Discount curve estimation by monotonizing McCulloch Splines

In this paper a new and very simple method for monotone estimation of discount curves is proposed. The main idea of this approach is a simple modification of the commonly used (unconstrained) Mc-Culloch Spline. We construct an integrated density estimate from the predicted values of the discount curve. It can be shown that this statistic is an estimate of the inverse of the discount function and the final estimate can easily be obtained by a numerical inversion. The resulting procedure is extremely simple and we have implemented it in Excel and VBA, respectively. The performance is illustrated by three examples, in which the curve was previously estimated with an unconstrained McCulloch Spline. --

Relational Galois connections between transitive fuzzy digraphs

Fuzzy-directed graphs are often chosen as the data structure to model and implement solutions to several problems in the applied sciences. Galois connections have also shown to be useful both in theoretical and in practical problems. In this paper, the notion of relational Galois connection is extended to be applied between transitive fuzzy directed graphs. In this framework, the components of the connection are crisp relations satisfying certain reasonable properties given in terms of the so-called full powering

Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information

We show how inter-asset dependence information derived from observed market prices of liquidly traded options can lead to improved model-free price bounds for multi-asset derivatives. Depending on the type of the observed liquidly traded option, we either extract correlation information or we derive restrictions on the set of admissible copulas that capture the inter-asset dependencies. To compute the resultant price bounds for some multi-asset options of interest, we apply a modified martingale optimal transport approach. In particular, we derive an adjusted pricing-hedging duality. Several examples based on simulated and real market data illustrate the improvement of the obtained price bounds and thus provide evidence for the relevance and tractability of our approach

Geochemical characteristics and implications of shale gas from the Longmaxi Formation, Sichuan Basin, China

AbstractGas geochemical analysis was conducted on the shale gas from the Longmaxi Formation in the Weiyuan-Changning areas, Sichuan Basin, China. Chemical composition was measured using an integrated method of gas chromatography combined with mass spectrometry. The results show that the Longmaxi shale gas, after hydraulic fracturing, is primarily dominated by methane (94.0%–98.6%) with low humidity (0.3%–0.6%) and minor non-hydrocarbon gasses which are primarily comprised of CO2, N2, as well as trace He. δ13CCO2 = −2.5‰−6.0‰3He/4He = 0.01–0.03Ra.The shale gas in the Weiyuan and Changning areas display carbon isotopes reversal pattern with a carbon number (δ13C1 > δ13C2) and distinct carbon isotopic composition. The shale gas from the Weiyuan pilot has heavier carbon isotopic compositions for methane (δ13C1: from −34.5‰ to −36.8‰), ethane (δ13C2: −37.6‰ to −41.9‰), and CO2 (δ13CCO2: −4.5‰ to −6.0‰) than those in the Changning pilot (δ13C1: −27.2‰ to −27.3‰, δ13C2: −33.7‰ to −34.1‰, δ13CCO2: −2.5‰ to −4.6‰). The Longmaxi shale was thermally high and the organic matter was in over mature stage with good sealing conditions. The shale gas, after hydraulic fracturing, could possibly originate from the thermal decomposition of kerogen and the secondary cracking of liquid hydrocarbons which caused the reversal pattern of carbon isotopes. Some CO2 could be derived from the decomposition of carbonate. The difference in carbon isotopes between the Weiyuan and Changning areas could be derived from the different mixing proportion of gas from the secondary cracking of liquid hydrocarbons caused by specific geological and geochemical conditions

Nonparametric modelling of interest rates

We approximate interest rate financial data by homogeneous diffusion process with piecewise constant coefficients. Both drift and diffusion terms are estimated nonparametrically. For estimating of the drift term we use the taut string method which minimizes the numbers of peaks but for the diffusion term we minimize the number of intervals of constancy. For both estimators consistency is proved and convergence rate is calculated. Also the efficacy of the methods is demonstrated using simulated data

Two Studies in Representation of Signals

The thesis consists of two parts. In the first part deals with a multi-scale approach to vector quantization. An algorithm, dubbed reconstruction trees, is proposed and analyzed. Here the goal is parsimonious reconstruction of unsupervised data; the algorithm leverages a family of given partitions, to quickly explore the data in a coarse-to-fine multi-scale fashion. The main technical contribution is an analysis of the expected distortion achieved by the proposed algorithm, when the data are assumed to be sampled from a fixed unknown probability measure. Both asymptotic and finite sample results are provided, under suitable regularity assumptions on the probability measure. Special attention is devoted to the case in which the probability measure is supported on a smooth sub-manifold of the ambient space, and is absolutely continuous with respect to the Riemannian measure of it; in this case asymptotic optimal quantization is well understood and a benchmark for understanding the results is offered. The second part of the thesis deals with a novel approach to Graph Signal Processing which is based on Matroid Theory. Graph Signal Processing is the study of complex functions of the vertex set of a graph, based on the combinatorial Graph Laplacian operator of the underlying graph. This naturally gives raise to a linear operator, that to many regards resembles a Fourier transform, mirroring the graph domain into a frequency domain. On the one hand this structure asymptotically tends to mimic analysis on locally compact groups or manifolds, but on the other hand its discrete nature triggers a whole new scenario of algebraic phenomena. Hints towards making sense of this scenario are objects that already embody a discrete nature in continuous setting, such as measures with discrete support in time and frequency, also called Dirac combs. While these measures are key towards formulating sampling theorems and constructing wavelet frames in time-frequency Analysis, in the graph-frequency setting these boil down to distinguished combinatorial objects, the so called Circuits of a matroid, corresponding to the Fourier transform operator. In a particularly symmetric case, corresponding to Cayley graphs of finite abelian groups, the Dirac combs are proven to completely describe the so called lattice of cyclic flats, exhibiting the property of being atomistic, among other properties. This is a strikingly concise description of the matroid, that opens many questions concerning how this highly regular structure relaxes into more general instances. Lastly, a related problem concerning the combinatorial interplay between Fourier operator and its Spectrum is described, provided with some ideas towards its future development