Value at Risk: Implementing a Risk Measurement Standard

In the wake of recent failures of risk management, there has been a widespread call for improved quantification of the financial risks facing firms. At the forefront of this clamor has been Value at Risk. Previous research has identified differences in models, or Model Risk, as an important impediment to developing a Value at Risk standard. By contrast, this paper considers the divergence in a model's implementation in software and how it too, affects the establishment of a risk measurement standard. Different leading risk management systems' vendors were given identical portfolios of instruments of varying complexity, and were asked to assess the value at risk according to one common model, J.P. Morgan's RiskMetrics™. We analyzed the VaR results on a case by case basis, and in terms of prior expectations from the structure of financial instruments in the portfolio, as well as prior vendor expectations about the relative complexity of different asset classes. It follows that this research indicates the extent to which one particular model of risk can be effectively specified in advance, independent of the model's detailed implementation and use in practice. Key words: Risk Management, Financial Services, Model Management. This paper was presented at the Financial Institutions Center's October 1996 conference on "

Global existence, singular solutions, and ill-posedness for the Muskat problem

The Muskat, or Muskat--Leibenzon, problem describes the evolution of the interface between two immiscible fluids in a porous medium or Hele-Shaw cell under applied pressure gradients or fluid injection/extraction. In contrast to the Hele-Shaw problem (the one-phase version of the Muskat problem), there are few nontrivial exact solutions or analytic results for the Muskat problem. For the stable, forward Muskat problem, in which the higher viscosity fluid expands into the lower viscosity fluid, we show global in time existence for initial data that is a small perturbation of a flat interface. The initial data in this result may contain weak (e.g., curvature) singularities. For the unstable, backward problem, in which the higher viscosity fluid contracts, we construct singular solutions that start off with smooth initial data, but develop a point of infinite curvature at finite time

Magnetic-field enhancement of performance of superconducting nanowire single-photon detector

We present SNSPDs from NbN nanowires shaped after square-spiral that allows an increase not only in critical currents but also an extension of spectral detection efficiencies by just applying an external magnetic field. Using negative electron-beam lithography with the positive resist for shaping nanowires, made it possible to reduce the inner bend radius. Consequently, the effect of critical-current enhancement in the magnetic field becomes stronger than it was demonstrated earlier. Here we achieved a 13% increase of the critical current in the magnetic field. We measured spectra of the single-photon detection efficiency in the wavelength range from 400 to 1100 nm in the magnetic field. At zero field, the square spiral has the spectrum similar to that of a meander. At the field providing the maximum of the critical current, the detection efficiency and the cut-off wavelength in the spectrum increase by 20% and by 54%, correspondingly. The magnetic-field dependence of dark count rate is well described by proposed analytical model

Quantum Phase Dynamics in an LC shunted Josephson Junction

We have studied both theoretically and experimentally how an LC series circuit connected in parallel to a Josephson junction influences the Josephson dynamics. The presence of the shell circuit introduces two energy scales, which in specific cases can strongly differ from the plasma frequency of the isolated junction. Josephson junctions were manufactured using Nb/Al-AlOx/Nb fabrication technology with various on-chip LC shunt circuits. Spectroscopic measurements in the quantum limit show an excellent agreement with theory taking into account the shunt inductance and capacitance in the Resistively and Capacitively Shunted Junction model. The results clearly show that the dynamics of the system are two-dimensional, resulting in two resonant modes of the system. These findings have important implications for the design and operation of Josephson junctions based quantum bits