Application of theoretical models to financial innovation

The present paper is aimed at providing a general strategic overview of the existing theoretical models that have applications in the field of financial innovation. Whereas most financialdevelopments have relied upon traditional economic tools, a new stream of research is defining a novel paradigm in which mathematical models from diverse scientific disciplines are being applied to conceptualize and explain economic and financial behavior. Indeed, terms such as ‘econophysics’ or ‘quantum finance’ have recently appeared to embrace efforts in this direction. As a first contact with such research, the project will present a brief description of some of the main theoretical models that have applications in finance and economics, and will try to present, if possible, potential new applications to particular areas in financial analysis, or new applicable models. As a result, emphasiswill be put on the implications of this research for the financial sector and its future dynamics.

Multidelayed random walks: Theory and application to the neolithic transition in Europe

We present a model in which particles (or individuals of a biological population) disperse with a rest time between consecutive motions (or migrations) which may take several possible values from a discrete set. Particles (or individuals) may also react (or reproduce). We derive a new equation for the effective rest time T˜ of the random walk. Application to the neolithic transition in Europe makes it possible to derive more realistic theoretical values for its wavefront speed than those following from the single-delayed framework presented previously [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)]. The new results are consistent with the archaeological observations of this important historical process

Scale effect in hazard assessment - application to daily rainfall

Daily precipitation is recorded as the total amount of water collected by a rain-gauge in 24h. Events are modelled as a Poisson process and the 24h precipitation by a Generalized Pareto Distribution (GPD) of excesses. Hazard assessment is complete when estimates of the Poisson rate and the distribution parameters, together with a measure of their uncertainty, are obtained. The shape parameter of the GPD determines the support of the variable: Weibull domain of attraction (DA) corresponds to finite support variables, as should be for natural phenomena. However, Fréchet DA has been reported for daily precipitation, which implies an infinite support and a heavy-tailed distribution. We use the fact that a log-scale is better suited to the type of variable analyzed to overcome this inconsistency, thus showing that using the appropriate natural scale can be extremely important for proper hazard assessment. The approach is illustrated with precipitation data from the Eastern coast of the Iberian Peninsula affected by severe convective precipitation. The estimation is carried out by using Bayesian techniques

Analysis of sensitivity with respect to a compositional parameter : A comment on 'Local sensitivity analysis for compositional data with application to soil texture in hydrologic modelling' by L. Loosvelt and co-authors

A comment about the article “Local sensitivity analysis for compositional data with application to soil texture in hydrologic modelling” writen by L. Loosvelt and co-authors. The present comment is centered in three specific points. The first one is related to the fact that the authors avoid the use of ilr-coordinates. The second one refers to some generalization of sensitivity analysis when input parameters are compositional. The third tries to show that the role of the Dirichlet distribution in the sensitivity analysis is irrelevant

Model for interevent times with long tails and multifractality in human communications: An application to financial trading

Social, technological, and economic time series are divided by events which are usually assumed to be random, albeit with some hierarchical structure. It is well known that the interevent statistics observed in these contexts differs from the Poissonian profile by being long-tailed distributed with resting and active periods interwoven. Understanding mechanisms generating consistent statistics has therefore become a central issue. The approach we present is taken from the continuous-time random-walk formalism and represents an analytical alternative to models of nontrivial priority that have been recently proposed. Our analysis also goes one step further by looking at the multifractal structure of the interevent times of human decisions. We here analyze the intertransaction time intervals of several financial markets. We observe that empirical data describe a subtle multifractal behavior. Our model explains this structure by taking the pausing-time density in the form of a superstatistics where the integral kernel quantifies the heterogeneous nature of the executed tasks. A stretched exponential kernel provides a multifractal profile valid for a certain limited range. A suggested heuristic analytical profile is capable of covering a broader region.

Fronts with continuous waiting-time distributions: Theory and application to virus infections

We generalize to arbitrary waiting-time distributions some results which were previously derived for discrete distributions. We show that for any two waiting-time distributions with the same mean delay time, that with higher dispersion will lead to a faster front. Experimental data on the speed of virus infections in a plaque are correctly explained by the theoretical predictions using a Gaussian delay-time distribution, which is more realistic for this system than the Dirac delta distribution considered previously [J. Fort and V. Méndez, Phys. Rev. Lett.89, 178101 (2002)]

Vertical cultural transmission effects on demic front propagation: Theory and application to the Neolithic transition in Europe

It is shown that Lotka-Volterra interaction terms are not appropriate to describe vertical cultural transmission. Appropriate interaction terms are derived and used to compute the effect of vertical cultural transmission on demic front propagation. They are also applied to a specific example, the Neolithic transition in Europe. In this example, it is found that the effect of vertical cultural transmission can be important (about 30%). On the other hand, simple models based on differential equations can lead to large errors (above 50%). Further physical, biophysical, and cross-disciplinary applications are outlined

A note on the application of integrals involving cyclic products kernels

A l'estadística de processos estocàstics i camps aleatoris, una funció de moments o un cumulant d'un estimador de la funció de correlació o de la densitat espectral sovint pot contenir una integral amb un producte cíclic de nuclis. En aquest treball es defineix i s'investiga aquesta classe d'integrals i es demostra la desigualtat de Young-Hölder que permet estudiar el comportament asimptòtic de les esmentades integrals en la situació quan els nuclis depenen d'un pàràmetre. Es considera una aplicació al problema d'estimació de la funció de resposta en un sistema de Volterra.

Periodic orbits near a heteroclinic loop formed by one dimensional orbit and a 2-dimensional manifold: application to the charged collinear 3-body problem

The paper is devoted to the study of a type of differential systems which appear usually in the study of some Hamiltonian systems with 2 degrees of freedom. We prove the existence of infinitely many periodic orbits on each negative energy level. All these periodic orbits pass near the total collision. Finally we apply these results to study the existence of periodic orbits in the charged collinear 3–body problem.

Parametric and semiparametric estimation of sample selection models: an empirical application to the female labour force in Portugal

This comment corrects the errors in the estimation process that appear in Martins (2001). The first error is in the parametric probit estimation, as the previously presented results do not maximize the log-likelihood function. In the global maximum more variables become significant. As for the semiparametric estimation method, the kernel function used in Martins (2001) can take on both positive and negative values, which implies that the participation probability estimates may be outside the interval [0,1]. We have solved the problem by applying local smoothing in the kernel estimation, as suggested by Klein and Spady (1993).

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.

Can genetic algorithms explain experimental anomalies? An application to common property resources

It is common to find in experimental data persistent oscillations in the aggregate outcomes and high levels of heterogeneity in individual behavior. Furthermore, it is not unusual to find significant deviations from aggregate Nash equilibrium predictions. In this paper, we employ an evolutionary model with boundedly rational agents to explain these findings. We use data from common property resource experiments (Casari and Plott, 2003). Instead of positing individual-specific utility functions, we model decision makers as selfish and identical. Agent interaction is simulated using an individual learning genetic algorithm, where agents have constraints in their working memory, a limited ability to maximize, and experiment with new strategies. We show that the model replicates most of the patterns that can be found in common property resource experiments.

A proposal for a new specification for a conditionally heteroskedastic variance model: the Quadratic Moving-Average Conditional Heteroskedasticity and an application to the D. Mark-U.S. dollar Exchange Rate

Ever since the appearance of the ARCH model [Engle(1982a)], an impressive array of variance specifications belonging to the same class of models has emerged [i.e. Bollerslev's (1986) GARCH; Nelson's (1990) EGARCH]. This recent domain has achieved very successful developments. Nevertheless, several empirical studies seem to show that the performance of such models is not always appropriate [Boulier(1992)]. In this paper we propose a new specification: the Quadratic Moving Average Conditional heteroskedasticity model. Its statistical properties, such as the kurtosis and the symmetry, as well as two estimators (Method of Moments and Maximum Likelihood) are studied. Two statistical tests are presented, the first one tests for homoskedasticity and the second one, discriminates between ARCH and QMACH specification. A Monte Carlo study is presented in order to illustrate some of the theoretical results. An empirical study is undertaken for the DM-US exchange rate.

Hausman tests for inefficient estimators: application to demand for health care service (revised)

The Hausman (1978) test is based on the vector of differences of two estimators. It is usually assumed that one of the estimators is fully efficient, since this simplifies calculation of the test statistic. However, this assumption limits the applicability of the test, since widely used estimators such as the generalized method of moments (GMM) or quasi maximum likelihood (QML) are often not fully efficient. This paper shows that the test may easily be implemented, using well-known methods, when neither estimator is efficient. To illustrate, we present both simulation results as well as empirical results for utilization of health care services.

An input-output analysis of the "key" sectors in CO2 emissions from a production perspective: an application to the spanish economy

Here we present an approach that allows the identification of the "key" productive sectors responsible for CO2 emission. For this purpose, we develop an input–output methodology from a supply perspective. We focus on the impact of an increase in the value-added of the different productive sectors on total CO2 emissions and we identify the productive sectors responsible for the increase in CO2 emissions when there is an increase in the income of the economy. The approach shows the contribution of the various sectors to CO2 emission from a production perspective and allows us to identify the sectors that deserve more consideration for mitigation policies. This analysis is complementary to the input–output analysis from a demand perspective. The methodology is applied to the Spanish economy.