Calibration of Local Volatility Model with Stochastic Interest Rates by Efficient Numerical PDE Method

Long maturity options or a wide class of hybrid products are evaluated using a local volatility type modelling for the asset price S(t) with a stochastic interest rate r(t). The calibration of the local volatility function is usually time-consuming because of the multi-dimensional nature of the problem. In this paper, we develop a calibration technique based on a partial differential equation (PDE) approach which allows an efficient implementation. The essential idea is based on solving the derived forward equation satisfied by P(t; S; r)Z(t; S; r), where P(t; S; r) represents the risk neutral probability density of (S(t); r(t)) and Z(t; S; r) the projection of the stochastic discounting factor in the state variables (S(t); r(t)). The solution provides effective and sufficient information for the calibration and pricing. The PDE solver is constructed by using ADI (Alternative Direction Implicit) method based on an extension of the Peaceman-Rachford scheme. Furthermore, an efficient algorithm to compute all the corrective terms in the local volatility function due to the stochastic interest rates is proposed by using the PDE solutions and grid points. Different numerical experiments are examined and compared to demonstrate the results of our theoretical analysis

Nanomagnetism of magnetoelectric granular thin-film antiferromagnets

Antiferromagnets have recently emerged as attractive platforms for spintronics applications, offering fundamentally new functionalities compared to their ferromagnetic counterparts. While nanoscale thin film materials are key to the development of future antiferromagnetic spintronics technologies, experimental tools to explore such films on the nanoscale are still sparse. Here, we offer a solution to this technological bottleneck, by addressing the ubiquitous surface magnetisation of magnetoelectic antiferromagnets in a granular thin film sample on the nanoscale using single-spin magnetometry in combination with spin-sensitive transport experiments. Specifically, we quantitatively image the evolution of individual nanoscale antiferromagnetic domains in 200-nm thin-films of Cr$_2$O$_3$ in real space and across the paramagnet-to-antiferromagnet phase transition. These experiments allow us to discern key properties of the Cr$_2$O$_3$ thin film, including the mechanism of domain formation and the strength of exchange coupling between individual grains comprising the film. Our work offers novel insights into Cr$_2$O$_3$'s magnetic ordering mechanism and establishes single spin magnetometry as a novel, widely applicable tool for nanoscale addressing of antiferromagnetic thin films.Comment: 22 pages, 7 figure

Nanomagnetism of Magnetoelectric Granular Thin-Film Antiferromagnets

Antiferromagnets have recently emerged as attractive platforms for spintronics applications, offering fundamentally new functionalities compared with their ferromagnetic counterparts. Whereas nanoscale thin-film materials are key to the development of future antiferromagnetic spintronic technologies, existing experimental tools tend to suffer from low resolution or expensive and complex equipment requirements. We offer a simple, high-resolution alternative by addressing the ubiquitous surface magnetization of magnetoelectric antiferromagnets in a granular thin-film sample on the nanoscale using single-spin magnetometry in combination with spin-sensitive transport experiments. Specifically, we quantitatively image the evolution of individual nanoscale antiferromagnetic domains in 200 nm thin films of Cr 2 O 3 in real space and across the paramagnet-to-antiferromagnet phase transition, finding an average domain size of 230 nm, several times larger than the average grain size in the film. These experiments allow us to discern key properties of the Cr 2 O 3 thin film, including the boundary magnetic moment density, the variation of critical temperature throughout the film, the mechanism of domain formation, and the strength of exchange coupling between individual grains comprising the film. Our work offers novel insights into the magnetic ordering mechanism of Cr 2 O 3 and firmly establishes single-spin magnetometry as a versatile and widely applicable tool for addressing antiferromagnetic thin films on the nanoscale. © 2019 American Chemical Society

Search for Gravitational-wave Signals Associated with Gamma-Ray Bursts during the Second Observing Run of Advanced LIGO and Advanced Virgo

We present the results of targeted searches for gravitational-wave transients associated with gamma-ray bursts during the second observing run of Advanced LIGO and Advanced Virgo, which took place from 2016 November to 2017 August. We have analyzed 98 gamma-ray bursts using an unmodeled search method that searches for generic transient gravitational waves and 42 with a modeled search method that targets compact-binary mergers as progenitors of short gamma-ray bursts. Both methods clearly detect the previously reported binary merger signal GW170817, with p-values of <9.38 × 10−6 (modeled) and 3.1 × 10−4 (unmodeled). We do not find any significant evidence for gravitational-wave signals associated with the other gamma-ray bursts analyzed, and therefore we report lower bounds on the distance to each of these, assuming various source types and signal morphologies. Using our final modeled search results, short gamma-ray burst observations, and assuming binary neutron star progenitors, we place bounds on the rate of short gamma-ray bursts as a function of redshift for z ≤ 1. We estimate 0.07─1.80 joint detections with Fermi-GBM per year for the 2019─20 LIGO-Virgo observing run and 0.15─3.90 per year when current gravitational-wave detectors are operating at their design sensitivities

Search for subsolar-mass black hole binaries in the second part of Advanced LIGO’s and Advanced Virgo’s third observing run

We describe a search for gravitational waves from compact binaries with at least one component with mass 0.2–1.0 M and mass ratio q ≥ 0.1 in Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and Advanced Virgo data collected between 2019 November 1, 15:00 UTC and 2020 March 27, 17:00 UTC. No signals were detected. The most significant candidate has a false alarm rate of 0.2 yr−1. We estimate the sensitivity of our search over the entirety of Advanced LIGO’s and Advanced Virgo’s third observing run, and present the most stringent limits to date on the merger rate of binary black holes with at least one subsolar-mass component. We use the upper limits to constrain two fiducial scenarios that could produce subsolar-mass black holes: primordial black holes (PBH) and a model of dissipative dark matter. The PBH model uses recent prescriptions for the merger rate of PBH binaries that include a rate suppression factor to effectively account for PBH early binary disruptions. If the PBHs are monochromatically distributed, we can exclude a dark matter fraction in PBHs fPBH 0.6 (at 90 per cent confidence) in the probed subsolar-mass range. However, if we allow for broad PBH mass distributions, we are unable to rule out fPBH = 1. For the dissipative model, where the dark matter has chemistry that allows a small fraction to cool and collapse into black holes, we find an upper bound fDBH &lt; 10−5 on the fraction of atomic dark matter collapsed into black holes

Na2B6Si2: A Prototype Silico-boride with Closo (B6)2– Clusters

The compound Na2B6Si2 was synthesized under high-pressure, high-temperature conditions at pressures ranging from 6 to 9.5 GPa and temperatures from 1070 to 1270 K before quenching to room temperature followed by slow decompression. The crystal structure was determined from microcrystals using precession-assisted electron diffraction tomography, validated by dynamical refinement and full-profile refinements using optimized coordinates from quantum chemical calculations (space group R3m, Pearson symbol hR30, a = 5.0735(1) &amp; Aring; and c = 16.0004(7) &amp; Aring;). The atomic arrangement consists of a unique framework formed by electron-precise octahedral closo (B6)(2-) clusters connected via ethane-like (Si-2)(0) dumbbells. The Na+ cations occupy cavities in the hierarchical variation of a Heusler-type framework. The balance (Na+)(2)([B-6](2-))(Si0)(2) reveals an electron precise Zintl-Wade phase, which is in line with electronic band structure calculations predicting semiconducting behavior