An Empirical Analysis of the Pricing of Collateralized Debt Obligations

We study the pricing of collateralized debt obligations (CDOs) using an extensive new data set for the actively-traded CDX credit index and its tranches. We find that a three-factor portfolio credit model allowing for firm-specific, industry, and economywide default events explains virtually all of the time-series and crosssectional variation in CDX index tranche prices. These tranches are priced as if losses of 0.4, 6, and 35 percent of the portfolio occur with expected frequencies of 1.2, 41.5, and 763 years, respectively. On average, 65 percent of the CDX spread is due to firm-specific default risk, 27 percent to clustered industry or sector default risk, and 8 percent to catastrophic or systemic default risk. Recently, however, firm-specific default risk has begun to play a larger role.

The Value of Information in Public Decisions

This paper considers the problem of an imperfectly informed regulator constrained in his choice of environmental regulation by the political opposition of those affected by the policy. We compare the value of two types of information to the regulator: the social cost of pollution and the profitability of firms present in the economy. We find that in environments where small increases in the losses to regulated firms greatly affect the regulator's ability to implement the policy, it is most valuable to learn the types of firms, while it is most valuable to learn the social cost of pollution when small increases in losses are relatively ineffectual.Environmental Policy, Pollution, Optimal Taxation

Squeezed Fock state by inconclusive photon subtraction

We analyze in details the properties of the conditional state recently obtained by J. Wenger, et al. [Phys. Rev. Lett. {\bf 92}, 153601 (2004)] by means of inconclusive photon subtraction (IPS) on a squeezed vacuum state $S(r)\ket{0}$. The IPS process can be characterized by two parameters: the IPS transmissivity $\tau$ and the photodetection quantum efficiency $\eta$. We found that the conditional state approaches the squeezed Fock state $S(r)\ket{1}$ when $\tau,\eta \to 1$, i.e., in the limit of single-photon subtraction. For non-unit IPS transmissivity and efficiency, the conditioned state remains close to the target state, {\em i.e.} shows a high fidelity for a wide range of experimental parameters. The nonclassicality of the conditional state is also investigated and a nonclassicality threshold on the IPS parameters is derived.Comment: 10 pages, 7 figure

Simulating a single qubit channel using a mixed state environment

We analyze the class of single qubit channels with the environment modeled by a one-qubit mixed state. The set of affine transformations for this class of channels is computed analytically, employing the canonical form for the two-qubit unitary operator. We demonstrate that, 3/8 of the generalized depolarizing channels can be simulated by the one-qubit mixed state environment by explicitly obtaining the shape of the volume occupied by this class of channels within the tetrahedron representing the generalized depolarizing channels. Further, as a special case, we show that the two-Pauli Channel cannot be simulated by a one-qubit mixed state environment.Comment: Published version with minor change

Models and Phenomenology of Maximal Flavor Violation

We consider models of maximal flavor violation (MxFV), in which a new scalar mediates large q_3 q_1 or q_3 q_2 flavor changing transitions (q_i is an i'th generation quark), while q_3 q_3 transitions are suppressed, e.g., \xi_{31}, \xi_{13} ~ V_{tb} and \xi_{33} ~ V_{td}, where \xi_{ij} are the new scalar couplings to quarks and V is the CKM matrix. We show that, contrary to the conventional viewpoint, such models are not ruled out by the existing low energy data on K^0, B^0 and D^0 oscillations and rare K and B-decays. We also show that these models of MxFV can have surprising new signatures at the LHC and the Tevatron.Comment: Latex, 4 pages, 1 figure. Version as publishe

Smoothed Analysis of the Condition Numbers and Growth Factors of Matrices

Let \orig{A} be any matrix and let $A$ be a slight random perturbation of \orig{A}. We prove that it is unlikely that $A$ has large condition number. Using this result, we prove it is unlikely that $A$ has large growth factor under Gaussian elimination without pivoting. By combining these results, we bound the smoothed precision needed by Gaussian elimination without pivoting. Our results improve the average-case analysis of Gaussian elimination without pivoting performed by Yeung and Chan (SIAM J. Matrix Anal. Appl., 1997).Comment: corrected some minor mistake