Reforming Capital Requirements in Emerging Countries: Calibrating Basel II using Historical Argentine Credit Bureau Data and CreditRisk+

Emerging economies are likely to be more volatile and asset risk more correlated than in industrialized countries. In this paper we discuss how credit scoring techniques and modern credit risk portfolio models can be used to measure credit risk and check Basel II calibration for such an environment. After reviewing the development of credit risk portfolio models, to explain our choice in using CreditRisk+, we discuss the definition and estimation methodology for a set of essential parameter inputs, which in turn depend on the data available - in this case from the Argentine public credit bureau. We then simulate, bank by bank, the introduction of Basel II's foundation IRB approach using the same data for Argentina and compare the results. We analyze how the IRB approach might be recalibrated and finally discuss a set of other issues regarding IRB implementation in an emerging economy.

Reforming capital requirements in emerging countries

This paper then attempts to show how a PCR, in this case from Argentina, can help to set capital and provisioning rules. In order to so this, we employ an econometric credit scoring model on the PCR data - an ordered probit - and we use a recently developed "off the shelf" credit risk portfolio model - CreditRisk+. Section 2 provides a review of the development in credit risk measurement, with emerging countries in mind, to motivate this modeling choice. We then provide a description of the Argentine PCR (section 3) and discuss some of the issues in applying CreditRisk+ to Argentine data (section 4). We then turn our attention to Basel II and show how the PCR and the credit-scoring model can be used to simulate the effect of the Basel II IRB approach as currently proposed. We compare our IRB simulation with our CreditRisk+ estimates of provisioning and capital requirements (section 5). We discuss how the IRB approach might be recalibrated to "fit" the local data (section 6). In section 7 we then discuss the regulatory choices faced by an emerging country regulator given the Basel II proposals and section 8 concludes.Para cualquier uso del contenido del presente documento debe ponerse en contacto con el autor

On the Number of Closed Gaps of Discrete Periodic One-Dimensional Operators

From the general inverse theory of periodic Jacobi matrices, it is known that a periodic Jacobi matrix of minimal period $p \geq 2$ may have at most $p-2$ closed spectral gaps. We discuss the maximal number of closed gaps for one-dimensional periodic discrete Schr\"odinger operators of period $p$. We prove nontrivial upper and lower bounds on this quantity for large $p$ and compute it exactly for $p \leq 6$. Among our results, we show that a discrete Schr\"odinger operator of period four or five may have at most a single closed gap, and we characterize exactly which potentials may exhibit a closed gap. For period six, we show that at most two gaps may close. In all cases in which the maximal number of closed gaps is computed, it is seen to be strictly smaller than $p-2$, the bound guaranteed by the inverse theory. We also discuss similar results for purely off-diagonal Jacobi matrices.Comment: 26 page