Essays on energy derivatives pricing and financial risk management

This thesis consists of an introductory chapter (essay I) and five more empirical essays on electricity markets and CO2 spot price behaviour, derivatives pricing analysis and hedging. Essay I presents the structure of the thesis and electricity markets functioning and characteristics, as well as the type of products traded, to be analyzed on the following essays. In the second essay we conduct an empirical study on co-movements in electricity markets resorting to wavelet analysis, discussing long-term dynamics and markets integration. Essay three is about hedging performance and multiscale relationships in the German electricity spot and futures markets, also using wavelet analysis. We concentrate the investigation on the relationship between coherence evolution and hedge ratio analysis, on a time-frequency-scale approach, between spot and futures which conditions the effectiveness of the hedging strategy. Essays four, five and six are interrelated between them and with the other two previous essays given the nature of the commodity analyzed, CO2 emission allowances, traded in electricity markets. Relationships between electricity prices, primary energy fuel prices and carbon dioxide permits are analyzed on essay four. The efficiency of the European market for allowances is examined taking into account markets heterogeneity. Essay five analyzes stylized statistical properties of the recent traded asset CO2 emission allowances, for spot and futures returns, examining also the relation linking convenience yield and risk premium, for the German European Energy Exchange (EEX) between October 2005 and October 2009. The study was conducted through empirical estimations of CO2 allowances risk premium, convenience yield, and their relation. Future prices from an ex-post perspective are examined to show evidence for significant negative risk premium, or else a positive forward premium. Finally, essay six analyzes emission allowances futures hedging effectiveness, providing evidence for utility gains increases with investor’s preference over risk. Deregulation of electricity markets has led to higher uncertainty in electricity prices and by presenting these essays we try to shed new lights about structuring, pricing and hedging in this type of markets.

Analysis of the organic matter associated to sea salt : definition of potential molecular markers based on the volatile composition and presence of glycosidic derivatives and polysaccharides

Sea salt is a natural product obtained from the evaporation of seawater in saltpans due to the combined effect of wind and sunlight. Nowadays, there is a growing interest for protection and re-valorisation of saltpans intrinsically associated to the quality of sea salt that can be evaluated by its physico-chemical properties. These man-made systems can be located in different geographical areas presenting different environmental surroundings. During the crystallization process, organic compounds coming from these surroundings can be incorporated into sea salt crystals, influencing their final composition. The organic matter associated to sea salt arises from three main sources: algae, surrounding bacterial community, and anthropogenic activity. Based on the hypothesis that sea salt contains associated organic compounds that can be used as markers of the product, including saltpans surrounding environment, the aim of this PhD thesis was to identify these compounds. With this purpose, this work comprised: 1) a deep characterisation of the volatile composition of sea salt by headspace solid phase microextraction combined with comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry (HS-SPME/GCGC–ToFMS) methodology, in search of potential sea salt volatile markers; 2) the development of a methodology to isolate the polymeric material potentially present in sea salt, in amounts that allow its characterisation in terms of polysaccharides and protein; and 3) to explore the possible presence of triacylglycerides. The high chromatographic resolution and sensitivity of GC×GC–ToFMS enabled the separation and identification of a higher number of volatile compounds from sea salt, about three folds, compared to unidimentional chromatography (GC–qMS). The chromatographic contour plots obtained revealed the complexity of marine salt volatile composition and confirmed the relevance of GC×GC–ToFMS for this type of analysis. The structured bidimentional chromatographic profile arising from 1D volatility and 2D polarity was demonstrated, allowing more reliable identifications. Results obtained for analysis of salt from two locations in Aveiro and harvested over three years suggest the loss of volatile compounds along the time of storage of the salt. From Atlantic Ocean salts of seven different geographical origins, all produced in 2007, it was possible to identify a sub-set of ten compounds present in all salts, namely 6-methyl-5-hepten-2-one, 2,2,6-trimethylcyclohexanone, isophorone, ketoisophorone, β-ionone-5,6-epoxide, dihydroactinidiolide, 6,10,14-trimethyl-2-pentadecanone, 3-hydroxy-2,4,4-trimethylpentyl 2-methylpropanoate, 2,4,4-trimethylpentane-1,3-diyl bis(2-methylpropanoate), and 2-ethyl-1-hexanol. These ten compounds were considered potential volatile markers of sea salt. Seven of these compounds are carotenoid-derived compounds, and the other three may result from the integration of compounds from anthropogenic activity as metabolites of marine organisms. The present PhD work also allowed the isolation and characterisation, for the first time, of polymeric material from sea salt, using 16 Atlantic Ocean salts. A dialysis-based methodology was developed to isolate the polymeric material from sea salt in amounts that allowed its characterisation. The median content of polymeric material isolated from the 16 salts was 144 mg per kg of salt, e.g. 0.014% (w/w). Mid-infrared spectroscopy and thermogravimetry revealed the main occurrence of sulfated polysaccharides, as well as the presence of protein in the polymeric material from sea salt. Sea salt polysaccharides were found to be rich in uronic acid residues (21 mol%), glucose (18), galactose (16), and fucose (13). Sulfate content represented a median of 45 mol%, being the median content of sulfated polysaccharides 461 mg/g of polymeric material, which accounted for 66 mg/kg of dry salt. Glycosidic linkage composition indicates that the main sugar residues that could carry one or more sulfate groups were identified as fucose and galactose. This fact allowed to infer that the polysaccharides from sea salt arise mainly from algae, due to their abundance and composition. The amino acid profile of the polymeric material from the 16 Atlantic Ocean salts showed as main residues, as medians, alanine (25 mol%), leucine (14), and valine (14), which are hydrophobic, being the median protein content 35 mg/g, i.e. 4,9 mg per kg of dry salt. Beside the occurrence of hydrophobic volatile compounds in sea salt, hydrophobic non-volatile compounds were also detected. Triacylglycerides were obtained from sea salt by soxhlet extraction with n-hexane. Fatty acid composition revealed palmitic acid as the major residue (43 mol%), followed by stearic (13), linolenic (13), oleic (12), and linoleic (9). Sea salt triacylglycerides median content was 1.5 mg per kg of dry salt. Both protein and triacylglycerides seem to arise from macro and microalgae, phytoplankton and cyanobacteria, due to their abundance and composition. Despite the variability resulting from saltpans surrounding environment, this PhD thesis allowed the identification of a sea salt characteristic organic compounds profile based on volatile compounds, polysaccharides, protein, and triacylglycerides.

A numerical method to solve higher-order fractional differential equations

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order derivatives only. With this, we can rewrite FDEs in terms of a classical one and then apply any known technique. With some examples, we show the accuracy of the method.