Distribution of metals in several vineyards of North Italy: from soil to wine

Nowadays we live in densely populated regions and this leads to many environmental issues. Among all pollutants that human activities originate, metals are relevant because they can be potentially toxic for most of living beings. We studied the fate of Cd, Cr, Cu, Fe, Mn, Ni, Pb and Zn in a vineyard environment analysing samples of plant, wine and soil. Sites were chosen considering the type of wine produced, the type of cultivation (both organic and conventional agriculture) and the geographic location. We took vineyards that cultivate the same grape variety, the Trebbiano). We investigated 5 vineyards located in the Ravenna district (Italy): two on the Lamone Valley slopes, one in the area of river-bank deposits near Ravenna city, then a farm near Lugo and one near Bagnacavallo in interfluve regions. We carried out a very detailed characterization of soils in the sites, including the analysis of: pH, electric conductivity, texture, total carbonate and extimated content of dolomite, active carbonate, iron from ammonium oxalate, Iron Deficiency Chlorosis Index (IDCI), total nitrogen and organic carbon, available phosphorous, available potassium and Cation Exchange Capacity (CEC). Then we made the analysis of the bulk chemical composition and a DTPA extraction to determine the available fraction of elements in soils. All the sites have proper ground to cultivate, with already a good amount of nutrients, such as not needing strong fertilisations, but a vineyard on hills suffers from iron deficiency chlorosis due to the high level of active carbonate. We found some soils with much silica and little calcium oxide that confirm the marly sandstone substratum, while other soils have more calcium oxide and more aluminium oxide that confirm the argillaceous marlstone substratum. We found some critical situations, such as high concentrations of Chromium, especially in the farm near Lugo, and we noticed differences between organic vineyards and conventional ones: the conventional ones have a higher enrichment in soils of some metals (Copper and Zinc). Each metal accumulates differently in every single part of grapevines. We found differences between hill plants and lowland ones: behaviors of plants in metal accumulations seems to have patterns. Metals are more abundant in barks, then in leaves or sometimes in roots. Plants seem trying to remove excesses of metal storing them in bark. Two wines have excess of acetic acid and one conventional farm produces wine with content of Zinc over the Italian law limit. We already found evidence of high values relating them with uncontaminated environments, but more investigations are suggested to link those values to their anthropogenic supplies.

The Libor Market Model: from theory to calibration

This thesis is focused on the financial model for interest rates called the LIBOR Market Model. In the appendixes, we provide the necessary mathematical theory. In the inner chapters, firstly, we define the main interest rates and financial instruments concerning with the interest rate models, then, we set the LIBOR market model, demonstrate its existence, derive the dynamics of forward LIBOR rates and justify the pricing of caps according to the Black’s formula. Then, we also present the Swap Market Model, which models the forward swap rates instead of the LIBOR ones. Even this model is justified by a theoretical demonstration and the resulting formula to price the swaptions coincides with the Black’s one. However, the two models are not compatible from a theoretical point. Therefore, we derive various analytical approximating formulae to price the swaptions in the LIBOR market model and we explain how to perform a Monte Carlo simulation. Finally, we present the calibration of the LIBOR market model to the markets of both caps and swaptions, together with various examples of application to the historical correlation matrix and the cascade calibration of the forward volatilities to the matrix of implied swaption volatilities provided by the market.