Activity autocorrelation in financial markets. A comparative study between several models

We study the activity, i.e., the number of transactions per unit time, of financial markets. Using the diffusion entropy technique we show that the autocorrelation of the activity is caused by the presence of peaks whose time distances are distributed following an asymptotic power law which ultimately recovers the Poissonian behavior. We discuss these results in comparison with ARCH models, stochastic volatility models and multi-agent models showing that ARCH and stochastic volatility models better describe the observed experimental evidences.Comment: 15 pages, 4 figure

Uncertain growth and the value of the future

For environmental problems such as global warming future costs must be balanced against present costs. This is traditionally done using an exponential function with a constant discount rate, which reduces the present value of future costs. The result is highly sensitive to the choice of discount rate and has generated a major controversy as to the urgency for immediate action. We study analytically several standard interest rate models from finance and compare their properties to empirical data. From historical time series for nominal interest rates and inflation covering 14 countries over hundreds of years, we find that extended periods of negative real interest rates are common, occurring in many epochs in all countries. This leads us to choose the Ornstein-Uhlenbeck model, in which real short run interest rates fluctuate stochastically and can become negative, even if they revert to a positive mean value. We solve the model in closed form and prove that the long-run discount rate is always less than the mean; indeed it can be zero or even negative, despite the fact that the mean short term interest rate is positive. We fit the parameters of the model to the data, and find that nine of the countries have positive long run discount rates while five have negative long-run discount rates. Even if one rejects the countries where hyperinflation has occurred, our results support the low discounting rate used in the Stern report over higher rates advocated by others.Comment: 8 pages, 4 figure

Statistical analysis and stochastic interest rate modelling for valuing the future with implications in climate change mitigation

High future discounting rates favor inaction on present expending while lower rates advise for a more immediate political action. A possible approach to this key issue in global economy is to take historical time series for nominal interest rates and inflation, and to construct then real interest rates and finally obtaining the resulting discount rate according to a specific stochastic model. Extended periods of negative real interest rates, in which inflation dominates over nominal rates, are commonly observed, occurring in many epochs and in all countries. This feature leads us to choose a well-known model in statistical physics, the Ornstein-Uhlenbeck model, as a basic dynamical tool in which real interest rates randomly fluctuate and can become negative, even if they tend to revert to a positive mean value. By covering 14 countries over hundreds of years we suggest different scenarios and include an error analysis in order to consider the impact of statistical uncertainty in our results. We find that only 4 of the countries have positive long-run discount rates while the other ten countries have negative rates. Even if one rejects the countries where hyperinflation has occurred, our results support the need to consider low discounting rates. The results provided by these fourteen countries significantly increase the priority of confronting global actions such as climate change mitigation. We finally extend the analysis by first allowing for fluctuations of the mean level in the Ornstein-Uhlenbeck model and secondly by considering modified versions of the Feller and lognormal models. In both cases, results remain basically unchanged thus demonstrating the robustness of the results presented.Comment: 29 pages, 5 figures, 5 tables. arXiv admin note: text overlap with arXiv:1311.406

The escape problem under stochastic volatility: the Heston model

We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts to solving the complete escape problem) as well as for the mean exit time. We also average the volatility in order to work out the problem for the return alone regardless volatility. We look over these results in terms of the dimensionless normal level of volatility --a ratio of the three parameters that appear in the Heston model-- and analyze their form in several assymptotic limits. Thus, for instance, we show that the mean exit time grows quadratically with large spans while for small spans the growth is systematically slower depending on the value of the normal level. We compare our results with those of the Wiener process and show that the assumption of stochastic volatility, in an apparent paradoxical way, increases survival and prolongs the escape time.Comment: 29 pages, 12 figure

Stochastic volatility and leverage effect

We prove that a wide class of correlated stochastic volatility models exactly measure an empirical fact in which past returns are anticorrelated with future volatilities: the so-called ``leverage effect''. This quantitative measure allows us to fully estimate all parameters involved and it will entail a deeper study on correlated stochastic volatility models with practical applications on option pricing and risk management.Comment: 4 pages, 2 figure

Introduction to the study of the iron mining, in the catalan and the Andorran Pyrenees

In the Catalan and in the Andorran Pyrenees, as in the ariegian one, there is an enormous conjunct ofold mining explotations, dedicated to the extraction and to the benefit of the iron minerals. This explotations had his principal apogee during the Middle and the Moderns Ages, and contributed to the development ofthe process ofthe obtainment ofiron called farga catala,na. As it's known, that metaHurgical process was initiality extended in Catalonia and in the Foix Country, and then it was propagated over aH the known world (MATAPERELLO and RIBA, 1993

Effect of garlic extract on seed germination, seedling health, and vigour of pathogen-infested wheat

The effect of garlic extract containing bioactive allicin on the germination and subsequent seedling vigour of pathogeninfested wheat seeds, was tested. The first aim was to characterize the antifungal activities of garlic extract and pure allicin, on the most frequently occurring wheat pathogens of the Helminthosporium genus (sensu lato) in Argentina. The second aim was to characterize the antifungal activities of garlic extract and pure allicin on moulds belonging to the natural endogenous microflora. Garlic extract showed fungicidal activity on the endogenous fungal contamination of the wheat seeds and particularly reduced the degree of disease caused by Bipolaris sorokiniana and Drechslera tritici-repentis. Allicin in garlic juice corrected the poor germination of wheat seeds caused by natural mycoflora of grain. Growth promoting activities of garlic juice on wheat seedling vigour was reported. Interestingly, the inoculum on naturally infected wheat seeds could be reduced with garlic juice as a seed dressing biofungicide, before sowing. In this study, we demonstrated the efficacy and the high control potential of garlic extract against seed-borne wheat fungi. Such results suggest that using garlic extract can minimise the risk of infection as well as minimise the risk of chemical fungicide exposure. On the basis of these results, scale-up to field trials using garlic extract and allicin as the dressing biofungicide before sowing for disinfection of wheat seeds, seems justified as a sustainable alternative to the use of chemical fungicides.Facultad de Ciencias Agrarias y ForestalesCentro de Investigaciones de Fitopatologí

Accounting for risk of non linear portfolios: a novel Fourier approach

The presence of non linear instruments is responsible for the emergence of non Gaussian features in the price changes distribution of realistic portfolios, even for Normally distributed risk factors. This is especially true for the benchmark Delta Gamma Normal model, which in general exhibits exponentially damped power law tails. We show how the knowledge of the model characteristic function leads to Fourier representations for two standard risk measures, the Value at Risk and the Expected Shortfall, and for their sensitivities with respect to the model parameters. We detail the numerical implementation of our formulae and we emphasizes the reliability and efficiency of our results in comparison with Monte Carlo simulation.Comment: 10 pages, 12 figures. Final version accepted for publication on Eur. Phys. J.

In vitro efficacy of garlic extract to control fungal pathogens of wheat

In vitro studies were carried out to investigate the inhibitory effect of allicin in garlic juice on hyphal growth and spore germination of Drechslera tritici-repetis, Bipolaris sorokiniana and Septoria tritici. The purpose was to investigate the possibility of developing an organic agriculture compatible garlic/allicin-based management strategy for the wheat fungal spotting complex. Allicin in garlic juice inhibited radial colony growth of all three pathogens on agar plates. Spore germination of all three pathogens was inhibited by allicin in garlic juice in seeded agar plates and in conidial suspensions. At high concentrations of allicin (>80 µg/ml) in garlic juice and pure (synthetic) allicin, conidia lysed. The minimum inhibitory amount of pure synthetic allicin which inhibited spore germination completely ranged between 80-120 µg/ml depending on fungal species. At 10 µg/ml Allicin caused morphological abnormalities in hyphae and conidia of D. tritici-repentis and B. sorokiniana. Allicin-treated hyphae were either collapsed, damaged or thinner when compared with the control. These results suggest that use of garlic juice is a promising, effective and environmentally friendly management measure against fungal pathogens that could be used in the production of an organically grown wheat crop.Facultad de Ciencias Agrarias y Forestale

Effect of garlic extract on seed germination, seedling health, and vigour of pathogen-infested wheat

The effect of garlic extract containing bioactive allicin on the germination and subsequent seedling vigour of pathogeninfested wheat seeds, was tested. The first aim was to characterize the antifungal activities of garlic extract and pure allicin, on the most frequently occurring wheat pathogens of the Helminthosporium genus (sensu lato) in Argentina. The second aim was to characterize the antifungal activities of garlic extract and pure allicin on moulds belonging to the natural endogenous microflora. Garlic extract showed fungicidal activity on the endogenous fungal contamination of the wheat seeds and particularly reduced the degree of disease caused by Bipolaris sorokiniana and Drechslera tritici-repentis. Allicin in garlic juice corrected the poor germination of wheat seeds caused by natural mycoflora of grain. Growth promoting activities of garlic juice on wheat seedling vigour was reported. Interestingly, the inoculum on naturally infected wheat seeds could be reduced with garlic juice as a seed dressing biofungicide, before sowing. In this study, we demonstrated the efficacy and the high control potential of garlic extract against seed-borne wheat fungi. Such results suggest that using garlic extract can minimise the risk of infection as well as minimise the risk of chemical fungicide exposure. On the basis of these results, scale-up to field trials using garlic extract and allicin as the dressing biofungicide before sowing for disinfection of wheat seeds, seems justified as a sustainable alternative to the use of chemical fungicides.Facultad de Ciencias Agrarias y ForestalesCentro de Investigaciones de Fitopatologí