Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

Linear least squares estimation of the first order moving average parameter

We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the first order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed

Estimating biophysical variable dependences with kernels

This paper introduces a nonlinear measure of dependence between random variables in the context of remote sensing data analysis. The Hilbert-Schmidt Independence Criterion (HSIC) is a kernel method for evaluating statistical dependence. HSIC is based on computing the Hilbert-Schmidt norm of the cross-covariance operator of mapped samples in the corresponding Hilbert spaces. The HSIC empirical estimator is very easy to compute and has good theoretical and practical properties. We exploit the capabilities of HSIC to explain nonlinear dependences in two remote sensing problems: temperature estimation and chlorophyll concentration prediction from spectra. Results show that, when the relationship between random variables is nonlinear or when few data are available, the HSIC criterion outperforms other standard methods, such as the linear correlation or mutual information.

Performance anxiety : cardiorespiratory activity in high- and low-anxious professional music students in a performance situation

Questionnaire studies indicate that high-anxious musicians may suffer from hyperventilation symptoms before and/or during performance. Reported symptoms include amongst others shortness of breath, fast or deep breathing, dizziness and thumping heart. A self-report study by Widmer, Conway, Cohen and Davies (1997) shows that up to seventy percent of the tested highly anxious musicians are hyperventilators during performance. However, no study has yet tested if these self-reported symptoms reflect actual cardiorespiratory changes just before and during performance. Disturbances in breathing patterns and hyperventilation may negatively affect the performance quality in stressful performance situations. The main goal of this study is to determine if music performance anxiety is manifest physiologically in specific correlates of cardiorespiratory activity. We studied 74 professional music students of Swiss Music Universities divided into two groups (high- and lowanxious) based on their self-reported performance anxiety (State-Trait Anxiety Inventory by Spielberger). The students were tested in three distinct situations: baseline, performance without audience, performance with audience. We measured a) breathing patterns, end-tidal carbon dioxide, which is a good non-invasive estimator for hyperventilation, and cardiac activation and b) self-perceived emotions and self-perceived physiological activation. Analyses of heart rate, respiratory rate, self-perceived palpitations, self-perceived shortness of breath and self-perceived anxiety for the 15 most and the 15 least anxious musicians show that high-anxious and low-anxious music students have a comparable physiological activation during the different measurement periods. However, highanxious music students feel significantly more anxious and perceive significantly stronger palpitations and significantly stronger shortness of breath just before and during a public performance. The results indicate that low- and high-anxious music students a) do not differ in the considered physiological responses and b) differ in the considered self-perceived physiological symptoms and the selfreported anxiety before and/or during a public performance.

An Analysis of OWI Arrests and Convictions in Iowa, 2011

The primary goal of the project was to document the demographic profile of OWI offenders in Iowa. The study is based on both aggregate and case-level data. The case level data produced a final sample of 118,675 OWI convictions. That occurred from 2000 through 2009. The great majority of convicted offenders were White males. From 2000 through 2009 the percentage of convictions received by women increased by 34%. Defendants’ average age of was 30 years old, and the age cohorts of 15 to 24, 25 to 34, and 34 to 45 were overrepresented among convicted offenders. Whites were underrepresented among OWI defendants. African Americans, Hispanics and Native Americans were overrepresented. From 2000 through 2009, the percentage of aggravated misdemeanor felony OWI convictions received by Hispanics and African Americans increased significantly. The percentage of OWI convictions received by women and African Americans increased significantly after implementation of the .08 BAC law. We did not find convincing evidence of a direct relationship between enforcement trends and the alcohol related traffic fatalities (ARTFs). However, the ten year Iowa conviction trends did provide evidence of a conviction lag effect on Iowa’s ARTFs. The research findings established the basis for a phase two project that would assess the efficacy of OWI sentencing practices in Iowa.

Robust accelerated failure time regression

Robust estimators for accelerated failure time models with asymmetric (or symmetric) error distribution and censored observations are proposed. It is assumed that the error model belongs to a log-location-scale family of distributions and that the mean response is the parameter of interest. Since scale is a main component of mean, scale is not treated as a nuisance parameter. A three steps procedure is proposed. In the first step, an initial high breakdown point S estimate is computed. In the second step, observations that are unlikely under the estimated model are rejected or down weighted. Finally, a weighted maximum likelihood estimate is computed. To define the estimates, functions of censored residuals are replaced by their estimated conditional expectation given that the response is larger than the observed censored value. The rejection rule in the second step is based on an adaptive cut-off that, asymptotically, does not reject any observation when the data are generat ed according to the model. Therefore, the final estimate attains full efficiency at the model, with respect to the maximum likelihood estimate, while maintaining the breakdown point of the initial estimator. Asymptotic results are provided. The new procedure is evaluated with the help of Monte Carlo simulations. Two examples with real data are discussed.

On the relationship between connections and the asymptotic properties of predictive distributions

In a recent paper, Komaki studied the second-order asymptotic properties of predictive distributions, using the Kullback-Leibler divergence as a loss function. He showed that estimative distributions with asymptotically efficient estimators can be improved by predictive distributions that do not belong to the model. The model is assumed to be a multidimensional curved exponential family. In this paper we generalize the result assuming as a loss function any f divergence. A relationship arises between alpha connections and optimal predictive distributions. In particular, using an alpha divergence to measure the goodness of a predictive distribution, the optimal shift of the estimate distribution is related to alpha-covariant derivatives. The expression that we obtain for the asymptotic risk is also useful to study the higher-order asymptotic properties of an estimator, in the mentioned class of loss functions.

Lag-one autocorrelation in short series: Estimation and hypothesis testing

In the first part of the study, nine estimators of the first-order autoregressive parameter are reviewed and a new estimator is proposed. The relationships and discrepancies between the estimators are discussed in order to achieve a clear differentiation. In the second part of the study, the precision in the estimation of autocorrelation is studied. The performance of the ten lag-one autocorrelation estimators is compared in terms of Mean Square Error (combining bias and variance) using data series generated by Monte Carlo simulation. The results show that there is not a single optimal estimator for all conditions, suggesting that the estimator ought to be chosen according to sample size and to the information available of the possible direction of the serial dependence. Additionally, the probability of labelling an actually existing autocorrelation as statistically significant is explored using Monte Carlo sampling. The power estimates obtained are quite similar among the tests associated with the different estimators. These estimates evidence the small probability of detecting autocorrelation in series with less than 20 measurement times.

Estimating slope and level change in N=1 designs

The current study proposes a new procedure for separately estimating slope change and level change between two adjacent phases in single-case designs. The procedure eliminates baseline trend from the whole data series prior to assessing treatment effectiveness. The steps necessary to obtain the estimates are presented in detail, explained, and illustrated. A simulation study is carried out to explore the bias and precision of the estimators and compare them to an analytical procedure matching the data simulation model. The experimental conditions include two data generation models, several degrees of serial dependence, trend, level and/or slope change. The results suggest that the level and slope change estimates provided by the procedure are unbiased for all levels of serial dependence tested and trend is effectively controlled for. The efficiency of the slope change estimator is acceptable, whereas the variance of the level change estimator may be problematic for highly negatively autocorrelated data series.

Increased eeg synchronization in schizophrenia patients by the glutathione precursor, n-acetyl-cysteine

Background: Glutathione (GSH) dysregulation at the gene, protein and functional levels observed in schizophrenia patients, and schizophrenia-like anomalies in GSH deficit experimental models, suggest that genetic glutathione synthesis impairments represent one major risk factor for the disease (Do et al., 2009). In a randomized, double blind, placebo controlled, add-on clinical trial of 140 patients, the GSH precursor N-Acetyl-Cysteine (NAC, 2 g/day, 6 months) significantly improved the negative symptoms and reduced side-effects due to antipsychotics (Berk et al., 2008). In a subset of patients (n=7), NAC (2 g/day, 2 months, cross-over design) also improved auditory evoked potentials, the NMDAdependent mismatch negativity (Lavoie et al, 2008). Methods: To determine whether increased GSH levels would modulate the topography of functional brain connectivity, we applied a multivariate phase synchronization (MPS) estimator (Knyazeva et al, 2008) to dense-array EEGs recorded during rest with eyes closed at the protocol onset, the point of crossover, and at its end. Phase synchronization phenomena are appealing because they can be associated to synchronized phases while the amplitudes stay uncorrelated. MPS measures the degree of interactions among the recorded neuronal oscillators by quantifiying to what extent they behave like a macro-oscillator (i.e. the oscillators are phase synchronous). To assess the whole-head synchronization topography, we computed the MPS sensor-wise over the cluster of locations defined by the sensor itself and he surrounding ones belonging to its second-order neighborhood (Carmeli et al, 2005). Such a cluster spans about 12 cm on average. Abstracts 245 Results: The whole-head imaging revealed a specific synchronization landscape in NAC compared to placebo condition. In particular, NAC increased MPS over frontal and left temporal regions in a frequency-specific manner. Importantly, the topography and direction of MPS changes were similar and robust in all 7 patients. Moreover, these changes correlated with the changes in the Liddle's score of disorganization (Liddle, 1987) thus linking EEG synchronization to the improvement of clinical picture. Discussion: The data suggest an important pathway towards new therapeutic strategies that target GSH dysregulation in schizophrenia. They also show the utility of MPS mapping as a marker of treatment efficacy.

Music Performance Anxiety (MPA) : cardiorespiratory activity in high- and low-anxious professional music students before a performance situation

Descriptors: music performance anxiety, respiration, hyperventilation Surveys indicate that high-anxious musicians may suffer from hyperventilation (HV) before or during performance. Reported symptoms include shortness of breath, fast/ deep breathing and thumping heart. However, no study has yet tested if these selfreported symptoms reflect actual cardiorespiratory activity. Themain goal of this study was to determine if MPA is manifested physiologically in specific correlates of cardiorespiratory activity associated with HV.We studied 74 professional music students from Swiss Music Academies. In this study, we compared the most anxious students (highanxious; n 5 20) with the least anxious students (low-anxious; n 5 23) based on their self-reported performance anxiety. We measured cardiorespiratory patterns with the Lifeshirt system, end-tidal CO2 with a capnograph (EtCO2, a good non-invasive estimator of HV), self-perceived physiological activation and affective experience in three situations on different days: baseline, performance without audience, and performance with audience. Comparing measures for the private vs. the public concert, high- compared to low-anxious students showed a significant drop in EtCO2 before the public concert and reported larger increases in anxiety, tension, palpitations and breathing difficulties. In contrast, heart rate, respiratory rate and volume did not differ significantly between groups. The results of this study support the hypothesis thatMPA may be associated with a tendency to hyperventilate and, thus, point to a potential hyperventilation problem in high-anxious music students.

Bortezomib(Velcade®)-Thalidomide-Dexamethasone (VTD) Is Superior to Thalidomide-Dexamethasone (TD) In Patients with Multiple Myeloma (MM) Progressing or Relapsing After Autologous Transplantation

Introduction: The Thalidomide-Dexamethasone (TD) regimen has provided encouraging results in relapsed MM. To improve results, bortezomib (Velcade) has been added to the combination in previous phase II studies, the so called VTD regimen. In January 2006, the European Group for Blood and Marrow Transplantation (EBMT) and the Intergroupe Francophone du Myélome (IFM) initiated a prospective, randomized, parallel-group, open-label phase III, multicenter study, comparing VTD (arm A) with TD (arm B) for MM patients progressing or relapsing after autologous transplantation. Patients and Methods: Inclusion criteria: patients in first progression or relapse after at least one autologous transplantation, including those who had received bortezomib or thalidomide before transplant. Exclusion criteria: subjects with neuropathy above grade 1 or non secretory MM. Primary study end point was time to progression (TTP). Secondary end points included safety, response rate, progression-free survival (PFS) and overall survival (OS). Treatment was scheduled as follows: bortezomib 1.3 mg/m2 was given as an i.v bolus on Days 1, 4, 8 and 11 followed by a 10-Day rest period (days 12 to 21) for 8 cycles (6 months) and then on Days 1, 8, 15, 22 followed by a 20-Day rest period (days 23 to 42) for 4 cycles (6 months). In both arms, thalidomide was scheduled at 200 mg/Day orally for one year and dexamethasone 40 mg/Day orally four days every three weeks for one year. Patients reaching remission could proceed to a new stem cell harvest. However, transplantation, either autologous or allogeneic, could only be performed in patients who completed the planned one year treatment period. Response was assessed by EBMT criteria, with additional category of near complete remission (nCR). Adverse events were graded by the NCI-CTCAE, Version 3.0.The trial was based on a group sequential design, with 4 planned interim analyses and one final analysis that allowed stopping for efficacy as well as futility. The overall alpha and power were set equal to 0.025 and 0.90 respectively. The test for decision making was based on the comparison in terms of the ratio of the cause-specific hazards of relapse/progression, estimated in a Cox model stratified on the number of previous autologous transplantations. Relapse/progression cumulative incidence was estimated using the proper nonparametric estimator, the comparison was done by the Gray test. PFS and OS probabilities were estimated by the Kaplan-Meier curves, the comparison was performed by the Log-Rank test. An interim safety analysis was performed when the first hundred patients had been included. The safety committee recommended to continue the trial. Results: As of 1st July 2010, 269 patients had been enrolled in the study, 139 in France (IFM 2005-04 study), 21 in Italy, 38 in Germany, 19 in Switzerland (a SAKK study), 23 in Belgium, 8 in Austria, 8 in the Czech republic, 11 in Hungary, 1 in the UK and 1 in Israel. One hundred and sixty nine patients were males and 100 females; the median age was 61 yrs (range 29-76). One hundred and thirty six patients were randomized to receive VTD and 133 to receive TD. The current analysis is based on 246 patients (124 in arm A, 122 in arm B) included in the second interim analysis, carried out when 134 events were observed. Following this analysis, the trial was stopped because of significant superiority of VTD over TD. The remaining patients were too premature to contribute to the analysis. The number of previous autologous transplants was one in 63 vs 60 and two or more in 61 vs 62 patients in arm A vs B respectively. The median follow-up was 25 months. The median TTP was 20 months vs 15 months respectively in arm A and B, with cumulative incidence of relapse/progression at 2 years equal to 52% (95% CI: 42%-64%) vs 70% (95% CI: 61%-81%) (p=0.0004, Gray test). The same superiority of arm A was also observed when stratifying on the number of previous autologous transplantations. At 2 years, PFS was 39% (95% CI: 30%-51%) vs 23% (95% CI: 16%-34%) (A vs B, p=0.0006, Log-Rank test). OS in the first two years was comparable in the two groups. Conclusion: VTD resulted in significantly longer TTP and PFS in patients relapsing after ASCT. Analysis of response and safety data are on going and results will be presented at the meeting.

Relationship between grain colour and preharvest sprouting-resistance in wheat

Since red alleles (R) of the genes that control grain colour are important for the improvement of preharvest sprouting resistance in wheat and there are three independently inherited loci, on chromosomes 3A, 3B and 3D of hexaploid wheat, it is possible to vary the dosage of dominant alleles in a breeding program. The objective of this work was to evaluate the dosage effect of R genes on preharvest sprouting, in a single seed descent population, named TRL, derived from the cross between Timgalen, white-grained wheat, and RL 4137, red-grained wheat. The study was carried out using sprouting data in ripe ears obtained under artificial conditions in a rainfall simulator over three years. According to the results there is a significant effect on preharvest sprouting provided by colour and a weaker effect of increasing R dosage. However, the significant residual genotypic variation between red lines and all lines (reds and whites) at 0.1% level showed that preharvest sprouting was also controlled by other genes. There are no significant correlations between sprouting and date of ripeness or between ripeness, R dosage and colour intensity.

Robust parametric indirect estimates of the expected cost of a hospital stay with covariates and censored data.

We consider the problem of estimating the mean hospital cost of stays of a class of patients (e.g., a diagnosis-related group) as a function of patient characteristics. The statistical analysis is complicated by the asymmetry of the cost distribution, the possibility of censoring on the cost variable, and the occurrence of outliers. These problems have often been treated separately in the literature, and a method offering a joint solution to all of them is still missing. Indirect procedures have been proposed, combining an estimate of the duration distribution with an estimate of the conditional cost for a given duration. We propose a parametric version of this approach, allowing for asymmetry and censoring in the cost distribution and providing a mean cost estimator that is robust in the presence of extreme values. In addition, the new method takes covariate information into account.

Metabolic syndrome and the risk of cardiovascular disease in older adults.

OBJECTIVES: The purpose of this study was to assess whether metabolic syndrome (MetSyn) predicts a higher risk for cardiovascular events in older adults. BACKGROUND: The importance of MetSyn as a risk factor has not previously focused on older adults and deserves further study. METHODS: We studied the impact of MetSyn (38% prevalence) on outcomes in 3,035 participants in the Health, Aging, and Body Composition (Health ABC) study (51% women, 42% black, ages 70 to 79 years). RESULTS: During a 6-year follow-up, there were 434 deaths overall, 472 coronary events (CE), 213 myocardial infarctions (MI), and 231 heart failure (HF) hospital stays; 59% of the subjects had at least one hospital stay. Coronary events, MI, HF, and overall hospital stays occurred significantly more in subjects with MetSyn (19.9% vs. 12.9% for CE, 9.1% vs. 5.7% for MI, 10.0% vs. 6.1% for HF, and 63.1% vs. 56.1% for overall hospital stay; all p < 0.001). No significant differences in overall mortality was seen; however, there was a trend toward higher cardiovascular mortality (5.1% vs. 3.8%, p = 0.067) and coronary mortality (4.5% vs. 3.2%, p = 0.051) in patients with MetSyn. After adjusting for baseline characteristics, patients with MetSyn were at a significantly higher risk for CE (hazard ratio [HR] 1.56, 95% confidence interval [CI] 1.28 to 1.91), MI (HR 1.51, 95% CI 1.12 to 2.05), and HF hospital stay (HR 1.49, 95% CI 1.10 to 2.00). Women and whites with MetSyn had a higher coronary mortality rate. The CE rate was higher among subjects with diabetes and with MetSyn; those with both had the highest risk. CONCLUSIONS: Overall, subjects over 70 years are at high risk for cardiovascular events; MetSyn in this group is associated with a significantly greater risk.