Exact arbitrage, well-diversified portfolios and asset pricing in large markets

: In a model of a nancial market with an atomless continuum of assets, we give a precise and rigorous meaning to the intuitive idea of a \well-diversi ed" portfolio and to a notion of \exact arbitrage". We show this notion to be necessary and su cient for an APT pricing formula to hold, to be strictly weaker than the more conventional notion of \asymptotic arbitrage", and to have novel implications for the continuity of the cost functional as well as for various versions of APT asset pricing. We further justify the idealized measure-theoretic setting in terms of a pricing formula based on \essential" risk, one of the three components of a tri-variate decomposition of an asset's rate of return, and based on a speci c index portfolio constructed from endogenously extracted factors and factor loadings. Our choice of factors is also shown to satisfy an optimality property that the rst m factors always provide the best approximation. We illustrate how the concepts and results translate to markets with a large but nite number of assets, and relate to previous work.

Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory.rnAs its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained.rnThe constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point.rnFinally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of existing computations, taking the independent running of the Euler topological term into account. Known perturbative results are reproduced in this case from the renormalization group equation, identifying however a unique non-Gaussian fixed point.rn

Orthogonal gamma-based expansions for volatility option prices under jump-diffusion dynamics

In my work I derive closed-form pricing formulas for volatility based options by suitably approximating the volatility process risk-neutral density function. I exploit and adapt the idea, which stands behind popular techniques already employed in the context of equity options such as Edgeworth and Gram-Charlier expansions, of approximating the underlying process as a sum of some particular polynomials weighted by a kernel, which is typically a Gaussian distribution. I propose instead a Gamma kernel to adapt the methodology to the context of volatility options. VIX vanilla options closed-form pricing formulas are derived and their accuracy is tested for the Heston model (1993) as well as for the jump-diffusion SVJJ model proposed by Duffie et al. (2000).

Kernel density correlation based non-rigid point set matching for statistical model-based 2D/3D reconstruction

This paper presents a kernel density correlation based nonrigid point set matching method and shows its application in statistical model based 2D/3D reconstruction of a scaled, patient-specific model from an un-calibrated x-ray radiograph. In this method, both the reference point set and the floating point set are first represented using kernel density estimates. A correlation measure between these two kernel density estimates is then optimized to find a displacement field such that the floating point set is moved to the reference point set. Regularizations based on the overall deformation energy and the motion smoothness energy are used to constraint the displacement field for a robust point set matching. Incorporating this non-rigid point set matching method into a statistical model based 2D/3D reconstruction framework, we can reconstruct a scaled, patient-specific model from noisy edge points that are extracted directly from the x-ray radiograph by an edge detector. Our experiment conducted on datasets of two patients and six cadavers demonstrates a mean reconstruction error of 1.9 mm

Seismic hazards of the Iberian Peninsula - evaluation with Kernel functions

The seismic hazard of the Iberian Peninsula is analysed using a nonparametric methodology based on statistical kernel functions; the activity rate is derived from the catalogue data, both its spatial dependence (without a seismogenetic zonation) and its magnitude dependence (without using Gutenberg–Richter's law). The catalogue is that of the Instituto Geográfico Nacional, supplemented with other catalogues around the periphery; the quantification of events has been homogenised and spatially or temporally interrelated events have been suppressed to assume a Poisson process. The activity rate is determined by the kernel function, the bandwidth and the effective periods. The resulting rate is compared with that produced using Gutenberg–Richter statistics and a zoned approach. Three attenuation laws have been employed, one for deep sources and two for shallower events, depending on whether their magnitude was above or below 5. The results are presented as seismic hazard maps for different spectral frequencies and for return periods of 475 and 2475 yr, which allows constructing uniform hazard spectra.

A bivariate return period based on copulas for hydrologic dam design: accounting for reservoir routing in risk estimation

A multivariate analysis on flood variables is needed to design some hydraulic structures like dams, as the complexity of the routing process in a reservoir requires a representation of the full hydrograph. In this work, a bivariate copula model was used to obtain the bivariate joint distribution of flood peak and volume, in order to know the probability of occurrence of a given inflow hydrograph. However, the risk of dam overtopping is given by the maximum water elevation reached during the routing process, which depends on the hydrograph variables, the reservoir volume and the spillway crest length. Consequently, an additional bivariate return period, the so-called routed return period, was defined in terms of risk of dam overtopping based on this maximum water elevation obtained after routing the inflow hydrographs. The theoretical return periods, which give the probability of occurrence of a hydrograph prior to accounting for the reservoir routing, were compared with the routed return period, as in both cases hydrographs with the same probability will draw a curve in the peak-volume space. The procedure was applied to the case study of the Santillana reservoir in Spain. Different reservoir volumes and spillway lengths were considered to investigate the influence of the dam and reservoir characteristics on the results. The methodology improves the estimation of the Design Flood Hydrograph and can be applied to assess the risk of dam overtopping

Seismic hazard of the Iberian Peninsula: evaluation with Kernel functions

The seismic hazard of the Iberian Peninsula is analysed using a nonparametric methodology based on statistical kernel functions; the activity rate is derived from the catalogue data, both its spatial dependence (without a seismogenic zonation) and its magnitude dependence (without using Gutenberg–Richter's relationship). The catalogue is that of the Instituto Geográfico Nacional, supplemented with other catalogues around the periphery; the quantification of events has been homogenised and spatially or temporally interrelated events have been suppressed to assume a Poisson process. The activity rate is determined by the kernel function, the bandwidth and the effective periods. The resulting rate is compared with that produced using Gutenberg–Richter statistics and a zoned approach. Three attenuation relationships have been employed, one for deep sources and two for shallower events, depending on whether their magnitude was above or below 5. The results are presented as seismic hazard maps for different spectral frequencies and for return periods of 475 and 2475 yr, which allows constructing uniform hazard spectra

Power flow based monetary flow method for electricity transmission and wheeling pricing

This paper proposes a transmission and wheeling pricing method based on the monetary flow tracing along power flow paths: the monetary flow-monetary path method. Active and reactive power flows are converted into monetary flows by using nodal prices. The method introduces a uniform measurement for transmission service usages by active and reactive powers. Because monetary flows are related to the nodal prices, the impacts of generators and loads on operation constraints and the interactive impacts between active and reactive powers can be considered. Total transmission service cost is separated into more practical line-related costs and system-wide cost, and can be flexibly distributed between generators and loads. The method is able to reconcile transmission service cost fairly and to optimize transmission system operation and development. The case study on the IEEE 30 bus test system shows that the proposed pricing method is effective in creating economic signals towards the efficient use and operation of the transmission system. (c) 2005 Elsevier B.V. All rights reserved.

Calendar effects and the pricing of risk:the UK evidence

For some time there has been a puzzle surrounding the seasonal behaviour of stock returns. This paper demonstrates that there is an asymmetric relationship between risk and return across the different months of the year. The paper finds that systematic risk is only priced during the months of January, April and July. Variance risk and firm size are priced during several months of the year including January. An analysis of the relative behaviour of size based securities reveals that firm capitalization makes a valuable contribution to the magnitude of risk premiums.