Importance sampling for integrated market and credit portfolio models

Abstract: Standard credit portfolio models do not model market risk factors, such as risk-free interest rates or credit spreads, as stochastic variables. Various studies have documented that a severe underestimation of economic capital can be the consequence. However, integrating market risk factors into credit portfolio models increases the computational burden of computing credit portfolio risk measures. In this paper, the application of various importance sampling techniques to an integrated market and credit portfolio model are presented and the effectiveness of these approaches is tested by numerical experiments. The main result is that importance sampling can reduce the standard error of the percentile estimators, but it is rather difficult to make statements about when the IS approach is especially effective. Besides, the combination of importance sampling techniques originally developed for pure market risk portfolio models with techniques originally developed for pure default mode credit risk portfolio models is less effective than simpler two step-IS approaches

Who fans the flames of Alzheimer's disease brains? Misfolded tau on the crossroad of neurodegenerative and inflammatory pathways

Neurodegeneration, induced by misfolded tau protein, and neuroinflammation, driven by glial cells, represent the salient features of Alzheimer's disease (AD) and related human tauopathies. While tau neurodegeneration significantly correlates with disease progression, brain inflammation seems to be an important factor in regulating the resistance or susceptibility to AD neurodegeneration. Previously, it has been shown that there is a reciprocal relationship between the local inflammatory response and neurofibrillary lesions. Numerous independent studies have reported that inflammatory responses may contribute to the development of tau pathology and thus accelerate the course of disease. It has been shown that various cytokines can significantly affect the functional and structural properties of intracellular tau. Notwithstanding, anti-inflammatory approaches have not unequivocally demonstrated that inhibition of the brain immune response can lead to reduction of neurofibrillary lesions. On the other hand, our recent data show that misfolded tau could represent a trigger for microglial activation, suggesting the dual role of misfolded tau in the Alzheimer's disease inflammatory cascade. On the basis of current knowledge, we can conclude that misfolded tau is located at the crossroad of the neurodegenerative and neuroinflammatory pathways. Thus disease-modified tau represents an important target for potential therapeutic strategies for patients with Alzheimer's disease

Peroxiredoxin 6 in human brain: molecular forms, cellular distribution and association with Alzheimer’s disease pathology

Peroxiredoxin 6 is an antioxidant enzyme and is the 1-cys member of the peroxiredoxin family. Using two-dimensional electrophoresis and Western blotting, we have shown for the first time that, in human control and brain tissue of patient’s with Alzheimer’s disease (AD), this enzyme exists as three major and five minor forms with pIs from 5.3 to 6.1. Using specific cellular markers, we have shown that peroxiredoxin 6 is present in astrocytes with very low levels in neurons, but not detectable in microglia or oligodendrocytes. In control brains, there was a very low level of peroxiredoxin 6 staining in astrocytes that was confined to a “halo” around the nucleus. In AD, there were marked increases in the number and staining intensity of peroxiredoxin 6 positive astrocytes in both gray and white matter in the midfrontal cortex, cingulate, hippocampus and amygdala. Confocal microscopy using antibodies to Aβ peptide, tau and peroxiredoxin 6 showed that peroxiredoxin 6 positive astrocytes are closely involved with diffuse plaques and to a lesser extent with neuritic plaques, suggesting that plaques are producing reactive oxygen species. There appeared to be little astrocytic response to tau containing neurons. Although peroxiredoxin 6 positive astrocytes were seen to make multiple contacts with tau positive neurons, there was no intraneuronal colocalization. In brain tissue of patients with AD, many blood vessels exhibited peroxiredoxin 6 staining that appeared to be due to the astrocytic foot processes. These results suggest that oxidative stress conditions exist in AD and that peroxiredoxin 6 is an important antioxidant enzyme in human brain defenses

Importance sampling for integrated market and credit portfolio models

A sophisticated approach for computing the total economic capital needed for various stochastically dependent risk types is the bottom-up approach. In this approach, usually, market and credit risks of financial instruments are modeled simultaneously. As integrating market risk factors into standard credit portfolio models increases the computational burden of calculating risk measures, it is analyzed to which extent importance sampling techniques previously developed either for pure market portfolio models or for pure credit portfolio models can be successfully applied to integrated market and credit portfolio models. Specific problems which arise in this context are discussed. The effectiveness of these techniques is tested by numerical experiments for linear and non-linear portfolios.Bottom-up approach Credit risk Importance sampling Interest rate risk Risk management Value-at-risk

Top-down approaches for integrated risk management: How accurate are they?

Banks and other financial institutions try to compute the necessary amount of total capital that they need for absorbing stochastically dependent losses from different risk types (e.g., credit risk and market risk). Two sophisticated procedures of this so-called integrated risk management are the top-down and the bottom-up approaches. When banks apply a more sophisticated risk integration approach at all, it is usually the top-down approach where copula functions are employed for linking the marginal distributions of profit and losses resulting from different risk types. However, it is not clear at all how accurate this approach is. Assuming that the bottom-up approach corresponds to the real-word data-generating process and using a comprehensive simulation study, it is shown that the top-down approach can underestimate the necessary amount of total capital for lower credit qualities. Furthermore, the direction and strength of the stochastic dependence between the risk types, the copula function employed, and the loss definitions all have an impact on the performance of the top-down approach. In addition, a goodness-of-fit test shows that, based on time series of loss data with realistic length, it is rather difficult to decide which copula function is the right one.Bottom-up approach Copula function Goodness-of-fit test Risk management Top-down approach