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.

Cost limitation through constrained oviposition site in a plant-pollinator/seed predator mutualism

Mutualism often involves reciprocal exploitation due to individual selection for increased benefits even at the expense of the partner. Therefore, stability and outcomes of such interactions crucially depend on cost limitation mechanisms. In the plant, pollinator /seed predator interaction between Silene latifolia (Caryophyllaceae) and Hadena bicruris (Lepidoptera: Noctuidae), moths generate pollination benefits as adults but impose seed predation costs as larvae. We examined whether floral morphology limits over-exploitation by constraining oviposition site. Oviposition site varies naturally inside vs. outside the corolla tube, but neither its determinants nor its effect on the interaction have been investigated. In a common garden with plants originating from eight populations, corolla tube length predicted oviposition site, but not egg presence or pollination efficiency, suggesting that long corolla tubes constrain the moth to lay eggs on petals. Egg position was also predicted by the combined effect of corolla tube and moth ovipositor lengths, with shorter ovipositor than corolla tube resulting in higher probability for eggs outside. Egg position on a given plant was repeatable over different exposure nights. When egg position was experimentally manipulated, eggs placed on the petal resulted in significantly fewer successful fruit attacks compared with eggs placed inside the corolla tube, suggesting differences in egg/larval mortality. Egg position also differently affected larval mass, fruit mass and fruit development. Our results indicate that constraining oviposition site through a long corolla tube reduces seed predation costs suffered by the plant without negatively affecting pollination efficiency and, hence may act to limit over-exploitation. However, the net effects of corolla tube depth variation on this interaction may fluctuate with extrinsic factors affecting egg mortality, and with patterns of gene flow affecting trait matching between the interacting species. The intermediate fitness costs incurred by both plant and insect associated with the different egg positions may reduce selective pressures for this interaction to evolve towards antagonism, favouring instead a mutualistic outcome. While a role for oviposition site variation in cost limitation is a novel finding in this system, it may apply more generally also to other mutualisms involving pollinating seed predators.

Estimation of the correlation structure of crustal velocity heterogeneity from seismic reflection data

Numerous sources of evidence point to the fact that heterogeneity within the Earth's deep crystalline crust is complex and hence may be best described through stochastic rather than deterministic approaches. As seismic reflection imaging arguably offers the best means of sampling deep crustal rocks in situ, much interest has been expressed in using such data to characterize the stochastic nature of crustal heterogeneity. Previous work on this problem has shown that the spatial statistics of seismic reflection data are indeed related to those of the underlying heterogeneous seismic velocity distribution. As of yet, however, the nature of this relationship has remained elusive due to the fact that most of the work was either strictly empirical or based on incorrect methodological approaches. Here, we introduce a conceptual model, based on the assumption of weak scattering, that allows us to quantitatively link the second-order statistics of a 2-D seismic velocity distribution with those of the corresponding processed and depth-migrated seismic reflection image. We then perform a sensitivity study in order to investigate what information regarding the stochastic model parameters describing crustal velocity heterogeneity might potentially be recovered from the statistics of a seismic reflection image using this model. Finally, we present a Monte Carlo inversion strategy to estimate these parameters and we show examples of its application at two different source frequencies and using two different sets of prior information. Our results indicate that the inverse problem is inherently non-unique and that many different combinations of the vertical and lateral correlation lengths describing the velocity heterogeneity can yield seismic images with the same 2-D autocorrelation structure. The ratio of all of these possible combinations of vertical and lateral correlation lengths, however, remains roughly constant which indicates that, without additional prior information, the aspect ratio is the only parameter describing the stochastic seismic velocity structure that can be reliably recovered.

Durable, Cost-Effective Pavement Markings Phase I: Synthesis of Current Reseaech, June 2001

Pavement marking technology is a continually evolving subject. There are numerous types of materials used in the field today, including (but not limited to) paint, epoxy, tape, and thermoplastic. Each material has its own set of unique characteristics related to durability, retroreflectivity, installation cost, and life-cycle cost. The Iowa Highway Research Board was interested in investigating the possibility of developing an ongoing program to evaluate the various products used in pavement marking. This potential program would maintain a database of performance and cost information to assist state and local agencies in determining which materials and placement methods are most appropriate for their use. The Center for Transportation Research and Education at Iowa State University has completed Phase I of this research: to identify the current practice and experiences from around the United States to recommend a further course of action for the State of Iowa. There has been a significant amount of research completed in the last several years. Research from Michigan, Pennsylvania, South Dakota, Ohio, and Alaska all had some common findings: white markings are more retroreflective than yellow markings; paint is by-and-large the least expensive material; paint tends to degrade faster than other materials; thermoplastic and tapes had higher retroreflective characteristics. Perhaps the most significant program going on in the area of pavement markings is the National Transportation Product Evaluation Program (NTPEP). This is an ongoing research program jointly conducted by the American Association of State Highway and Transportation Officials and its member states. Field and lab tests on numerous types of pavement marking materials are being conducted at sites representing four climatological areas. These results are published periodically for use by any jurisdiction interested in pavement marking materials performance. At this time, it is recommended that the State of Iowa not embark on a test deck evaluation program. Instead, close attention should be paid to the ongoing evaluations of the NTPEP program. Materials that fare well on the NTPEP test de cks should be considered for further field studies in Iowa.

Cost-effectiveness of temozolomide for the treatment of newly diagnosed glioblastoma multiforme.

AIM: To perform a systematic review on the costs and cost-effectiveness of concomitant and adjuvant temozolomide with radiotherapy for the treatment of newly diagnosed glioblastoma compared with initial radiotherapy alone. METHODS: Electronic databases were searched for relevant publications on costs and cost-effectiveness until October 2008. RESULTS: We found four relevant clinical trials, one cost study and two economic models. The mean survival benefit in the radiotherapy plus temozolomide group varied between 0.21 and 0.25 life-years. Treatment costs were between 27,365 euros and 39,092 euros. The costs of temozolomide amounted to approximately 40% of the total treatment costs. The incremental cost-effectiveness ratios found in the literature were 37,361 euros per life-year gained and 42,912 euros per quality-adjusted life-year gained. However, the models are not comparable because different outcomes are used (i.e., life-years and quality-adjusted life-years). CONCLUSION: Although the models are not comparable according to outcome, the incremental cost-effectiveness ratios found are within acceptable ranges. We concluded that despite the high temozolomide acquisition costs, the costs per life-year gained and the costs per quality-adjusted life-year gained are comparable with other accepted first-line treatments with chemotherapy in patients with cancer.

Bio-electrical impedance analysis for estimation of fat-free mass and muscle mass in cystic fibrosis patients.

The nutritional status of cystic fibrosis (CF) patients has to be regularly evaluated and alimentary support instituted when indicated. Bio-electrical impedance analysis (BIA) is a recent method for determining body composition. The present study evaluates its use in CF patients without any clinical sign of malnutrition. Thirty-nine patients with CF and 39 healthy subjects aged 6-24 years were studied. Body density and mid-arm muscle circumference were determined by anthropometry and skinfold measurements. Fat-free mass was calculated taking into account the body density. Muscle mass was obtained from the urinary creatinine excretion rate. The resistance index was calculated by dividing the square of the subject's height by the body impedance. We show that fat-free mass, mid-arm muscle circumference and muscle mass are each linearly correlated to the resistance index and that the regression equations are similar for both CF patients and healthy subjects.

A comment on the cost of capital for investments with non-homogeneous components

In this paper, the expression for the cost of capital is derived when net and replacement investments exhibit differences in their effective prices due to a different fiscal treatment. It is shown that, contrary to previous results in the literature, the cost of capital should be constructed under an opportunity cost criterion rather than a historical one. This result has some important economic consequences, since the optimizing firm will take into account not only the effective price for the new investments but also consider the opportunity cost of replacing them.

User cost of capital with delayed investment grants

The usual assumption when considering investment grants is that grant payments are automatic when investments are undertaken. However, evidence from case studies shows that there can exist some time lag until funds are received by granted firms. In this paper the effects of delays in grant payments on the optimal investment policy of the firm are analyzed. It is shown how these delays lead not only to a higher financing cost but to an effective reduction in the investment grant rate, and in some cases, how benefits from investment grants could be canceled due to interactions with tax effects.

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

Osteoporotic fracture risk in elderly women: estimation with quantitative heel US and clinical risk factors

PURPOSE: To derive a prediction rule by using prospectively obtained clinical and bone ultrasonographic (US) data to identify elderly women at risk for osteoporotic fractures. MATERIALS AND METHODS: The study was approved by the Swiss Ethics Committee. A prediction rule was computed by using data from a 3-year prospective multicenter study to assess the predictive value of heel-bone quantitative US in 6174 Swiss women aged 70-85 years. A quantitative US device to calculate the stiffness index at the heel was used. Baseline characteristics, known risk factors for osteoporosis and fall, and the quantitative US stiffness index were used to elaborate a predictive rule for osteoporotic fracture. Predictive values were determined by using a univariate Cox model and were adjusted with multivariate analysis. RESULTS: There were five risk factors for the incidence of osteoporotic fracture: older age (>75 years) (P < .001), low heel quantitative US stiffness index (<78%) (P < .001), history of fracture (P = .001), recent fall (P = .001), and a failed chair test (P = .029). The score points assigned to these risk factors were as follows: age, 2 (3 if age > 80 years); low quantitative US stiffness index, 5 (7.5 if stiffness index < 60%); history of fracture, 1; recent fall, 1.5; and failed chair test, 1. The cutoff value to obtain a high sensitivity (90%) was 4.5. With this cutoff, 1464 women were at lower risk (score, <4.5) and 4710 were at higher risk (score, >or=4.5) for fracture. Among the higher-risk women, 6.1% had an osteoporotic fracture, versus 1.8% of women at lower risk. Among the women who had a hip fracture, 90% were in the higher-risk group. CONCLUSION: A prediction rule obtained by using quantitative US stiffness index and four clinical risk factors helped discriminate, with high sensitivity, women at higher versus those at lower risk for osteoporotic fracture.

Validation of a wrist monitor for accurate estimation of RR intervals during sleep.

While the incidence of sleep disorders is continuously increasing in western societies, there is a clear demand for technologies to asses sleep-related parameters in ambulatory scenarios. The present study introduces a novel concept of accurate sensor to measure RR intervals via the analysis of photo-plethysmographic signals recorded at the wrist. In a cohort of 26 subjects undergoing full night polysomnography, the wrist device provided RR interval estimates in agreement with RR intervals as measured from standard electrocardiographic time series. The study showed an overall agreement between both approaches of 0.05 ± 18 ms. The novel wrist sensor opens the door towards a new generation of comfortable and easy-to-use sleep monitors.

Development and application of a one-step low cost procedure to concentrate viruses from seawater samples

A novel and simple procedure for concentrating adenoviruses from seawater samples is described. The technique entails the adsorption of viruses to pre-flocculated skimmed milk proteins, allowing the flocs to sediment by gravity, and dissolving the separated sediment in phosphate buffer. Concentrated virus may be detected by PCR techniques following nucleic acid extraction. The method requires no specialized equipment other than that usually available in routine public health laboratories, and due to its straightforwardness it allows the processing of a larger number of water samples simultaneously. The usefulness of the method was demonstrated in concentration of virus in multiple seawater samples during a survey of adenoviruses in coastal waters.

Whole-rat protein content estimation: applicability of the Nx6.25 factor

The amino acid composition of the protein from three strains of rat (Wistar, Zucker lean and Zucker obese), subjected to reference and high-fat diets has been used to determine the mean empirical formula, molecular weight and N content of whole-rat protein. The combined whole protein of the rat was uniform for the six experimental groups, containing an estimate of 17.3% N and a mean aminoacyl residue molecular weight of 103.7. This suggests that the appropriate protein factor for the calculation of rat protein from its N content should be 5.77 instead of the classical 6.25. In addition, an estimate of the size of the non-protein N mass in the whole rat gave a figure in the range of 5.5 % of all N. The combination of the two calculations gives a protein factor of 5.5 for the conversion of total N into rat protein.