Pricing derivatives with stochastic volatility

This Ph.D. thesis contains 4 essays in mathematical finance with a focus on pricing Asian option (Chapter 4), pricing futures and futures option (Chapter 5 and Chapter 6) and time dependent volatility in futures option (Chapter 7). In Chapter 4, the applicability of the Albrecher et al.(2005)'s comonotonicity approach was investigated in the context of various benchmark models for equities and com- modities. Instead of classical Levy models as in Albrecher et al.(2005), the focus is the Heston stochastic volatility model, the constant elasticity of variance (CEV) model and the Schwartz (1997) two-factor model. It is shown that the method delivers rather tight upper bounds for the prices of Asian Options in these models and as a by-product delivers super-hedging strategies which can be easily implemented. In Chapter 5, two types of three-factor models were studied to give the value of com- modities futures contracts, which allow volatility to be stochastic. Both these two models have closed-form solutions for futures contracts price. However, it is shown that Model 2 is better than Model 1 theoretically and also performs very well empiri- cally. Moreover, Model 2 can easily be implemented in practice. In comparison to the Schwartz (1997) two-factor model, it is shown that Model 2 has its unique advantages; hence, it is also a good choice to price the value of commodity futures contracts. Fur- thermore, if these two models are used at the same time, a more accurate price for commodity futures contracts can be obtained in most situations. In Chapter 6, the applicability of the asymptotic approach developed in Fouque et al.(2000b) was investigated for pricing commodity futures options in a Schwartz (1997) multi-factor model, featuring both stochastic convenience yield and stochastic volatility. It is shown that the zero-order term in the expansion coincides with the Schwartz (1997) two-factor term, with averaged volatility, and an explicit expression for the first-order correction term is provided. With empirical data from the natural gas futures market, it is also demonstrated that a significantly better calibration can be achieved by using the correction term as compared to the standard Schwartz (1997) two-factor expression, at virtually no extra effort. In Chapter 7, a new pricing formula is derived for futures options in the Schwartz (1997) two-factor model with time dependent spot volatility. The pricing formula can also be used to find the result of the time dependent spot volatility with futures options prices in the market. Furthermore, the limitations of the method that is used to find the time dependent spot volatility will be explained, and it is also shown how to make sure of its accuracy.

Mining and Energy Boom, Dutch Disease and Informality in Colombia: a DSGE Approach

The paper develops a Dynamic Stochastic General Equilibrium (DSGE) model, which assesses the macroeconomic and labor market effects derived from simulating a positive shock to the stochastic component of the mining-energy sector productivity. Calibrating the model for the Colombian economy, this shock generates a whole increase in formal wages and a raise in tax revenues, expanding total consumption of the household members. These facts increase non-tradable goods prices relative to tradable goods prices, then real exchange rate decreases (appreciation) and occurs a displacement of productive resources from the tradable (manufacturing) sector to the non-tradable sector, followed by an increase in formal GDP and formal job gains. This situation makes the formal sector to absorb workers from the informal sector through the non-tradable formal subsector, which causes informal GDP to go down. As a consequence, in the net consumption falls for informal workers, which leads some members of the household not to offer their labor force in the informal sector but instead they prefer to keep unemployed. Therefore, the final result on the labor market is a decrease in the number of informal workers, of which a part are in the formal sector and the rest are unemployed.

THE STOCHASTIC NAVIER STOKES EQUATIONS FOR HEAT CONDUCTING, COMPRESSIBLE FLUIDS

This dissertation is devoted to the equations of motion governing the evolution of a fluid or gas at the macroscopic scale. The classical model is a PDE description known as the Navier-Stokes equations. The behavior of solutions is notoriously complex, leading many in the scientific community to describe fluid mechanics using a statistical language. In the physics literature, this is often done in an ad-hoc manner with limited precision about the sense in which the randomness enters the evolution equation. The stochastic PDE community has begun proposing precise models, where a random perturbation appears explicitly in the evolution equation. Although this has been an active area of study in recent years, the existing literature is almost entirely devoted to incompressible fluids. The purpose of this thesis is to take a step forward in addressing this statistical perspective in the setting of compressible fluids. In particular, we study the well posedness for the corresponding system of Stochastic Navier Stokes equations, satisfied by the density, velocity, and temperature. The evolution of the momentum involves a random forcing which is Brownian in time and colored in space. We allow for multiplicative noise, meaning that spatial correlations may depend locally on the fluid variables. Our main result is a proof of global existence of weak martingale solutions to the Cauchy problem set within a bounded domain, emanating from large initial datum. The proof involves a mix of deterministic and stochastic analysis tools. Fundamentally, the approach is based on weak compactness techniques from the deterministic theory combined with martingale methods. Four layers of approximate stochastic PDE's are built and analyzed. A careful study of the probability laws of our approximating sequences is required. We prove appropriate tightness results and appeal to a recent generalization of the Skorohod theorem. This ultimately allows us to deduce analogues of the weak compactness tools of Lions and Feireisl, appropriately interpreted in the stochastic setting.

Multi-level, Multi-stage and Stochastic Optimization Models for Energy Conservation in Buildings for Federal, State and Local Agencies

Energy Conservation Measure (ECM) project selection is made difficult given real-world constraints, limited resources to implement savings retrofits, various suppliers in the market and project financing alternatives. Many of these energy efficient retrofit projects should be viewed as a series of investments with annual returns for these traditionally risk-averse agencies. Given a list of ECMs available, federal, state and local agencies must determine how to implement projects at lowest costs. The most common methods of implementation planning are suboptimal relative to cost. Federal, state and local agencies can obtain greater returns on their energy conservation investment over traditional methods, regardless of the implementing organization. This dissertation outlines several approaches to improve the traditional energy conservations models. Any public buildings in regions with similar energy conservation goals in the United States or internationally can also benefit greatly from this research. Additionally, many private owners of buildings are under mandates to conserve energy e.g., Local Law 85 of the New York City Energy Conservation Code requires any building, public or private, to meet the most current energy code for any alteration or renovation. Thus, both public and private stakeholders can benefit from this research. The research in this dissertation advances and presents models that decision-makers can use to optimize the selection of ECM projects with respect to the total cost of implementation. A practical application of a two-level mathematical program with equilibrium constraints (MPEC) improves the current best practice for agencies concerned with making the most cost-effective selection leveraging energy services companies or utilities. The two-level model maximizes savings to the agency and profit to the energy services companies (Chapter 2). An additional model presented leverages a single congressional appropriation to implement ECM projects (Chapter 3). Returns from implemented ECM projects are used to fund additional ECM projects. In these cases, fluctuations in energy costs and uncertainty in the estimated savings severely influence ECM project selection and the amount of the appropriation requested. A risk aversion method proposed imposes a minimum on the number of “of projects completed in each stage. A comparative method using Conditional Value at Risk is analyzed. Time consistency was addressed in this chapter. This work demonstrates how a risk-based, stochastic, multi-stage model with binary decision variables at each stage provides a much more accurate estimate for planning than the agency’s traditional approach and deterministic models. Finally, in Chapter 4, a rolling-horizon model allows for subadditivity and superadditivity of the energy savings to simulate interactive effects between ECM projects. The approach makes use of inequalities (McCormick, 1976) to re-express constraints that involve the product of binary variables with an exact linearization (related to the convex hull of those constraints). This model additionally shows the benefits of learning between stages while remaining consistent with the single congressional appropriations framework.

Texture-Detail Preservation Measurement in Camera Phones: An Updated Approach

Recent advances in mobile phone cameras have poised them to take over compact hand-held cameras as the consumer’s preferred camera option. Along with advances in the number of pixels, motion blur removal, face-tracking, and noise reduction algorithms have significant roles in the internal processing of the devices. An undesired effect of severe noise reduction is the loss of texture (i.e. low-contrast fine details) of the original scene. Current established methods for resolution measurement fail to accurately portray the texture loss incurred in a camera system. The development of an accurate objective method to identify the texture preservation or texture reproduction capability of a camera device is important in this regard. The ‘Dead Leaves’ target has been used extensively as a method to measure the modulation transfer function (MTF) of cameras that employ highly non-linear noise-reduction methods. This stochastic model consists of a series of overlapping circles with radii r distributed as r−3, and having uniformly distributed gray level, which gives an accurate model of occlusion in a natural setting and hence mimics a natural scene. This target can be used to model the texture transfer through a camera system when a natural scene is captured. In the first part of our study we identify various factors that affect the MTF measured using the ‘Dead Leaves’ chart. These include variations in illumination, distance, exposure time and ISO sensitivity among others. We discuss the main differences of this method with the existing resolution measurement techniques and identify the advantages. In the second part of this study, we propose an improvement to the current texture MTF measurement algorithm. High frequency residual noise in the processed image contains the same frequency content as fine texture detail, and is sometimes reported as such, thereby leading to inaccurate results. A wavelet thresholding based denoising technique is utilized for modeling the noise present in the final captured image. This updated noise model is then used for calculating an accurate texture MTF. We present comparative results for both algorithms under various image capture conditions.

Development of new scenario decomposition techniques for linear and nonlinear stochastic programming

Une approche classique pour traiter les problèmes d’optimisation avec incertitude à deux- et multi-étapes est d’utiliser l’analyse par scénario. Pour ce faire, l’incertitude de certaines données du problème est modélisée par vecteurs aléatoires avec des supports finis spécifiques aux étapes. Chacune de ces réalisations représente un scénario. En utilisant des scénarios, il est possible d’étudier des versions plus simples (sous-problèmes) du problème original. Comme technique de décomposition par scénario, l’algorithme de recouvrement progressif est une des méthodes les plus populaires pour résoudre les problèmes de programmation stochastique multi-étapes. Malgré la décomposition complète par scénario, l’efficacité de la méthode du recouvrement progressif est très sensible à certains aspects pratiques, tels que le choix du paramètre de pénalisation et la manipulation du terme quadratique dans la fonction objectif du lagrangien augmenté. Pour le choix du paramètre de pénalisation, nous examinons quelques-unes des méthodes populaires, et nous proposons une nouvelle stratégie adaptive qui vise à mieux suivre le processus de l’algorithme. Des expériences numériques sur des exemples de problèmes stochastiques linéaires multi-étapes suggèrent que la plupart des techniques existantes peuvent présenter une convergence prématurée à une solution sous-optimale ou converger vers la solution optimale, mais avec un taux très lent. En revanche, la nouvelle stratégie paraît robuste et efficace. Elle a convergé vers l’optimalité dans toutes nos expériences et a été la plus rapide dans la plupart des cas. Pour la question de la manipulation du terme quadratique, nous faisons une revue des techniques existantes et nous proposons l’idée de remplacer le terme quadratique par un terme linéaire. Bien que qu’il nous reste encore à tester notre méthode, nous avons l’intuition qu’elle réduira certaines difficultés numériques et théoriques de la méthode de recouvrement progressif.

Development of new scenario decomposition techniques for linear and nonlinear stochastic programming

Une approche classique pour traiter les problèmes d’optimisation avec incertitude à deux- et multi-étapes est d’utiliser l’analyse par scénario. Pour ce faire, l’incertitude de certaines données du problème est modélisée par vecteurs aléatoires avec des supports finis spécifiques aux étapes. Chacune de ces réalisations représente un scénario. En utilisant des scénarios, il est possible d’étudier des versions plus simples (sous-problèmes) du problème original. Comme technique de décomposition par scénario, l’algorithme de recouvrement progressif est une des méthodes les plus populaires pour résoudre les problèmes de programmation stochastique multi-étapes. Malgré la décomposition complète par scénario, l’efficacité de la méthode du recouvrement progressif est très sensible à certains aspects pratiques, tels que le choix du paramètre de pénalisation et la manipulation du terme quadratique dans la fonction objectif du lagrangien augmenté. Pour le choix du paramètre de pénalisation, nous examinons quelques-unes des méthodes populaires, et nous proposons une nouvelle stratégie adaptive qui vise à mieux suivre le processus de l’algorithme. Des expériences numériques sur des exemples de problèmes stochastiques linéaires multi-étapes suggèrent que la plupart des techniques existantes peuvent présenter une convergence prématurée à une solution sous-optimale ou converger vers la solution optimale, mais avec un taux très lent. En revanche, la nouvelle stratégie paraît robuste et efficace. Elle a convergé vers l’optimalité dans toutes nos expériences et a été la plus rapide dans la plupart des cas. Pour la question de la manipulation du terme quadratique, nous faisons une revue des techniques existantes et nous proposons l’idée de remplacer le terme quadratique par un terme linéaire. Bien que qu’il nous reste encore à tester notre méthode, nous avons l’intuition qu’elle réduira certaines difficultés numériques et théoriques de la méthode de recouvrement progressif.

Phosphate Regulated Proteins Of Xanthomonas Citri Subsp. Citri: A Proteomic Approach.

Xanthomonas citri subsp. citri (X. citri) is the causative agent of the citrus canker, a disease that affects several citrus plants in Brazil and across the world. Although many studies have demonstrated the importance of genes for infection and pathogenesis in this bacterium, there are no data related to phosphate uptake and assimilation pathways. To identify the proteins that are involved in the phosphate response, we performed a proteomic analysis of X. citri extracts after growth in three culture media with different phosphate concentrations. Using mass spectrometry and bioinformatics analysis, we showed that X. citri conserved orthologous genes from Pho regulon in Escherichia coli, including the two-component system PhoR/PhoB, ATP binding cassette (ABC transporter) Pst for phosphate uptake, and the alkaline phosphatase PhoA. Analysis performed under phosphate starvation provided evidence of the relevance of the Pst system for phosphate uptake, as well as both periplasmic binding proteins, PhoX and PstS, which were formed in high abundance. The results from this study are the first evidence of the Pho regulon activation in X. citri and bring new insights for studies related to the bacterial metabolism and physiology. Biological significance Using proteomics and bioinformatics analysis we showed for the first time that the phytopathogenic bacterium X. citri conserves a set of proteins that belong to the Pho regulon, which are induced during phosphate starvation. The most relevant in terms of conservation and up-regulation were the periplasmic-binding proteins PstS and PhoX from the ABC transporter PstSBAC for phosphate, the two-component system composed by PhoR/PhoB and the alkaline phosphatase PhoA.

A New Extraction Approach To Correct The Effect Of Apparent Increase In The Secoiridoid Content After Filtration Of Virgin Olive Oil.

In the current study, a new approach has been developed for correcting the effect that moisture reduction after virgin olive oil (VOO) filtration exerts on the apparent increase of the secoiridoid content by using an internal standard during extraction. Firstly, two main Spanish varieties (Picual and Hojiblanca) were submitted to industrial filtration of VOOs. Afterwards, the moisture content was determined in unfiltered and filtered VOOs, and liquid-liquid extraction of phenolic compounds was performed using different internal standards. The resulting extracts were analyzed by HPLC-ESI-TOF/MS, in order to gain maximum information concerning the phenolic profiles of the samples under study. The reduction effect of filtration on the moisture content, phenolic alcohols, and flavones was confirmed at the industrial scale. Oleuropein was chosen as internal standard and, for the first time, the apparent increase of secoiridoids in filtered VOO was corrected, using a correction coefficient (Cc) calculated from the variation of internal standard area in filtered and unfiltered VOO during extraction. This approach gave the real concentration of secoiridoids in filtered VOO, and clarified the effect of the filtration step on the phenolic fraction. This finding is of great importance for future studies that seek to quantify phenolic compounds in VOOs.

The Crystal-t Algorithm: A New Approach To Calculate The Sle Of Lipidic Mixtures Presenting Solid Solutions.

Lipidic mixtures present a particular phase change profile highly affected by their unique crystalline structure. However, classical solid-liquid equilibrium (SLE) thermodynamic modeling approaches, which assume the solid phase to be a pure component, sometimes fail in the correct description of the phase behavior. In addition, their inability increases with the complexity of the system. To overcome some of these problems, this study describes a new procedure to depict the SLE of fatty binary mixtures presenting solid solutions, namely the Crystal-T algorithm. Considering the non-ideality of both liquid and solid phases, this algorithm is aimed at the determination of the temperature in which the first and last crystal of the mixture melts. The evaluation is focused on experimental data measured and reported in this work for systems composed of triacylglycerols and fatty alcohols. The liquidus and solidus lines of the SLE phase diagrams were described by using excess Gibbs energy based equations, and the group contribution UNIFAC model for the calculation of the activity coefficients of both liquid and solid phases. Very low deviations of theoretical and experimental data evidenced the strength of the algorithm, contributing to the enlargement of the scope of the SLE modeling.

Effects Of Therapeutic Approach On The Neonatal Evolution Of Very Low Birth Weight Infants With Patent Ductus Arteriosus.

To analyze the effects of treatment approach on the outcomes of newborns (birth weight [BW] < 1,000 g) with patent ductus arteriosus (PDA), from the Brazilian Neonatal Research Network (BNRN) on: death, bronchopulmonary dysplasia (BPD), severe intraventricular hemorrhage (IVH III/IV), retinopathy of prematurity requiring surgical (ROPsur), necrotizing enterocolitis requiring surgery (NECsur), and death/BPD. This was a multicentric, cohort study, retrospective data collection, including newborns (BW < 1000 g) with gestational age (GA) < 33 weeks and echocardiographic diagnosis of PDA, from 16 neonatal units of the BNRN from January 1, 2010 to Dec 31, 2011. Newborns who died or were transferred until the third day of life, and those with presence of congenital malformation or infection were excluded. Groups: G1 - conservative approach (without treatment), G2 - pharmacologic (indomethacin or ibuprofen), G3 - surgical ligation (independent of previous treatment). Factors analyzed: antenatal corticosteroid, cesarean section, BW, GA, 5 min. Apgar score < 4, male gender, Score for Neonatal Acute Physiology Perinatal Extension (SNAPPE II), respiratory distress syndrome (RDS), late sepsis (LS), mechanical ventilation (MV), surfactant (< 2 h of life), and time of MV. death, O2 dependence at 36 weeks (BPD36wks), IVH III/IV, ROPsur, NECsur, and death/BPD36wks. Student's t-test, chi-squared test, or Fisher's exact test; Odds ratio (95% CI); logistic binary regression and backward stepwise multiple regression. Software: MedCalc (Medical Calculator) software, version 12.1.4.0. p-values < 0.05 were considered statistically significant. 1,097 newborns were selected and 494 newborns were included: G1 - 187 (37.8%), G2 - 205 (41.5%), and G3 - 102 (20.6%). The highest mortality was observed in G1 (51.3%) and the lowest in G3 (14.7%). The highest frequencies of BPD36wks (70.6%) and ROPsur were observed in G3 (23.5%). The lowest occurrence of death/BPD36wks occurred in G2 (58.0%). Pharmacological (OR 0.29; 95% CI: 0.14-0.62) and conservative (OR 0.34; 95% CI: 0.14-0.79) treatments were protective for the outcome death/BPD36wks. The conservative approach of PDA was associated to high mortality, the surgical approach to the occurrence of BPD36wks and ROPsur, and the pharmacological treatment was protective for the outcome death/BPD36wks.

Applying The Maternal Near Miss Approach For The Evaluation Of Quality Of Obstetric Care: A Worked Example From A Multicenter Surveillance Study.

To assess quality of care of women with severe maternal morbidity and to identify associated factors. This is a national multicenter cross-sectional study performing surveillance for severe maternal morbidity, using the World Health Organization criteria. The expected number of maternal deaths was calculated with the maternal severity index (MSI) based on the severity of complication, and the standardized mortality ratio (SMR) for each center was estimated. Analyses on the adequacy of care were performed. 17 hospitals were classified as providing adequate and 10 as nonadequate care. Besides almost twofold increase in maternal mortality ratio, the main factors associated with nonadequate performance were geographic difficulty in accessing health services (P < 0.001), delays related to quality of medical care (P = 0.012), absence of blood derivatives (P = 0.013), difficulties of communication between health services (P = 0.004), and any delay during the whole process (P = 0.039). This is an example of how evaluation of the performance of health services is possible, using a benchmarking tool specific to Obstetrics. In this study the MSI was a useful tool for identifying differences in maternal mortality ratios and factors associated with nonadequate performance of care.

A Modified Acidic Approach For Dna Extraction From Plant Species Containing High Levels Of Secondary Metabolites.

Purified genomic DNA can be difficult to obtain from some plant species because of the presence of impurities such as polysaccharides, which are often co-extracted with DNA. In this study, we developed a fast, simple, and low-cost protocol for extracting DNA from plants containing high levels of secondary metabolites. This protocol does not require the use of volatile toxic reagents such as mercaptoethanol, chloroform, or phenol and allows the extraction of high-quality DNA from wild and cultivated tropical species.

A Brazilian Original Pedagogical Approach To The Teaching Of Neurology.

The two-arm Clinical Decisions/Diagnostic Workshop (CD/DW) approach to undergraduate medical education has been successfully used in Brazil. Present the CD/DW approach to the teaching of stroke, with the results of its pre-experimental application and of a comparative study with the traditional lecture-case discussion approach. Application of two questionnaires (opinion and Knowledge-Attitudes-Perceptions-KAP) to investigate the non-inferiority of the CD/DW approach. The method was well accepted by teachers and students alike, the main drawback being the necessarily long time for its completion by the students, a feature that may better cater for different educational needs. The comparative test showed the CD/DW approach to lead to slightly higher cognitive acquisition as opposed to the traditional method, clearly showing its non-inferiority status. The CD/DW approach seems to be another option for teaching neurology in undergraduate medical education, with the bonus of respecting each learner`s time.

Systemic Granulomatous Diseases Associated With Multiple Palpable Masses That May Involve The Breast: Case Presentation And An Approach To The Differential Diagnosis.

Palpable mass is a common complaint presented to the breast surgeon. It is very uncommon for patients to report breast mass associated with palpable masses in other superficial structures. When these masses are related to systemic granulomatous diseases, the diagnosis and initiation of specific therapy can be challenging. The purpose of this paper is to report a case initially assessed by the breast surgeon and ultimately diagnosed as granulomatous variant of T-cell lymphoma, and discuss the main systemic granulomatous diseases associated with palpable masses involving the breast.