We develop a practical framework for identifying and quantifying the hidden layers of risks and optionality embedded in American options by introducing stochasticity into one or more of their underlying determinants. The heuristic approach remedies the problems of conventional pricing systems, which treat some key inputs deterministically, hence systematically underestimate the flexibility and convexity inherent in early-exercise features.
This note outlines an approach to stress testing of covariance of financial time series, in the context of financial risk management. It discusses how the geodesic distance between covariance matrices implies a notion of plausibility of covariance stress tests. In this approach, correlation stress tests span a submanifold of constant determinant of the Fisher--Rao manifold of covariance matrices. A parsimonious geometrically invariant definition of arbitrarily large correlation stress tests is proposed, and a few examples are discussed.
Gulsan Ara Sathi Kazi, Areef Billah, Azusa Takahashi
et al.
Abstract The influence of multi‐step sintering at high temperatures was used to meticulously characterize the crystallization, mechanical, and optical properties of a glass system with the addition of and . The research began with a novel base glass composition of 3.8 wt% , 4.2 wt% , 4.5 wt% , 35 wt% , and 2.5 wt% , to which 47 wt% and 3 wt% added. The initial glass powder was sintered in two steps at low temperatures. Either 500 for 10 min or 500 for 10 min then a raise to 650 for 20 min was used in the first step. Then, the second step of sintering was done at 850. Finally, after the pellet preparation, final calcination was conducted at 1450. The resulting microstructure was a composite material with various grain components embedded within a glass matrix. The low first sintering temperature triggered the optimum crystal growth, and after the final calcination process, a new glass‐ceramic named – was synthesized. The synthesized ceramics demonstrated strong diametral tensile strength and excellent Vickers micro‐hardness values, a remarkable refractive index, and optical band gaps larger than 3.1 eV. Consequently, the process of multi‐step sintering at high temperatures clenches the impending manufacture of a novel composite ceramic having remarkable hardness and good optical properties that encourage several biological, technological, and industrial applications.
Based on supermodularity ordering properties, we show that convex risk measures of credit losses are nondecreasing w.r.t. credit-credit and, in a wrong-way risk setup, credit-market, covariances of elliptically distributed latent factors. These results support the use of such setups for computing credit provisions and economic capital or for conducting stress test exercises and risk management analysis.
A bstractResults are reported from a search for supersymmetric particles in the final state with multiple jets and large missing transverse momentum. The search uses a sample of proton-proton collisions at s$$ \sqrt{s} $$ = 13 TeV collected with the CMS detector in 2016–2018, corresponding to an integrated luminosity of 137 fb−1, representing essentially the full LHC Run 2 data sample. The analysis is performed in a four-dimensional search region defined in terms of the number of jets, the number of tagged bottom quark jets, the scalar sum of jet transverse momenta, and the magnitude of the vector sum of jet transverse momenta. No significant excess in the event yield is observed relative to the expected background contributions from standard model processes. Limits on the pair production of gluinos and squarks are obtained in the framework of simplified models for supersymmetric particle production and decay processes. Assuming the lightest supersymmetric particle to be a neutralino, lower limits on the gluino mass as large as 2000 to 2310 GeV are obtained at 95% confidence level, while lower limits on the squark mass as large as 1190 to 1630 GeV are obtained, depending on the production scenario.
Copulas are widely used in financial economics as well as in other areas of applied mathematics. Yet, there is much arbitrariness in their choice. The author proposes "a natural copula" concept, which minimizes Wasserstein distance between distributions in some space, in which both these distributions are embedded. Transport properties and hydrodynamic interpretation are discussed with two examples of distributions of financial significance. A natural copula can be parsimoniously estimated by the methods of linear programming.
In this short paper we introduce a new class of performance measures based on certainty equivalents defined via scaled utility functions. We analyse their properties, show that the corresponding portfolio optimization problem is well-posed under generic conditions, and analyse the link between portfolio dynamics, benchmark process, and utility function choice in the long-run setting.
In this paper, we model the rating process of an entity as a piecewise homogeneous continuous time Markov chain. We focus specifically on calibrating the model to both historical data (rating transition matrices) and market data (CDS quotes), relying on a simple change of measure to switch from the historical probability to the risk-neutral one. We overcome some of the imperfections of the data by proposing a novel calibration procedure, which leads to an improvement of the entire scheme. We apply our model to compute bilateral credit and debit valuation adjustments of a netting set under a CSA with thresholds depending on ratings of the two parties.
Josselin Garnier, Jean-Baptiste Gaudemet, Anne Gruz
This paper addresses estimates of climate risk embedded within a bank credit portfolio. The proposed Climate Extended Risk Model (CERM) adapts well known credit risk models and makes it possible to calculate incremental credit losses on a loan portfolio that are rooted into physical and transition risks. The paper provides detailed description of the model hypotheses and steps.
Model risk in credit portfolio models is a serious issue for banks but has so far not been tackled comprehensively. We will demonstrate how to deal with uncertainty in all model parameters in an all-embracing, yet easy-to-implement way.
In this paper we will study the approximation of arbitrary law invariant risk measures. As a starting point, we approximate the average value at risk using stochastic gradient Langevin dynamics, which can be seen as a variant of the stochastic gradient descent algorithm. Further, the Kusuoka's spectral representation allows us to bootstrap the estimation of the average value at risk to extend the algorithm to general law invariant risk measures. We will present both theoretical, non-asymptotic convergence rates of the approximation algorithm and numerical simulations.
A bstractA search is presented for a heavy resonance decaying into either a pair of Z bosons or a Z boson and a W boson (ZZ or WZ), with a Z boson decaying into a pair of neutrinos and the other boson decaying hadronically into two collimated quarks that are reconstructed as a highly energetic large-cone jet. The search is performed using the data collected with the CMS detector at the CERN LHC during 2016 in proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to a total integrated luminosity of 35.9 fb−1. No excess is observed in data with regard to background expectations. Results are interpreted in scenarios of physics beyond the standard model. Limits at 95% confidence level on production cross sections are set at 0.9 fb (63 fb) for spin-1 W′ bosons, included in the heavy vector triplet model, with mass 4.0 TeV (1.0 TeV), and at 0.5 fb (40 fb) for spin-2 bulk gravitons with mass 4.0 TeV (1.0 TeV). Lower limits are set on the masses of W′ bosons in the context of two versions of the heavy vector triplet model of 3.1TeV and 3.4 TeV, respectively.
We report a successful observation of pressure-induced superconductivity in a topological compound Bi2Te3 with Tc of ∼3 K between 3 to 6 GPa. The combined high-pressure structure investigations with synchrotron radiation indicated that the superconductivity occurred at the ambient phase without crystal structure phase transition. The Hall effects measurements indicated the hole-type carrier in the pressure-induced superconducting Bi2Te3 single crystal. Consequently, the first-principles calculations based on the structural data obtained by the Rietveld refinement of X-ray diffraction patterns at high pressure showed that the electronic structure under pressure remained topologically nontrivial. The results suggested that topological superconductivity can be realized in Bi2Te3 due to the proximity effect between superconducting bulk states and Dirac-type surface states. We also discuss the possibility that the bulk state could be a topological superconductor.
This paper presents a measurement of the inclusive 3-jet production differential cross section at a proton–proton centre-of-mass energy of 7 TeV using data corresponding to an integrated luminosity of 5$$\,\mathrm{fb}^{-1}$$fb-1collected with the CMS detector. The analysis is based on the three jets with the highest transverse momenta. The cross section is measured as a function of the invariant mass of the three jets in a range of 445–3270 GeV and in two bins of the maximum rapidity of the jets up to a value of 2. A comparison between the measurement and the prediction from perturbative QCD at next-to-leading order is performed. Within uncertainties, data and theory are in agreement. The sensitivity of the observable to the strong coupling constant $$\alpha _\mathrm {S}$$αS is studied. A fit to all data points with 3-jet masses larger than 664 GeV gives a value of the strong coupling constant of $$\alpha _S(M_\mathrm{Z}) = 0.1171 \pm 0.0013\,\text {(exp)} \,^{+0.0073}_{-0.0047}\,\text {(theo)} $$αS(MZ)=0.1171±0.0013(exp)-0.0047+0.0073(theo).