Semi-parametric forecasts of the implied volatility surface using regression trees

We present a new semi-parametric model for the prediction of implied volatility surfaces that can be estimated using machine learning algorithms. Given a reasonable starting model, a boosting algorithm based on regression trees sequentially minimizes generalized residuals computed as differences between observed and estimated implied volatilities. To overcome the poor predictive power of existing models, we include a grid in the region of interest, and implement a cross-validation strategy to find an optimal stopping value for the boosting procedure. Back testing the out-of-sample performance on a large data set of implied volatilities from S&P 500 options, we provide empirical evidence of the strong predictive power of our model.     

Estimation of semiparametric regression model with longitudinal data

In a longitudinal study, an individual is followed up over a period of time. Repeated measurements on the response and some time-dependent covariates are taken at a series of sampling times. The sampling times are often irregular and depend on covariates. In this paper, we propose a sampling adjusted procedure for the estimation of the proportional mean model without having to specify a sampling model. Unlike existing procedures, the proposed method is robust to model misspecification of the sampling times. Large sample properties are investigated for the estimators of both regression coefficients and the baseline function. We show that the proposed estimation procedure is more efficient than the existing procedures. Large sample confidence intervals for the baseline function are also constructed by perturbing the estimation equations. A simulation study is conducted to examine the finite sample properties of the proposed estimators and to compare with some of the existing procedures. The method is illustrated with a data set from a recurrent bladder cancer study.     

A martingale residual diagnostic for longitudinal and recurrent event data

One method of assessing the fit of an event history model is to plot the empirical standard deviation of standardised martingale residuals. We develop an alternative procedure which is valid also in the presence of measurement error and applicable to both longitudinal and recurrent event data. Since the covariance between martingale residuals at times t ₀ and t > t ₀ is independent of t, a plot of these covariances should, for fixed t ₀, have no time trend. A test statistic is developed from the increments in the estimated covariances, and we investigate its properties under various types of model misspecification. Applications of the approach are presented using two Brazilian studies measuring daily prevalence and incidence of infant diarrhoea and a longitudinal study into treatment of schizophrenia.     

Sparse conformal predictors

Conformal predictors, introduced by Vovk et al. (Algorithmic Learning in a Random World, Springer, New York, 2005), serve to build prediction intervals by exploiting a notion of conformity of the new data point with previously observed data. We propose a novel method for constructing prediction intervals for the response variable in multivariate linear models. The main emphasis is on sparse linear models, where only few of the covariates have significant influence on the response variable even if the total number of covariates is very large. Our approach is based on combining the principle of conformal prediction with the ℓ ₁ penalized least squares estimator (LASSO). The resulting confidence set depends on a parameter ε>0 and has a coverage probability larger than or equal to 1−ε. The numerical experiments reported in the paper show that the length of the confidence set is small. Furthermore, as a by-product of the proposed approach, we provide a data-driven procedure for choosing the LASSO penalty. The selection power of the method is illustrated on simulated and real data.     

Models and estimation for systems with recurrent events and usage processes

This paper considers settings where populations of units may experience recurrent events, termed failures for convenience, and where the units are subject to varying levels of usage. We provide joint models for the recurrent events and usage processes, which facilitate analysis of their relationship as well as prediction of failures. Data on usage are often incomplete and we show how to implement maximum likelihood estimation in such cases. Random effects models with linear usage processes and gamma usage processes are considered in some detail. Data on automobile warranty claims are used to illustrate the proposed models and estimation methodology.     

Expected sample moments of concomitants of selected order statistics

In this paper, the task of determining expected values of sample moments, where the sample members have been selected based on noisy information, is considered. This task is a recurring problem in the theory of evolution strategies. Exact expressions for expected values of sums of products of concomitants of selected order statistics are derived. Then, using Edgeworth and Cornish-Fisher approximations, explicit results that depend on coefficients that can be determined numerically are obtained. While the results are exact only for normal populations, it is shown experimentally that including skewness and kurtosis in the calculations can yield greatly improved results for other distributions.     

Accurate ARL computation for EWMA-S<Superscript>2</Superscript> control charts

Originally, the exponentially weighted moving average (EWMA) control chart was developed for detecting changes in the process mean. The average run length (ARL) became the most popular performance measure for schemes with this objective. When monitoring the mean of independent and normally distributed observations the ARL can be determined with high precision. Nowadays, EWMA control charts are also used for monitoring the variance. Charts based on the sample variance S² are an appropriate choice. The usage of ARL evaluation techniques known from mean monitoring charts, however, is difficult. The most accurate method—solving a Fredholm integral equation with the Nyström method—fails due to an improper kernel in the case of chi-squared distributions. Here, we exploit the collocation method and the product Nyström method. These methods are compared to Markov chain based approaches. We see that collocation leads to higher accuracy than currently established methods.     

The Migrant Mortality Advantage: A 70 Month Follow-up of the Brussels Population

There is considerable evidence that first generation immigrants to developed countries tend to have lower mortality than does the population as a whole at their destination. This advantage is usually ascribed to a selection process which makes migrants more robust than the local population and/or an acculturation process whereby third-world migrants lose their natural healthy life style as they take on modern urban dietary and living habits. We investigate immigrant-local mortality differences using a 6-year follow-up of the complete Brussels population aged 25–55, as enumerated at the Belgian census, 1991. We show that adult migrants have lower mortality than their native-born counterparts, despite their often poorer living arrangements, work status and human capital. This effect differs by origin group. The effects of age on mortality are similar for all groups, with mortality increasing about 8% a year. This increase is slightly greater for the Belgian born than for immigrants, which makes the selectivity explanation unlikely. Years since migration does not significantly increase the mortality risk for most groups, contradicting the acculturation hypothesis. Thus, explanations ascribing immigrants' mortality advantage to migrant selectivity, pre-modern cultural practices, or an artefact of population recording practices are insufficient. We propose, instead, an explanation based on the meaning migration has for the immigrant, and the hope engendered in the move, particularly that from a lesser to a more developed country.     

Contexte local et migration: l’exemple des dynamiques migratoires internationales de quartiers dans la ville sénégalaise de Kaolack

Despite the diversity of the variables considered, explanatory models of migration do not fully incorporate the locality of origin as a scale of observation for migratory behaviour. Migration is often perceived to generate notions of territory; conversely, are local territories drivers of mobility? If so, in what forms, and by what means? This article analyses international migration from the city of Kaolack in Senegal, with particular focus on the role of the neighbourhood in migration dynamics. Here, the neighbourhood is seen as relatively homogeneous and singular historical and social entity. The ties that are established and maintained from one generation to the next take the form of shared lifestyles and modes of organization which may influence inhabitants’ propensity to emigrate.