Decomposing and valuing callable convertible bonds: a new method based on exotic options

In the framework of Black-Scholes-Merton option pricing models, by employing exotic options instead of plain options or warrants, this paper presents an equivalent decomposition method for usual Callable Convertible Bonds (CCB). Furthermore, the analytic valuation formulae for CCB are worked out by using the analytic formulae for those simpler securities decomposed from CCB. Moreover, this method is validated by comparing with Monte Carlo simulation. Besides, the effects of call clauses, coupon clauses and soft call condition clauses are analyzed respectively. These give lots of new insights into the valuation and analysis of CCB and much help to hedge their risks.Callable convertible bonds; Equivalent decomposition; Up-and-out calls; American binary calls; Derivative pricing

Unsupervised Feature Learning by Deep Sparse Coding

In this paper, we propose a new unsupervised feature learning framework, namely Deep Sparse Coding (DeepSC), that extends sparse coding to a multi-layer architecture for visual object recognition tasks. The main innovation of the framework is that it connects the sparse-encoders from different layers by a sparse-to-dense module. The sparse-to-dense module is a composition of a local spatial pooling step and a low-dimensional embedding process, which takes advantage of the spatial smoothness information in the image. As a result, the new method is able to learn several levels of sparse representation of the image which capture features at a variety of abstraction levels and simultaneously preserve the spatial smoothness between the neighboring image patches. Combining the feature representations from multiple layers, DeepSC achieves the state-of-the-art performance on multiple object recognition tasks.Comment: 9 pages, submitted to ICL

(Z)-3-(2-Methoxy­anilino)-1-phenyl­but-2-en-1-one

In the title compound, C17H17NO2, the dihedral angle between the two benzene rings is 55.2 (2)°. The meth­oxy group is slightly twisted away from the aniline ring [dihedral angle = 10.3 (2)°]. An intra­molecular N—H⋯O inter­action is present. In the crystal, the mol­ecules are linked into a three-dimensional supra­molecular network through two sets of C—H⋯π inter­actions

Topolgical Charged Black Holes in Generalized Horava-Lifshitz Gravity

As a candidate of quantum gravity in ultrahigh energy, the $(3+1)$-dimensional Ho\v{r}ava-Lifshitz (HL) gravity with critical exponent $z\ne 1$, indicates anisotropy between time and space at short distance. In the paper, we investigate the most general $z=d$ Ho\v{r}ava-Lifshitz gravity in arbitrary spatial dimension $d$, with a generic dynamical Ricci flow parameter $\lambda$ and a detailed balance violation parameter $\epsilon$. In arbitrary dimensional generalized HL$_{d+1}$ gravity with $z\ge d$ at long distance, we study the topological neutral black hole solutions with general $\lambda$ in $z=d$ HL$_{d+1}$, as well as the topological charged black holes with $\lambda=1$ in $z=d$ HL$_{d+1}$. The HL gravity in the Lagrangian formulation is adopted, while in the Hamiltonian formulation, it reduces to Dirac$-$De Witt's canonical gravity with $\lambda=1$. In particular, the topological charged black holes in $z=5$ HL$_6$, $z=4$ HL$_5$, $z=3,4$ HL$_4$ and $z=2$ HL$_3$ with $\lambda=1$ are solved. Their asymptotical behaviors near the infinite boundary and near the horizon are explored respectively. We also study the behavior of the topological black holes in the $(d+1)$-dimensional HL gravity with $U(1)$ gauge field in the zero temperature limit and finite temperature limit, respectively. Thermodynamics of the topological charged black holes with $\lambda=1$, including temperature, entropy, heat capacity, and free energy are evaluated.Comment: 51 pages, published version. The theoretical framework of z=d HL gravity is set up, and higher curvature terms in spatial dimension become relevant at UV fixed point. Lovelock term, conformal term, new massive term, and Chern-Simons term with different critical exponent z are studie

Thermodynamics of Black Holes in Massive Gravity

We present a class of charged black hole solutions in an ($n+2)$-dimensional massive gravity with a negative cosmological constant, and study thermodynamics and phase structure of the black hole solutions both in grand canonical ensemble and canonical ensemble. The black hole horizon can have a positive, zero or negative constant curvature characterized by constant $k$. By using Hamiltonian approach, we obtain conserved charges of the solutions and find black hole entropy still obeys the area formula and the gravitational field equation at the black hole horizon can be cast into the first law form of black hole thermodynamics. In grand canonical ensemble, we find that thermodynamics and phase structure depends on the combination $k -\mu^2/4 +c_2 m^2$ in the four dimensional case, where $\mu$ is the chemical potential and $c_2m^2$ is the coefficient of the second term in the potential associated with graviton mass. When it is positive, the Hawking-Page phase transition can happen, while as it is negative, the black hole is always thermodynamically stable with a positive capacity. In canonical ensemble, the combination turns out to be $k+c_2m^2$ in the four dimensional case. When it is positive, a first order phase transition can happen between small and large black holes if the charge is less than its critical one. In higher dimensional ($n+2 \ge 5$) case, even when the charge is absent, the small/large black hole phase transition can also appear, the coefficients for the third ($c_3m^2$) and/or the fourth ($c_4m^2$) terms in the potential associated with graviton mass in the massive gravity can play the same role as the charge does in the four dimensional case.Comment: Latex 19 pages with 8 figure