Ehrhart h∗h^*-vectors of hypersimplices

We consider the Ehrhart $h^*$-vector for the hypersimplex. It is well-known that the sum of the $h_i^*$ is the normalized volume which equals an Eulerian numbers. The main result is a proof of a conjecture by R. Stanley which gives an interpretation of the $h^*_i$ coefficients in terms of descents and excedances. Our proof is geometric using a careful book-keeping of a shelling of a unimodular triangulation. We generalize this result to other closely related polytopes

The Implied Benchmark Rate in the Credit Default Swap Market of Sovereign Bonds

Credit default swap(CDS) is a new developed derivative to insure the credit risk of an underlying entity. This paper investigates the correlation relationship of the CDS market of sovereign borrowers and sovereign bond market. Applying the formula in the paper of Hull et al.(2004), an implied default-free rate(also called benchmark rate) of CDS market is computed; its correlations with US treasury and LIBOR are tested respectively. The tests indicate that,in sovereign CDS market, the benchmark is more related with US treasury, although LIBOR has been used as the best approximation of market benchmark in both academia and industry. Therefore, this paper suggest the importance of US treasury to sovereign CDS market in measuring market's reference and searching for mispriced chance.In addition, a spuriously controversy result are found as rating-specific CDS benchmark rates are contrasted. A monotonic decrease of these benchmarks is clearly observed for the sovereigns with lower credit rating and higher default risk. The phenomenon is carefully explained and the main reason comes from the higher CDS rate than yield spread. This invites a further comparison of the price discovery processes in sovereign CDS market and the corresponding sovereign bond market.