Credit risk premia and quadratic BSDEs with a single jump

This paper is concerned with the determination of credit risk premia of defaultable contingent claims by means of indifference valuation principles. Assuming exponential utility preferences we derive representations of indifference premia of credit risk in terms of solutions of Backward Stochastic Differential Equations (BSDE). The class of BSDEs needed for that representation allows for quadratic growth generators and jumps at random times. Since the existence and uniqueness theory for this class of BSDEs has not yet been developed to the required generality, the first part of the paper is devoted to fill that gap. By using a simple constructive algorithm, and known results on continuous quadratic BSDEs, we provide sufficient conditions for the existence and uniqueness of quadratic BSDEs with discontinuities at random times

Random Time Forward Starting Options

We introduce a natural generalization of the forward-starting options, first discussed by M. Rubinstein. The main feature of the contract presented here is that the strike-determination time is not fixed ex-ante, but allowed to be random, usually related to the occurrence of some event, either of financial nature or not. We will call these options {\bf Random Time Forward Starting (RTFS)}. We show that, under an appropriate "martingale preserving" hypothesis, we can exhibit arbitrage free prices, which can be explicitly computed in many classical market models, at least under independence between the random time and the assets' prices. Practical implementations of the pricing methodologies are also provided. Finally a credit value adjustment formula for these OTC options is computed for the unilateral counterparty credit risk.Comment: 19 pages, 1 figur

Extreme times for volatility processes

We present a detailed study on the mean first-passage time of volatility processes. We analyze the theoretical expressions based on the most common stochastic volatility models along with empirical results extracted from daily data of major financial indices. We find in all these data sets a very similar behavior that is far from being that of a simple Wiener process. It seems necessary to include a framework like the one provided by stochastic volatility models with a reverting force driving volatility toward its normal level to take into account memory and clustering effects in volatility dynamics. We also detect in data a very different behavior in the mean first-passage time depending whether the level is higher or lower than the normal level of volatility. For this reason, we discuss asymptotic approximations and confront them to empirical results with a good agreement, specially with the ExpOU model.Comment: 10, 6 colored figure

Preliminary investigations of elemental content, microporosity, and specific surface area of porous rocks using PIXE and X-ray microtomography techniques

Determination of physical properties of porous geological materials is of great importance for oil industry. The knowledge of rocks properties is usually obtained from porosity studies such as pore size distribution, specific surface area determination, and hydrodynamic permeability calculations. This study describes determination of elemental composition and measurements of the particular physical properties of geological samples (porous sandstone rocks) by means of the nuclear and X-ray microprobes at the Institute of Nuclear Physics, Polish Academy of Sciences in Kraków, Poland. The special emphasis has been put on the computed microtomography method. Measurements have been carried out in close cooperation with Department of Geophysics, FGGEP AGH in Kraków, Poland. Chemical composition of the Rotliegend sandstone rock samples (few millimeters diameter), extracted from a borehole at 2679.6 m, 2741.4 m and 2742.4 m depth have been investigated using the 2.2 MeV proton beam (proton induced X-ray emission technique). Next, measurements of the porosity and the specific surface area of the pore space have been carried out using the X-ray microtomography technique. Basing on microtomographic data obtained with the high spatial resolution, simulations of the fluid dynamic in the void space of porous media have been carried out. Lattice Boltzmann method in the 3DQ19 geometrical model has been used in order to predict the hydraulic permeability of the media. In order to avoid viscosity-permeability dependence the multiple-relaxation-time model with half-way bounce back boundary conditions has been used. Computing power-consuming processing has been performed with the use of modern grid infrastructure

Expected resolution limits of x-ray free-electron laser single-particle imaging for realistic source and detector properties

The unprecedented intensity of x-ray free-electron laser sources has enabled single-particle x-ray diffraction imaging (SPI) of various biological specimens in both two-dimensional projection and three dimensions (3D). The potential of studying protein dynamics in their native conditions, without crystallization or chemical staining, has encouraged researchers to aim for increasingly higher resolutions with this technique. The currently achievable resolution of SPI is limited to the sub-10 nanometer range, mainly due to background effects, such as instrumental noise and parasitic scattering from the carrier gas used for sample delivery. Recent theoretical studies have quantified the effects of x-ray pulse parameters, as well as the required number of diffraction patterns to achieve a certain resolution, in a 3D reconstruction, although the effects of detector noise and the random particle orientation in each diffraction snapshot were not taken into account. In this work, we show these shortcomings and address limitations on achievable image resolution imposed by the adaptive gain integrating pixel detector noise

3D atomic structure from a single XFEL pulse

X-ray Free Electron Lasers (XFEL) are the most advanced pulsed x-ray sources. Their extraordinary pulse parameters promise unique applications. Indeed, several new methods have been developed at XFEL-s. However, no methods are known, which would allow ab initio atomic level structure determination using only a single XFEL pulse. Here, we present experimental results, demonstrating the determination of the 3D atomic structure from data obtained during a single 25 fs XFEL pulse. Parallel measurement of hundreds of Bragg reflections was done by collecting Kossel line patterns of GaAs and GaP. With these measurements, we reached the ultimate temporal limit of the x-ray structure solution possible today. These measurements open the way for studying non-repeatable fast processes and structural transformations in crystals for example measuring the atomic structure of matter at extremely non-ambient conditions or transient structures formed in irreversible physical, chemical, or biological processes. It would also facilitate time resolved pump-probe structural studies making them significantly shorter than traditional serial crystallography.Comment: 16 pages of manuscript followed by 15 pages of supplementary informatio

Term Structure Models with Shot-noise Effects

This work proposes term structure models consisting of two parts: a part which can be represented in exponential quadratic form and a shot noise part. These term structure models allow for explicit expressions of various derivatives. In particular, they are very well suited for credit risk models. The goal of the paper is twofold. First, a number of key building blocks useful in term structure modelling are derived in closed-form. Second, these building blocks are applied to single and portfolio credit risk. This approach generalizes Duffie & Garleanu (2001) and is able to produce realistic default correlation and default clustering. We conclude with a specific model where all key building blocks are computed explicitly

Systemic Risk and Default Clustering for Large Financial Systems

As it is known in the finance risk and macroeconomics literature, risk-sharing in large portfolios may increase the probability of creation of default clusters and of systemic risk. We review recent developments on mathematical and computational tools for the quantification of such phenomena. Limiting analysis such as law of large numbers and central limit theorems allow to approximate the distribution in large systems and study quantities such as the loss distribution in large portfolios. Large deviations analysis allow us to study the tail of the loss distribution and to identify pathways to default clustering. Sensitivity analysis allows to understand the most likely ways in which different effects, such as contagion and systematic risks, combine to lead to large default rates. Such results could give useful insights into how to optimally safeguard against such events.Comment: in Large Deviations and Asymptotic Methods in Finance, (Editors: P. Friz, J. Gatheral, A. Gulisashvili, A. Jacqier, J. Teichmann) , Springer Proceedings in Mathematics and Statistics, Vol. 110 2015