Pricing swing options and other electricity derivatives

The deregulation of regional electricity markets has led to more competitive prices but also higher uncertainty in the future electricity price development. Most markets exhibit high volatilities and occasional distinctive price spikes, which results in demand for derivative products which protect the holder against high prices. A good understanding of the stochastic price dynamics is required for the purposes of risk management and pricing derivatives. In this thesis we examine a simple spot price model which is the exponential of the sum of an Ornstein-Uhlenbeck and an independent pure jump process. We derive the moment generating function as well as various approximations to the probability density function of the logarithm of this spot price process at maturity T. With some restrictions on the set of possible martingale measures we show that the risk neutral dynamics remains within the class of considered models and hence we are able to calibrate the model to the observed forward curve and present semi-analytic formulas for premia of path-independent options as well as approximations to call and put options on forward contracts with and without a delivery period. In order to price path-dependent options with multiple exercise rights like swing contracts a grid method is utilised which in turn uses approximations to the conditional density of the spot process. Further contributions of this thesis include a short discussion of interpolation methods to generate a continuous forward curve based on the forward contracts with delivery periods observed in the market, and an investigation into optimal martingale measures in incomplete markets. In particular we present known results of q-optimal martingale measures in the setting of a stochastic volatility model and give a first indication of how to determine the q-optimal measure for q=0 in an exponential Ornstein-Uhlenbeck model consistent with a given forward curve

Multi Jet Production at High Q2

Deep-inelastic $e^+p$ scattering data, taken with the H1 detector at HERA, are used to investigate jet production over a range of four-momentum transfers $150 < Q^2 < 15000 \mathrm{GeV}^2$ and transverse jet energies $5 < E_T < 50 \mathrm{GeV}$. The analysis is based on data corresponding to an integrated luminosity of $\mathcal{L}_\mathrm{int} = 65.4 \mathrm{pb}^{-1}$ taken in the years 1999-2000 at a centre-of-mass energy $\sqrt{s} \approx 319 \mathrm{GeV}$. Jets are defined by the inclusive $k_t$ algorithm in the Breit frame of reference. Dijet and trijet jet cross sections are measured with respect to the exchanged boson virtuality and in addition the ratio of the trijet to the dijet cross section $R_{3/2}$ is investigated. The results are compared to the predictions of perturbative QCD calculations in next-to-leading order in the strong coupling constant $\alpha_s$. The value of $\alpha_s(m_Z)$ determined from the study of $R_{3/2}$ is $\alpha_s(m_Z) = 0.1175 \pm 0.0017 (\mathrm{stat.}) \pm 0.0050 (\mathrm{syst.}) ^{+0.0054}_{-0.0068} (\mathrm{theo.})$.Comment: Contributed to 13th International Workshop on Deep Inelastic Scattering (DIS 05), Madison, Wisconsin, 27 Apr - 1 May 200

Prompt Photon Production at HERA and LEP

Results on isolated prompt photon production are presented. The measurements were performed at HERA in deep inelastic ep scattering and photoproduction, as well as at LEP in photon photon collisions. Differential cross sections are shown for inclusive prompt photons and those accompanied by a jet. The results are compared to predictions of perturbative QCD calculations in next to leading order and to predictions of the event generators PYTHIA and HERWIG.Comment: To appear in the proceedings of 32nd International Conference on High-Energy Physics (ICHEP 04), Beijing, China, 16-22 Aug 200

A Grammar of Papuan Malay

This book presents an in-depth linguistic description of one Papuan Malay variety, based on fifteen hours of recordings of spontaneous narratives and conversations between Papuan Malay speakers.‘Papuan Malay’ refers to the easternmost varieties of Malay (Austronesian). They are spoken in the coastal areas of West Papua, the western part of the island of New Guinea. The variety described here is spoken along West Papua’s northeast coast.After a general introduction to the language, its setting and its history, this grammar discusses the following topics, building up from smaller grammatical constituents to larger ones: phonology, word formation, noun and prepositional phrases, verbal and nonverbal clauses, non-declarative clauses, and conjunctions and constituent combining. Of special interest to linguists, typologists and Malay specialists are the following in-depth analyses and descriptions: affixation and its productivity across domains of language choice, reduplication and its gesamtbedeutung, personal pronouns and their adnominal uses, demonstratives and locatives and their extended uses, and adnominal possessive relations and their non-canonical uses.This study provides a point of comparison for further studies in other (Papuan) Malay varieties and a starting point for Papuan Malay language development efforts.Language Use in Past and Presen

Note on operadic harmonic oscillator

It is explained how the time evolution of the operadic variables may be introduced. As an example, an operadic Lax representation of the harmonic oscillator is considered.Comment: LaTeX2e, 6 pages, no figure