Game Options Analysis of the Information Role of Call Policies in Convertible Bonds

Abstract

In debt financing, existence of information asymmetry on the firm quality between the firm management and bond investors may lead to significant adverse selection costs. We develop the two-stage sequential dynamic two-person game option models to analyse the market signalling role of the callable feature in convertible bonds. We show that firms with positive private information on earning potential may signal their type to investors via the callable feature in a convertible bond. We present the variational inequalities formulation with respect to various equilibrium strategies in the two-person game option models via characterization of the optimal stopping rules adopted by the bond issuer and bondholders. The bondholders’ belief system on the firm quality may be revealed with the passage of time when the issuer follows his optimal strategy of declaring call or bankruptcy. Under separating equilibrium, the quality status of the firm is revealed so the information asymmetry game becomes a new game under complete information. To analyse pooling equilibrium, the corresponding incentive compatibility constraint is derived. We manage to deduce the sufficient conditions for the existence of signalling equilibrium of our game option model under information asymmetry. We analyse how the callable feature may lower the adverse selection costs in convertible bond financing. We show how a low-quality firm may benefit from information asymmetry and vice versa, underpricing of the value of debt issued by a high-quality firm.     

Dual Esterase‐ and Steroid‐Responsive Energy Transfer Modulation of Ruthenium(II) and Rhenium(I) Complex Functionalized Gold Nanoparticles

A number of adamantane‐containing ruthenium(II) and rhenium(I) complexes have been synthesized, characterized, and noncovalently functionalized with β‐cyclodextrin‐capped gold nanoparticles (β‐CD–GNPs) through the host–guest interaction between cyclodextrin and adamantane. The resultant nanoconjugates have been characterized by transmission electron microscopy (TEM), energy‐dispersive X‐ray analysis (EDX), and 2D ROESY ¹H NMR experiments. The Förster resonance energy transfer (FRET) properties of the nanoconjugates can be modulated by both esterase‐accelerated hydrolysis and competitive displacement of steroid, by monitoring the emission intensity and luminescence lifetime. The FRET efficiencies are found to vary with the nature of the chromophores and the length of the spacer between the transition metal complexes and the GNPs. This work constitutes a “proof‐of‐principle” assay method for the dual‐functional detection of important classes of biomolecules, such as enzymes and steroids.     

Fuzzy variational principle and its applications

Linear and non-linear peaky fuzzy numbers and their arithmetic operations are constructed for the analysis of engineering structures with fuzzy characteristic quantities. Fuzziness of the corresponding quantities is consistently incorporated into the functional of the total potential energy. A set of deterministic recursive equations is obtained as the alternative expressions of the fuzzy variational principle by means of the second-order perturbation technique. The fuzzy Ritz method and the fuzzy finite element method are presented as the applications of the fuzzy variational principle. Accordingly, the roundabout procedures frequently used in the formulations of the fuzzy finite element method are avoided. A benchmark problem of a bending beam with fuzzy Young's modulus under fuzzy external loading is solved by the developed fuzzy numerical methods. Numerical examples show that results determined by these two fuzzy methods are both little conservative, and are in good agreement with those obtained by the analytical method. Moreover, the fuzzy Ritz method or the fuzzy finite element method can provide more valuable information than the conventional deterministic methods.     

First synthesis of dioxadithiaporphycene with a benzene ring fused onto the double bond

Dioxadithiaporphycenes 5 and 5′ were synthesized by using the Suzuki cross-coupling and McMurry coupling reactions as the key steps. This approach provided an access to the first dioxadithiaporphycene derivative 15 with a benzene ring fused onto the double bond.     

In vitro and in vivo studies of androst‐4‐ene‐3,6,17‐trione in horses by gas chromatography–mass spectrometry

This paper describes the application of gas chromatography–mass spectrometry (GC‐MS) for in vitro and in vivo studies of 6‐OXO in horses, with a special aim to identify the most appropriate target metabolite to be monitored for controlling the administration of 6‐OXO in racehorses. In vitro studies of 6‐OXO were performed using horse liver microsomes. The major biotransformation observed was reduction of one keto group at the C3 or C6 positions. Three in vitro metabolites, namely 6α‐hydroxyandrost‐4‐ene‐3,17‐dione (M1), 3α‐hydroxyandrost‐4‐ene‐6,17‐dione (M2a) and 3β‐hydroxyandrost‐4‐ene‐6,17‐dione (M2b) were identified. For the in vivo studies, two thoroughbred geldings were each administered orally with 500 mg of androst‐4‐ene‐3,6,17‐trione (5 capsules of 6‐OXO_®) by stomach tubing. The results revealed that 6‐OXO was extensively metabolized. The three in vitro metabolites (M1, M2a and M2b) identified earlier were all detected in post‐administration urine samples. In addition, seven other urinary metabolites, derived from a further reduction of either one of the remaining keto groups or one of the remaining keto groups and the olefin group, were identified. These metabolites included 6α,17β‐dihydroxyandrost‐4‐en‐3‐one (M3a), 6,17‐dihydroxyandrost‐4‐en‐3‐one (M3b and M3c), 3β,6β‐dihydroxyandrost‐4‐en‐17‐one (M4a), 3,6‐dihydroxyandrost‐4‐en‐17‐one (M4b), 3,6‐dihydroxyandrostan‐17‐one (M5) and 3,17‐dihydroxyandrostan‐6‐one (M6). The longest detection time observed in urine was up to 46 h for the M6 metabolite. For blood samples, the peak 6‐OXO plasma concentration was observed 1 h post administration. Plasma 6‐OXO decreased rapidly and was not detectable 12 h post administration. Copyright © 2009 John Wiley & Sons, Ltd.     

Determination of Allosteric Effects and Interstrand Bidentate Interactions in DNA‐Peptide Molecular Recognition

To study DNA allostery, quantitative DNase I footprinting studies were carried out on a newly designed peptide His‐Hyp‐Lys‐Lys‐(Py)₄‐Lys‐Lys‐NH₂ (HypKK‐10) containing the XHypKK (Hyp = hydroxyproline) and polyamide motifs. The interconnection of DNA footprints of peptides HypKK‐10 and the parent peptide PyPro‐12 supports the proposal that interaction network cooperativity is preferred in DNA‐peptide interactions between multiple recognition sites. A simple method of determining interstrand bidentate interactions between the peptide moieties and DNA bases is introduced. It is envisaged that interstrand bidentate interactions also participate in the relay of conformational changes to recognition sites on the complementary strands. Circular dichroism studies of the titration of peptide HypKK‐10 with an oligonucleotide duplex indicate that this peptide binds in a dimeric fashion to DNA in the minor groove. This work may prompt the design of new DNA binding ligands for the study of DNA‐peptide allosteric interactions and DNA interaction network.     

Stable Anticancer Gold(III)–Porphyrin Complexes: Effects of Porphyrin Structure

In the design of physiologically stable anticancer gold(III) complexes, we have employed strongly chelating porphyrinato ligands to stabilize a gold(III) ion [Chem. Commun. 2003 , 1718; Coord. Chem. Rev. 2009 , 253, 1682]. In this work, a family of gold(III) tetraarylporphyrins with porphyrinato ligands containing different peripheral substituents on the meso‐aryl rings were prepared, and these complexes were used to study the structure–bioactivity relationship. The cytotoxic IC₅₀ values of [Au(Por)]⁺ (Por=porphyrinato ligand), which range from 0.033 to >100 μM , correlate with their lipophilicity and cellular uptake. Some of them induce apoptosis and display preferential cytotoxicity toward cancer cells than to normal noncancerous cells. A new gold(III)–porphyrin with saccharide conjugation [Au(4‐glucosyl‐TPP)]Cl ( 2 a ; H₂(4‐glucosyl‐TPP)=meso‐tetrakis(4‐β‐D ‐glucosylphenyl)porphyrin) exhibits significant cytostatic activity to cancer cells (IC₅₀=1.2–9.0 μM ) without causing cell death and is much less toxic to lung fibroblast cells (IC₅₀>100 μM ). The gold(III)–porphyrin complexes induce S‐phase cell‐cycle arrest of cancer cells as indicated by flow cytometric analysis, suggesting that the anticancer activity may be, in part, due to termination of DNA replication. The gold(III)–porphyrin complexes can bind to DNA in vitro with binding constants in the range of 4.9×10⁵ to 4.1×10⁶ dm³ mol^?1 as determined by absorption titration. Complexes 2 a and [Au(TMPyP)]Cl₅ ( 4 a ; [H₂TMPyP]⁴⁺=meso‐tetrakis(N‐methylpyridinium‐4‐yl)porphyrin) interact with DNA in a manner similar to the DNA intercalator ethidium bromide as revealed by gel mobility shift assays and viscosity measurements. Both of them also inhibited the topoisomerase I induced relaxation of supercoiled DNA. Complex 4 a , a gold(III) derivative of the known G‐quadruplex‐interactive porphyrin [H₂TMPyP]⁴⁺, can similarly inhibit the amplification of a DNA substrate containing G‐quadruplex structures in a polymerase chain reaction stop assay. In contrast to these reported complexes, complex 2 a and the parental gold(III)–porphyrin 1 a do not display a significant inhibitory effect (<10 %) on telomerase. Based on the results of protein expression analysis and computational docking experiments, the anti‐apoptotic bcl‐2 protein is a potential target for those gold(III)–porphyrin complexes with apoptosis‐inducing properties. Complex 2 a also displays prominent anti‐angiogenic properties in vitro. Taken together, the enhanced stabilization of the gold(III) ion and the ease of structural modification render porphyrins an attractive ligand system in the development of physiologically stable gold(III) complexes with anticancer and anti‐angiogenic activities.