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

catena-Poly[[tetra­aqua­manganese(II)]-μ-5-carboxyl­ato-1-carboxyl­atomethyl-2-oxidopyridinium-κ2 O 5:O 1]

In the title coordination polymer, [Mn(C8H5NO5)(H2O)4]n, the MnII atom is coordinated by two carboxyl­ate O atoms from two 5-carboxyl­ato-1-carboxyl­atomethyl-2-oxidopyridinium (L 2−) ligands and by four water mol­ecules in a distorted octa­hedral geometry. The L 2− ligands bridge the Mn atoms into an infinite chain motif along [100]; the chains are further inter­linked by O—H⋯O hydrogen bonds into a three-dimensional supra­molecular net

Single-photon transport and mechanical NOON state generation in microcavity optomechanics

We investigate the single-photon transport in a single-mode optical fiber coupled to an optomechanical system in the single-photon strong-coupling regime. The single-photon transmission amplitude is analytically obtained with a real-space approach and the effects of thermal noises are studied via master-equation simulations. The results provide an explicit understanding of optomechanical interaction and offer a useful guide for manipulating single photons in optomechanical systems. Based on the theoretical framework, we further propose a scheme to generate the mechanical NOON states with arbitrary phonon numbers by measuring the sideband photons. The probability for generating the NOON state with five phonons is over 0.15.Comment: 13 pages, 6 figure