D] concentration is inversely associated with peripheral arterial disease and hypertension. Vascular remodeling may play a role in this association, however, data relating vitamin D level to specific remodeling biomarkers among ESRD patients is sparse. We tested whether 25(OH)D concentration is associated with markers of vascular remodeling and inflammation in African American ESRD patients.METHODS: We conducted a cross-sectional study among ESRD patients receiving maintenance hemodialysis within Emory University-affiliated outpatient hemodialysis units. Demographic, clinical and dialysis treatment data were collected via direct patient interview and review of patients records at the time of enrollment, and each patient gave blood samples. Associations between 25(OH)D and biomarker concentrations were estimated in univariate analyses using Pearson's correlation coefficients and in multivariate analyses using linear regression models. 25(OH) D concentration was entered in multivariate linear regression models as a continuous variable and binary variable (<15 ng/ml and =15 ng/ml). Adjusted estimate concentrations of biomarkers were compared between 25(OH) D groups using analysis of variance (ANOVA). Finally, results were stratified by vascular access type.RESULTS: Among 91 patients, mean (standard deviation) 25(OH)D concentration was 18.8 (9.6) ng/ml, and was low (<15 ng/ml) in 43% of patients. In univariate analyses, low 25(OH) D was associated with lower serum calcium, higher serum phosphorus, and higher LDL concentrations. 25(OH) D concentration was inversely correlated with MMP-9 concentration (r = -0.29, p = 0.004). In multivariate analyses, MMP-9 concentration remained negatively associated with 25(OH) D concentration (P = 0.03) and anti-inflammatory IL-10 concentration positively correlated with 25(OH) D concentration (P = 0.04).CONCLUSIONS: Plasma MMP-9 and circulating 25(OH) D concentrations are significantly and inversely associated among ESRD patients. This finding may suggest a potential mechanism by which low circulating 25(OH) D functions as a cardiovascular risk factor.

The disturbing 'rise' of global income inequality

We use aggregate GDP data and within-country income shares for theperiod 1970-1998 to assign a level of income to each person in theworld. We then estimate the gaussian kernel density function for theworldwide distribution of income. We compute world poverty rates byintegrating the density function below the poverty lines. The $1/daypoverty rate has fallen from 20% to 5% over the last twenty five years.The $2/day rate has fallen from 44% to 18%. There are between 300 and500 million less poor people in 1998 than there were in the 70s.We estimate global income inequality using seven different popularindexes: the Gini coefficient, the variance of log-income, two ofAtkinson s indexes, the Mean Logarithmic Deviation, the Theil indexand the coefficient of variation. All indexes show a reduction in globalincome inequality between 1980 and 1998. We also find that most globaldisparities can be accounted for by across-country, not within-country,inequalities. Within-country disparities have increased slightly duringthe sample period, but not nearly enough to offset the substantialreduction in across-country disparities. The across-country reductionsin inequality are driven mainly, but not fully, by the large growth rateof the incomes of the 1.2 billion Chinese citizens. Unless Africa startsgrowing in the near future, we project that income inequalities willstart rising again. If Africa does not start growing, then China, India,the OECD and the rest of middle-income and rich countries diverge awayfrom it, and global inequality will rise. Thus, the aggregate GDP growthof the African continent should be the priority of anyone concerned withincreasing global income inequality.

Honey, I shrunk the sample covariance matrix

The central message of this paper is that nobody should be using the samplecovariance matrix for the purpose of portfolio optimization. It containsestimation error of the kind most likely to perturb a mean-varianceoptimizer. In its place, we suggest using the matrix obtained from thesample covariance matrix through a transformation called shrinkage. Thistends to pull the most extreme coefficients towards more central values,thereby systematically reducing estimation error where it matters most.Statistically, the challenge is to know the optimal shrinkage intensity,and we give the formula for that. Without changing any other step in theportfolio optimization process, we show on actual stock market data thatshrinkage reduces tracking error relative to a benchmark index, andsubstantially increases the realized information ratio of the activeportfolio manager.

An assessment of empirical Bayes and composite estimators for small areas

We compare a set of empirical Bayes and composite estimators of the population means of the districts (small areas) of a country, and show that the natural modelling strategy of searching for a well fitting empirical Bayes model and using it for estimation of the area-level means can be inefficient.

On the performance of small-area estimators: Fixed vs. random area parameters

Most methods for small-area estimation are based on composite estimators derived from design- or model-based methods. A composite estimator is a linear combination of a direct and an indirect estimator with weights that usually depend on unknown parameters which need to be estimated. Although model-based small-area estimators are usually based on random-effects models, the assumption of fixed effects is at face value more appropriate.Model-based estimators are justified by the assumption of random (interchangeable) area effects; in practice, however, areas are not interchangeable. In the present paper we empirically assess the quality of several small-area estimators in the setting in which the area effects are treated as fixed. We consider two settings: one that draws samples from a theoretical population, and another that draws samples from an empirical population of a labor force register maintained by the National Institute of Social Security (NISS) of Catalonia. We distinguish two types of composite estimators: a) those that use weights that involve area specific estimates of bias and variance; and, b) those that use weights that involve a common variance and a common squared bias estimate for all the areas. We assess their precision and discuss alternatives to optimizing composite estimation in applications.

Principal curves and principal oriented points

Principal curves have been defined Hastie and Stuetzle (JASA, 1989) assmooth curves passing through the middle of a multidimensional dataset. They are nonlinear generalizations of the first principalcomponent, a characterization of which is the basis for the principalcurves definition.In this paper we propose an alternative approach based on a differentproperty of principal components. Consider a point in the space wherea multivariate normal is defined and, for each hyperplane containingthat point, compute the total variance of the normal distributionconditioned to belong to that hyperplane. Choose now the hyperplaneminimizing this conditional total variance and look for thecorresponding conditional mean. The first principal component of theoriginal distribution passes by this conditional mean and it isorthogonal to that hyperplane. This property is easily generalized todata sets with nonlinear structure. Repeating the search from differentstarting points, many points analogous to conditional means are found.We call them principal oriented points. When a one-dimensional curveruns the set of these special points it is called principal curve oforiented points. Successive principal curves are recursively definedfrom a generalization of the total variance.

Weighted metric multidimensional scaling

This paper establishes a general framework for metric scaling of any distance measure between individuals based on a rectangular individuals-by-variables data matrix. The method allows visualization of both individuals and variables as well as preserving all the good properties of principal axis methods such as principal components and correspondence analysis, based on the singular-value decomposition, including the decomposition of variance into components along principal axes which provide the numerical diagnostics known as contributions. The idea is inspired from the chi-square distance in correspondence analysis which weights each coordinate by an amount calculated from the margins of the data table. In weighted metric multidimensional scaling (WMDS) we allow these weights to be unknown parameters which are estimated from the data to maximize the fit to the original distances. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing a matrix and displaying its rows and columns in biplots.

Estimating uncertainty of alcohol-attributable fractions for infectious and chronic diseases.

Background: Alcohol is a major risk factor for burden of disease and injuries globally. This paper presents a systematic method to compute the 95% confidence intervals of alcohol-attributable fractions (AAFs) with exposure and risk relations stemming from different sources.Methods: The computation was based on previous work done on modelling drinking prevalence using the gamma distribution and the inherent properties of this distribution. The Monte Carlo approach was applied to derive the variance for each AAF by generating random sets of all the parameters. A large number of random samples were thus created for each AAF to estimate variances. The derivation of the distributions of the different parameters is presented as well as sensitivity analyses which give an estimation of the number of samples required to determine the variance with predetermined precision, and to determine which parameter had the most impact on the variance of the AAFs.Results: The analysis of the five Asian regions showed that 150 000 samples gave a sufficiently accurate estimation of the 95% confidence intervals for each disease. The relative risk functions accounted for most of the variance in the majority of cases.Conclusions: Within reasonable computation time, the method yielded very accurate values for variances of AAFs.

Estimadores compuestos en estadística regional: aplicación para la tasa de variación de la ocupación en la industria

This work is part of a project studying the performance of model basedestimators in a small area context. We have chosen a simple statisticalapplication in which we estimate the growth rate of accupation for severalregions of Spain. We compare three estimators: the direct one based onstraightforward results from the survey (which is unbiassed), and a thirdone which is based in a statistical model and that minimizes the mean squareerror.

Resting metabolic rate in six- to ten-year-old obese and nonobese children.

The resting metabolic rate (RMR) and body composition of 130 obese and nonobese prepubertal children, aged 6 to 10 years, were assessed by indirect calorimetry and skin-fold thickness, respectively. The mean (+/- SD) RMR was 4619 +/- 449 kJ.day-1 (164 +/- 31 kJ.kg body weight-1 x day-1) in the 62 boys and 4449 +/- 520 kJ.day-1 (147 +/- 32 kJ.kg body weight-1 x day-1) in the 68 girls. Fat-free mass was the best single predictor of RMR (R2 = 0.64; p < 0.001). Step-down multiple regression analysis, with independent variables such as age, gender, weight, and height, allowed several RMR predictive equations to be developed. An equation for boys is as follows: RMR (kJ.day-1) = 1287 + 28.6 x Weight(kg) + 23.6 x Height(cm) - 69.1 x Age(yr) (R2 = 0.58; p < 0.001). An equation for girls is as follows: RMR (kJ.day-1 = 1552 + 35.8 x Weight (kg) + 15.6 x Height (cm) - 36.3 x Age (yr) (R2 = 0.69; p < 0.001). Comparison between the measured RMR and that predicted by currently used formulas showed that most of these equations tended to overestimate the RMR of both genders, especially in overweight children.

Breeding system and genetic variance in the monogamous, semi-social shrew, Crocidura russula

The population-genetic consequences of monogamy and male philopatry (a rare breeding system in mammals) were investigated using microsatellite markers in the semisocial and anthropophilic shrew Crocidura russula. A hierarchical sampling design over a 16-km geographical transect revealed a large genetic diversity (h = 0.813) with significant differentiation among subpopulations (F-ST = 5-6%), which suggests an exchange of 4.4 migrants per generation. Demic effective-size estimates were very high, due both to this limited gene inflow and to the inner structure of subpopulations. These were made of 13-20 smaller units (breeding groups), comprising an estimate of four breeding pairs each. Members of the same breeding groups displayed significant coancestries (F-LS = 9-10%), which was essentially due to strong male kinship: syntopic males were on average related at the half-sib level. Female dispersal among breeding groups was not complete (similar to 39%), and insufficient to prevent inbreeding. From our results, the breeding strategy of C. russula seems less efficient than classical mammalian systems (polygyny and male dispersal) in disentangling coancestry from inbreeding, but more so in retaining genetic variance.