CVA and FVA to Derivatives Trades Collateralized by Cash

In this article, we combine replication pricing with expectation pricing for derivative trades that are partially collateralized by cash. The derivatives are replicated by underlying assets and cash, using repurchasing agreement (repo) and margining, which incur funding costs. We derive a partial differential equation (PDE) for the derivatives price, obtain and decompose its solution into the risk-free value of the derivative plus credit valuation adjustment (CVA) and funding valuation adjustment (FVA). For most derivatives, as we shall show, CVAs can be evaluated analytically or semi-analytically, while FVAs, as well as the derivatives values, will have to be solved recursively through numerical procedures due to their interdependence. In numerical demonstrations, continuous and discrete margin revisions are considered, respectively, for an equity call option and a vanilla interest-rate swaps.Comment: 29 pages, 4 figure

MiniMax Entropy Network: Learning Category-Invariant Features for Domain Adaptation

How to effectively learn from unlabeled data from the target domain is crucial for domain adaptation, as it helps reduce the large performance gap due to domain shift or distribution change. In this paper, we propose an easy-to-implement method dubbed MiniMax Entropy Networks (MMEN) based on adversarial learning. Unlike most existing approaches which employ a generator to deal with domain difference, MMEN focuses on learning the categorical information from unlabeled target samples with the help of labeled source samples. Specifically, we set an unfair multi-class classifier named categorical discriminator, which classifies source samples accurately but be confused about the categories of target samples. The generator learns a common subspace that aligns the unlabeled samples based on the target pseudo-labels. For MMEN, we also provide theoretical explanations to show that the learning of feature alignment reduces domain mismatch at the category level. Experimental results on various benchmark datasets demonstrate the effectiveness of our method over existing state-of-the-art baselines.Comment: 8 pages, 6 figure

Constraints on a decomposed dark fluid with constant adiabatic sound speed by jointing the geometry test and growth rate after Planck data

In this paper, a unified dark fluid with constant adiabatic sound speed is decomposed into cold dark matter interacting with vacuum energy. Based on Markov chain Monte Carlo method, we constrain this model by jointing the geometry and dynamical measurement. The geometry test includes cosmic microwave background radiation from \textit{Planck}, baryon acoustic oscillation, and type Ia supernovae; the dynamic measurement is $f\sigma_8(z)$ data points which is obtained from the growth rate via redshift-space distortion, and $\sigma_8(z)$ is the root-mean-square amplitude of the density contrast $\delta$ at the comoving $8h^{-1}$ Mpc scale. The jointed constraint shows that $\alpha$ = $0.000662_{- 0.000662}^{+ 0.000173}$ and $\sigma_8$ = $0.824_{- 0.0166}^{+ 0.0128}$. The CMB and matter power spectra are both similar for the case of $\alpha=$ mean value and that of $\alpha=0$. However, the evolutionary curves of $f\sigma_8(z)$ are different. This means that, to some extent, the data points of the growth rate could break the degeneracy of the dark energy models.Comment: 11 pages, 5 figures. arXiv admin note: text overlap with arXiv:1311.341

A CO observation of the galactic methanol masers

Context: We investigated the molecular gas associated with 6.7 GHz methanol masers throughout the Galaxy using a J=1-0 transition of the CO isotopologues. Methods:Using the 13.7-meter telescope at the Purple Mountain Observatory (PMO), we have obtained ^{12}CO and ^{13}CO (1-0) lines for 160 methanol masers sources from the first to the third Galactic quadrants. We made efforts to resolve the distance ambiguity by careful comparison with the radio continuum and HI 21 cm observations. Results: First, the maser sources show increased ^{13}CO line widths toward the Galactic center, suggesting that the molecular gas are more turbulent toward the Galactic center. This trend can be noticeably traced by the ^{13}CO line width. Second, the ^{12}CO excitation temperature shows a noticeable correlation with the H_2 column density. A possible explanation consistent with the collapse model is that the higher surface-density gas is more efficient to the stellar heating and/or has a higher formation rate of high-mass stars. Third, comparing the IRDCs, the maser sources on average have significantly lower H_2 column densities, moderately higher temperatures, and similar line widths. Fourth, in the mapped regions, 51 ^{13}CO cores have been revealed. Only 17 coincide with the radio continuum emission (F_{cm}>6 mJy), while a larger fraction (30 cores) coincide with the infrared emissions. The IR-bright and radio-bright sources exhibit significantly higher $^{12}$CO excitation temperatures than the IR-faint and radio-faint sources, respectively. Conclusions: The 6.7 GHz masers show a moderately low ionization rate but have a common-existing stellar heating that generates the IR emissions. The relevant properties can be characterized by the ^{12}CO and ^{13}CO (1-0) emissions in several aspects as described above.Comment: 38 pages, 13 figures, 4 tables, accepted to Astronomy and Astrophysic