Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero-and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent a of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

Risk premiumin the global creditMarkets: 2006-2012

¿What have we learnt from the 2006-2012 crisis, including events such as the subprime crisis, the bankruptcy of Lehman Brothers or the European sovereign debt crisis, among others? It is usually assumed that in firms that have a CDS quotation, this CDS is the key factor in establishing the credit premiumrisk for a new financial asset. Thus, the CDS is a key element for any investor in taking relative value opportunities across a firm’s capital structure. In the first chapter we study the most relevant aspects of the microstructure of the CDS market in terms of pricing, to have a clear idea of how this market works. We consider that such an analysis is a necessary point for establishing a solid base for the rest of the chapters in order to carry out the different empirical studies we perform. In its document “Basel III: A global regulatory framework for more resilient banks and banking systems”, Basel sets the requirement of a capital charge for credit valuation adjustment (CVA) risk in the trading book and its methodology for the computation for the capital requirement. This regulatory requirement has added extra pressure for in-depth knowledge of the CDS market and this motivates the analysis performed in this thesis. The problem arises in estimating of the credit risk premium for those counterparties without a directly quoted CDS in the market. How can we estimate the credit spread for an issuer without CDS? In addition to this, given the high volatility period in the credit market in the last few years and, in particular, after the default of Lehman Brothers on 15 September 2008, we observe the presence of big outliers in the distribution of credit spread in the different combinations of rating, industry and region. After an exhaustive analysis of the results from the different models studied, we have reached the following conclusions. It is clear that hierarchical regression models fit the data much better than those of non-hierarchical regression. Furthermore,we generally prefer the median model (50%-quantile regression) to the mean model (standard OLS regression) due to its robustness when assigning the price to a new credit asset without spread,minimizing the “inversion problem”. Finally, an additional fundamental reason to prefer the median model is the typical "right skewness" distribution of CDS spreads...