An Eigenfunction Approach for Volatility Modeling.

In this paper, we introduce a new approach for volatility modeling in discrete and continuous time. We follow the stochastic volatility literature by assuming that the variance is a function of a state variable. However, instead of assuming that the loading function is ad hoc (e.g., exponential or affine), we assume that it is a linear combination of the eigenfunctions of the conditional expectation (resp. infinitesimal generator) operator associated to the state variable in discrete (resp. continuous) time. Special examples are the popular log-normal and square-root models where the eigenfunctions are the Hermite and Laguerre polynomials respectively. The eigenfunction approach has at least six advantages: i) it is general since any square integrable function may be written as a linear combination of the eigenfunctions; ii) the orthogonality of the eigenfunctions leads to the traditional interpretations of the linear principal components analysis; iii) the implied dynamics of the variance and squared return processes are ARMA and, hence, simple for forecasting and inference purposes; (iv) more importantly, this generates fat tails for the variance and returns processes; v) in contrast to popular models, the variance of the variance is a flexible function of the variance; vi) these models are closed under temporal aggregation.

American option valuation: implied calibration of GARCH pricing models

This study analyzes the issue of American option valuation when the underlying exhibits a GARCH-type volatility process. We propose the usage of Rubinstein's Edgeworth binomial tree (EBT) in contrast to simulation-based methods being considered in previous studies. The EBT-based valuation approach makes an implied calibration of the pricing model feasible. By empirically analyzing the pricing performance of American index and equity options, we illustrate the superiority of the proposed approach.

Reality check for volatility models

Asset allocation decisions and value at risk calculations rely strongly on volatility estimates. Volatility measures such as rolling window, EWMA, GARCH and stochastic volatility are used in practice. GARCH and EWMA type models that incorporate the dynamic structure of volatility and are capable of forecasting future behavior of risk should perform better than constant, rolling window volatility models. For the same asset the model that is the ‘best’ according to some criterion can change from period to period. We use the reality check test∗ to verify if one model out-performs others over a class of re-sampled time-series data. The test is based on re-sampling the data using stationary bootstrapping. For each re-sample we check the ‘best’ model according to two criteria and analyze the distribution of the performance statistics. We compare constant volatility, EWMA and GARCH models using a quadratic utility function and a risk management measurement as comparison criteria. No model consistently out-performs the benchmark.

Coordination and movement pathology: models of structure and function

Here we consider the role of abstract models in advancing our understanding of movement pathology. Models of movement coordination and control provide the frameworks necessary for the design and interpretation of studies of acquired and developmental disorders. These models do not however provide the resolution necessary to reveal the nature of the functional impairments that characterise specific movement pathologies. In addition, they do not provide a mapping between the structural bases of various pathologies and the associated disorders of movement. Current and prospective approaches to the study and treatment of movement disorders are discussed. It is argued that the appreciation of structure-function relationships, to which these approaches give rise, represents a challenge to current models of interlimb coordination, and a stimulus for their continued development. (C) 2002 Elsevier Science B.V. All rights reserved.

Stress correlation function evolution in lattice solid elasto-dynamic models of shear and fracture zones and earthquake prediction

It has been argued that power-law time-to-failure fits for cumulative Benioff strain and an evolution in size-frequency statistics in the lead-up to large earthquakes are evidence that the crust behaves as a Critical Point (CP) system. If so, intermediate-term earthquake prediction is possible. However, this hypothesis has not been proven. If the crust does behave as a CP system, stress correlation lengths should grow in the lead-up to large events through the action of small to moderate ruptures and drop sharply once a large event occurs. However this evolution in stress correlation lengths cannot be observed directly. Here we show, using the lattice solid model to describe discontinuous elasto-dynamic systems subjected to shear and compression, that it is for possible correlation lengths to exhibit CP-type evolution. In the case of a granular system subjected to shear, this evolution occurs in the lead-up to the largest event and is accompanied by an increasing rate of moderate-sized events and power-law acceleration of Benioff strain release. In the case of an intact sample system subjected to compression, the evolution occurs only after a mature fracture system has developed. The results support the existence of a physical mechanism for intermediate-term earthquake forecasting and suggest this mechanism is fault-system dependent. This offers an explanation of why accelerating Benioff strain release is not observed prior to all large earthquakes. The results prove the existence of an underlying evolution in discontinuous elasto-dynamic, systems which is capable of providing a basis for forecasting catastrophic failure and earthquakes.

Morphology, ultrastructure, and implied function of ciliated sensory structures on the developmental stages of Merizocotyle icopae (Monogenea : Monocotylidae)

Experimental infections were used to track the fate of the dorsal sensilla of Merizocotyle icopae (Monogenea: Monocotylidae) from nasal tissue of the shovelnose ray, Rhinobatos typus (Rhinobatidae). Scanning and transmission electron microscopy revealed that 3 types of uniciliate dorsal sensilla exist at different times in the development of the monogenean. Type 1 sensilla have little or no invagination where the cilium exits the distal end of the dendrite and possess a ring of epidermis surrounding the cilium distal to the invagination. Type 2 sensilla have a deep invagination where the cilium exits the dendrite. Type 3 sensilla can be distinguished from the other types by the shape of the dendrite. The larvae have predominantly Type I dorsal sensilla, most of which are lost approximately 24 h after infection and a few Type 2 sensilla, which are retained. Additional Type 2 sensilla (termed Adult Type 2 sensilla), which are slightly different morphologically from the Type 2 sensilla of the larvae, form in later stages of development. Numerous Type 3 sensilla are unique to the dorsal surface of adults. Loss of all Type I sensilla upon attachment to the host, R. typus, suggests that these may be chemo- or mechanoreceptors responsible for host location by the swimming infective larvae. Type 2 sensilla appear to be important in the larvae, juveniles, and adults whereas the modality mediated by Type 3 is specific to adults. (C) 2003 Wiley-Liss, Inc.

Options listing and the volatility of the underling asset: a study on the derivative market function

There are basic misunderstandings on derivative markets. Some professionals believe that they are a kind of casinos and have no utility for the investors. This work looks at the effects of options introduction in the Brazilian market, seeking for another benefit for this introduction: changes in the stocks risk leveI. Our results are the same found in the US and other markets: the options introduction reduces the stocks volatility. We also found that there is a slight indication that the volatility becames more stochastic with this alternative.

Volatility forecasting with range models: An evaluation of new alternatives to the CARR model

The aim of this paper is to analyze the forecasting ability of the CARR model proposed by Chou (2005) using the S&P 500. We extend the data sample, allowing for the analysis of different stock market circumstances and propose the use of various range estimators in order to analyze their forecasting performance. Our results show that there are two range-based models that outperform the forecasting ability of the GARCH model. The Parkinson model is better for upward trends and volatilities which are higher and lower than the mean while the CARR model is better for downward trends and mean volatilities.

Exploring the role of O-Mannosylation in the modulation of E-Cadherin function in Gastric Cancer cell line models

Dissertação de mestrado em Bioquímica Aplicada – Biomedicina

Are one factor logarithmic volatility models useful to fit the features of financial data? An application to microsoft data.

This paper provides empirical evidence that continuous time models with one factor of volatility, in some conditions, are able to fit the main characteristics of financial data. It also reports the importance of the feedback factor in capturing the strong volatility clustering of data, caused by a possible change in the pattern of volatility in the last part of the sample. We use the Efficient Method of Moments (EMM) by Gallant and Tauchen (1996) to estimate logarithmic models with one and two stochastic volatility factors (with and without feedback) and to select among them.

Well-posedness and invariant measures for HJM models with deterministic volatility and Lévy noise

We give sufficient conditions for existence, uniqueness and ergodicity of invariant measures for Musiela's stochastic partial differential equation with deterministic volatility and a Hilbert space valued driving Lévy noise. Conditions for the absence of arbitrage and for the existence of mild solutions are also discussed.

Identification of particular groups of microRNAs that positively or negatively impact on beta cell function in obese models of type 2 diabetes.

AIMS/HYPOTHESIS: MicroRNAs are key regulators of gene expression involved in health and disease. The goal of our study was to investigate the global changes in beta cell microRNA expression occurring in two models of obesity-associated type 2 diabetes and to assess their potential contribution to the development of the disease. METHODS: MicroRNA profiling of pancreatic islets isolated from prediabetic and diabetic db/db mice and from mice fed a high-fat diet was performed by microarray. The functional impact of the changes in microRNA expression was assessed by reproducing them in vitro in primary rat and human beta cells. RESULTS: MicroRNAs differentially expressed in both models of obesity-associated type 2 diabetes fall into two distinct categories. A group including miR-132, miR-184 and miR-338-3p displays expression changes occurring long before the onset of diabetes. Functional studies indicate that these expression changes have positive effects on beta cell activities and mass. In contrast, modifications in the levels of miR-34a, miR-146a, miR-199a-3p, miR-203, miR-210 and miR-383 primarily occur in diabetic mice and result in increased beta cell apoptosis. These results indicate that obesity and insulin resistance trigger adaptations in the levels of particular microRNAs to allow sustained beta cell function, and that additional microRNA deregulation negatively impacting on insulin-secreting cells may cause beta cell demise and diabetes manifestation. CONCLUSIONS/INTERPRETATION: We propose that maintenance of blood glucose homeostasis or progression toward glucose intolerance and type 2 diabetes may be determined by the balance between expression changes of particular microRNAs.

A general decomposition formula for derivative prices in stochastic volatility models

We see that the price of an european call option in a stochastic volatilityframework can be decomposed in the sum of four terms, which identifythe main features of the market that affect to option prices: the expectedfuture volatility, the correlation between the volatility and the noisedriving the stock prices, the market price of volatility risk and thedifference of the expected future volatility at different times. We alsostudy some applications of this decomposition.

Aggregations and Marginalization of GARCH and Stochastic Volatility Models

The GARCH and Stochastic Volatility paradigms are often brought into conflict as two competitive views of the appropriate conditional variance concept : conditional variance given past values of the same series or conditional variance given a larger past information (including possibly unobservable state variables). The main thesis of this paper is that, since in general the econometrician has no idea about something like a structural level of disaggregation, a well-written volatility model should be specified in such a way that one is always allowed to reduce the information set without invalidating the model. To this respect, the debate between observable past information (in the GARCH spirit) versus unobservable conditioning information (in the state-space spirit) is irrelevant. In this paper, we stress a square-root autoregressive stochastic volatility (SR-SARV) model which remains true to the GARCH paradigm of ARMA dynamics for squared innovations but weakens the GARCH structure in order to obtain required robustness properties with respect to various kinds of aggregation. It is shown that the lack of robustness of the usual GARCH setting is due to two very restrictive assumptions : perfect linear correlation between squared innovations and conditional variance on the one hand and linear relationship between the conditional variance of the future conditional variance and the squared conditional variance on the other hand. By relaxing these assumptions, thanks to a state-space setting, we obtain aggregation results without renouncing to the conditional variance concept (and related leverage effects), as it is the case for the recently suggested weak GARCH model which gets aggregation results by replacing conditional expectations by linear projections on symmetric past innovations. Moreover, unlike the weak GARCH literature, we are able to define multivariate models, including higher order dynamics and risk premiums (in the spirit of GARCH (p,p) and GARCH in mean) and to derive conditional moment restrictions well suited for statistical inference. Finally, we are able to characterize the exact relationships between our SR-SARV models (including higher order dynamics, leverage effect and in-mean effect), usual GARCH models and continuous time stochastic volatility models, so that previous results about aggregation of weak GARCH and continuous time GARCH modeling can be recovered in our framework.