The Risk Premium and the Esscher Transform in Power Markets

In power markets one frequently encounters a risk premium being positive in the short end of the forward curve and negative in the long end. Economically it has been argued that the positive premium is reflecting retailers aversion for spike risk, wheras in the long end of the forward curve, the hedging pressure kicks in as in other commodity markets. Mathematically, forward prices are expressed as risk-neutral expectations of the spot at delivery. We apply the Esscher transform on power spot models based on mean-reverting processes driven by independent increment (time-inhomogeneous Lévy) processes. It is shown that the Esscher transform is yielding a change of mean-reversion level. Moreover, we show that an Esscher transform together with jumps occuring seasonally may explain the occurence of a positive risk premium in the short end. This is demonstrated both mathematically and by a numerical example for a two-factor spot model being relevant for electricity markets.     

On numerical density approximations of solutions of SDEs with unbounded coefficients

We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in application oriented fields. In this paper we provide a rigorous analysis of the method that covers systems of equations with unbounded coefficients. Working in a natural space for densities, L ¹, we obtain stability, consistency, and new convergence results for the method, new well-posedness and semigroup generation results for the related Fokker-Planck-Kolmogorov equation, and a new and rigorous connection to the corresponding probability density functions for both the approximate and the exact problems. To prove the results we combine semigroup and PDE arguments in a new way that should be of independent interest.     

Ornstein–Uhlenbeck processes in Hilbert space with non-Gaussian stochastic volatility

We propose a non-Gaussian operator-valued extension of the Barndorff-Nielsen and Shephard stochastic volatility dynamics, defined as the square-root of an operator-valued Ornstein–Uhlenbeck process with Lévy noise and bounded drift. We derive conditions for the positive definiteness of the Ornstein–Uhlenbeck process, where in particular we must restrict to operator-valued Lévy processes with “non-decreasing paths”. It turns out that the volatility model allows for an explicit calculation of its characteristic function, showing an affine structure. We introduce another Hilbert space-valued Ornstein–Uhlenbeck process with Wiener noise perturbed by this class of stochastic volatility dynamics. Under a strong commutativity condition between the covariance operator of the Wiener process and the stochastic volatility, we can derive an analytical expression for the characteristic functional of the Ornstein–Uhlenbeck process perturbed by stochastic volatility if the noises are independent. The case of operator-valued compound Poisson processes as driving noise in the volatility is discussed as a particular example of interest. We apply our results to futures prices in commodity markets, where we discuss our proposed stochastic volatility model in light of ambit fields.     

On arbitrage‐free pricing of weather derivatives based on fractional Brownian motion

We derive an arbitrage‐free pricing dynamics for claims on temperature, where the temperature follows a fractional Ornstein–Uhlenbeck process. Using a fractional white noise calculus, one can express the dynamics as a special type of conditional expectation not coinciding with the classical one. Using a Fourier transformation technique, explicit expressions are derived for claims of European and average type, and it is shown that these pricing formulas are solutions of certain Black and Scholes partial differential equations. Our results partly confirm a conjecture made by Brody, Syroka and Zervos.     

X‐Ray Diffraction and Mössbauer Spectroscopy Studies of Pressure‐Induced Phase Transitions in a Mixed‐Valence Trinuclear Iron Complex

The mixed‐valence complex Fe₃O(cyanoacetate)₆(H₂O)₃ ( 1 ) has been studied by single‐crystal X‐ray diffraction analysis at pressures up to 5.3(1) GPa and by (synchrotron) Mössbauer spectroscopy at pressures up to 8(1) GPa. Crystal structure refinements were possible up to 4.0(1) GPa. In this pressure range, 1 undergoes two pressure‐induced phase transitions. The first phase transition at around 3 GPa is isosymmetric and involves a 60° rotation of 50 % of the cyanoacetate ligands. The second phase transition at around 4 GPa reduces the symmetry from rhombohedral to triclinic. Mössbauer spectra show that the complex becomes partially valence‐trapped after the second phase transition. This sluggish pressure‐induced valence‐trapping is in contrast to the very abrupt valence‐trapping observed when compound 1 is cooled from 130 to 120 K at ambient pressure.     

Acquisition and quantification of ion images with a camera-based detection system and classical quantification algorithms

The quantitative analytical characteristics of a camera-based detection system for secondary ion microscopy are studied in detail. Through multiple exposures, ion images with large dynamic ranges are obtained. The quantification of these images by the sensitivity factor method and the matrix ion species ratio method is described and evaluated by the analysis of steel and aluminum standard reference materials.     

Temperature‐Programmed Packed Capillary Liquid Chromatography Coupled to Fourier‐Transform Infrared Spectroscopy

Temperature‐programmed packed capillary liquid chromatography has been coupled off‐line to Fourier‐transform infrared spectroscopy, utilizing a commercially available interface with a pneumatic nebulizer rebuilt to handle low flow rates at elevated temperatures. The modified interface showed excellent performance with regard to non‐aqueous reversed phase separations of polymer additives, resulting in constructed Gram‐Schmidt chromatograms comparable to chromatograms obtained using UV detection. The spray of the in‐house constructed nebulizer was not influenced by temperature changes of the column effluent, and hence temperature‐programmed gradient separations could be used successfully. The relative standard deviation of peak height was 4.4% (n = 5) and the mass limit of detection was determined to be about 40 ng, using a polymer antioxidant as model compound. The present instrumental coupling has been used for characterization of the antioxidant Irgafos P‐EPQ.     

Quantitative microbeam analysis of particles

The ability to characterize individual microscopic particles is important in many areas of science and technology. A variety of microbeam analysis methods are capable of providing information on microscopic particles. With electron probe X-ray microanalysis quantitative analysis is possible under well controlled conditions. Using computer controlled electron microscopes it is feasible to characterize a large number of individual particles. The application of this technique requires the use of multivariate data analysis procedures for the interpretation of the large amount of data obtained.