2,848,326 research outputs found
Essays on variance risk
My PhD thesis consists of three papers which study the nature, structure, dynamics and price of variance risks. As tool I make use of multivariate affine jump-diffusion models with matrix-valued state spaces. The first chapter proposes a new three-factor model for index option pricing. A core feature of the model are unspanned skewness and term structure effects, i.e., it is possible that the structure of the volatility surface changes without a change in the volatility level. The model reduces pricing errors compared to benchmark two-factor models by up to 22%. Using a decomposition of the latent state, I show that this superior performance is directly linked to a third volatility factor which is unrelated to the volatility level. The second chapter studies the price of the smile, which is defined as the premia for individual option risk factors. These risk factors are directly linked to the variance risk premium (VRP). I find that option risk premia are spanned by mid-run and long-run volatility factors, while the large high-frequency factor does not enter the price of the smile. I find the VRP to be unambiguously negative and decompose it into three components: diffusive risk, jump risk and jump intensity risk. The distinct term structure patterns of these components explain why the term structure of the VRP is downward sloping in normal times and upward sloping during market distress. In predictive regressions, I find an economically relevant predictive power over returns to volatility positions and S&P 500 index returns. The last chapter introduces several numerical methods necessary for estimating matrix-valued affine option pricing models, including the Matrix Rotation Count algorithm and a fast evaluation scheme for the Likelihood function
Thermodynamically stable lithium silicides and germanides from density-functional theory calculations
Density-functional-theory (DFT) calculations have been performed on the Li-Si
and Li-Ge systems. Lithiated Si and Ge, including their metastable phases, play
an important technological r\^ole as Li-ion battery (LIB) anodes. The
calculations comprise structural optimisations on crystal structures obtained
by swapping atomic species to Li-Si and Li-Ge from the X-Y structures in the
International Crystal Structure Database, where X={Li,Na,K,Rb,Cs} and
Y={Si,Ge,Sn,Pb}. To complement this at various Li-Si and Li-Ge stoichiometries,
ab initio random structure searching (AIRSS) was also performed. Between the
ground-state stoichiometries, including the recently found LiSi
phase, the average voltages were calculated, indicating that germanium may be a
safer alternative to silicon anodes in LIB, due to its higher lithium insertion
voltage. Calculations predict high-density LiSi and LiGe
layered phases which become the ground state above 2.5 and 5 GPa
respectively and reveal silicon and germanium's propensity to form dumbbells in
the LiSi, stoichiometry range. DFT predicts the stability of
the LiGe , LiGe and LiGe
phases and several new Li-Ge compounds, with stoichiometries LiGe,
LiGe, LiGe and LiGe.Comment: 10 pages, 5 figure
Structural and electronic properties of Si/Ge nanoparticles
Results of a theoretical study of the electronic properties of (Si)Ge and
(Ge)Si core/shell nanoparticles, homogeneous SiGe clusters, and GeSi
clusters with an interphase separating the Si and Ge atoms are presented. In
general, (Si)Ge particles are more stable than (Ge)Si ones, and SiGe systems
are more stable than GeSi ones. It is found that the frontier orbitals, that
dictate the optical properties, are localized to the surface, meaning that
saturating dangling bonds on the surface with ligands may influence the optical
properties significantly. In the central parts we identify a weak tendency for
the Si atoms to accept electrons, whereas Ge atoms donate electrons.Comment: To appear in Phys. Rev.
Degree Sequences and Long Cycles in Graphs
Let be a graph on vertices with degree sequence . Let be the circumference - the order of a longest cycle
and the order of a longest path in . In 1952, Dirac proved: (i) every
graph with is hamiltonian; (ii) in every 2-connected graph, . Recently, the bounds and in
(i) and (ii) are improved to and ,
respectively, by Koulakzian, Mosesyan and Nikoghosyan. In this paper we present
two new sharp bounds and
instead of ,
as well as two new sharp bounds and
instead of .Comment: 9 page
Stellar laboratories: new Ge V and Ge VI oscillator strengths and their validation in the hot white dwarf RE 0503-289
State-of-the-art spectral analysis of hot stars by means of non-LTE
model-atmosphere techniques has arrived at a high level of sophistication. The
analysis of high-resolution and high-S/N spectra, however, is strongly
restricted by the lack of reliable atomic data for highly ionized species from
intermediate-mass metals to trans-iron elements. Especially data for the latter
has only been sparsely calculated. Many of their lines are identified in
spectra of extremely hot, hydrogen-deficient post-AGB stars. A reliable
determination of their abundances establishes crucial constraints for AGB
nucleosynthesis simulations and, thus, for stellar evolutionary theory.
In a previous analysis of the UV spectrum of RE 0503-289, spectral lines of
highly ionized Ga, Ge, As, Se, Kr, Mo, Sn, Te, I, and Xe were identified.
Individual abundance determinations are hampered by the lack of reliable
oscillator strengths. Most of these identified lines stem from Ge V. In
addition, we identified Ge VI lines for the first time. We calculated Ge V and
Ge VI oscillator strengths to consider their radiative and collisional
bound-bound transitions in detail in our non-LTE stellar-atmosphere models for
the analysis of the Ge IV - VI spectrum exhibited in high-resolution and
high-S/N UV spectra of RE 0503-289. We identify four Ge IV, 37 Ge V, and seven
Ge VI lines. Most of these are identified for the first time in any star. We
reproduce almost all Ge IV, Ge VI, and Ge VI lines in the observed spectrum of
RE 0503-289 (Teff = 70 kK, log g = 7.5) at log Ge = -3.8 +/- 0.3 (mass
fraction, about 650 times solar).
Reliable measurements and calculations of atomic data are a prerequisite for
stellar-atmosphere modeling. Our oscillator-strength calculations have allowed,
for the first time, Ge V and Ge VI lines to be successfully reproduced in a
white dwarf's spectrum and to determine its photospheric Ge abundance.Comment: 54 pages, 8 figure
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