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

Illness tracking in SARS-CoV-2 tested persons using a smartphone app: a non-interventional, prospective, cohort study

There are few data on the range and severity of symptoms of SARS-CoV-2 infection or the impact on life quality in infected, previously healthy, young adults such as Swiss Armed Forces personnel. It is also unclear if an app can be used to remotely monitor symptoms in persons who test positive. Using a smartphone app called ITITP (Illness Tracking in Tested Persons) and weekly pop-up questionnaires, we aimed to evaluate the spectrum, duration, and impact of symptoms reported after a positive SARS-CoV-2 test according to sex, age, location, and comorbidities, and to compare these to responses from persons who tested negative. We followed up 502 participants (57% active participation), including 68 (13.5%) positive tested persons. Hospitalisation was reported by 6% of the positive tested participants. We found that positives reported significantly more symptoms that are typical of COVID-19 compared to negatives. These symptoms with odds ratio (OR > 1) were having difficulty breathing (OR 3.35; 95% CI: 1.16, 9.65; p = 0.03), having a reduced sense of taste (OR 5.45; 95% CI: 1.22, 24.34; p = 0.03) and a reduced sense of smell (OR 18.24; 95% CI: 4.23, 78.69; p < 0.001). Using a random forest model, we showed that tiredness was the single symptom that was rated as having a significant impact on daily activities, whereas the other symptoms, although frequent, had less impact. The study showed that the use of an app was feasible to remotely monitor symptoms in persons infected with SARS-CoV-2 and could be adapted for other settings and new pandemic phases such as the current Omicron wave

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

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

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

Boundary-crossing identities for diffusions having the time-inversion property

We review and study a one-parameter family of functional transformations, denoted by (S (β)) β∈ℝ, which, in the case β<0, provides a path realization of bridges associated to the family of diffusion processes enjoying the time-inversion property. This family includes Brownian motions, Bessel processes with a positive dimension and their conservative h-transforms. By means of these transformations, we derive an explicit and simple expression which relates the law of the boundary-crossing times for these diffusions over a given function f to those over the image of f by the mapping S (β), for some fixed β∈ℝ. We give some new examples of boundary-crossing problems for the Brownian motion and the family of Bessel processes. We also provide, in the Brownian case, an interpretation of the results obtained by the standard method of images and establish connections between the exact asymptotics for large time of the densities corresponding to various curves of each family