S-matrix theory for transmission through billiards in tight-binding approach

In the tight-binding approximation we consider multi-channel transmission through a billiard coupled to leads. Following Dittes we derive the coupling matrix, the scattering matrix and the effective Hamiltonian, but take into account the energy restriction of the conductance band. The complex eigenvalues of the effective Hamiltonian define the poles of the scattering matrix. For some simple cases, we present exact values for the poles. We derive also the condition for the appearance of double poles.Comment: 29 pages, 9 figures, submitted to J. Phys. A: Math. and Ge

How Smart are Investors after the Subprime Mortgage Crisis? Evidence from the Securitization Market

Two factors have proven to be strongly relevant for the subprime mortgage crisis. The first is the lack of screening incentives of originators, which had not been anticipated by investors. The second is that investors relied too much on credit ratings. We examine whether investors have learned from these shortcomings. On the basis of securitizations from 2010 and 2011, we find that investors require a significantly higher risk premium when there is a high degree of asymmetric information. The credit spreads of information sensitive tranches are significantly higher if originators do not retain a part of the securitization or if they choose vertical slice retention instead of retaining the equity tranche. Moreover, the relevance of credit ratings in comparison to other credit factors has significantly decreased. Apparently, investors mainly consider ratings to discriminate between information sensitive and information insensitive tranches, beyond that they rely on their own risk analysis. This suggests that investors have learned their lesson from the subprime mortgage crisis