Pricing vulnerable European options with stochastic default barriers

CF Lo and KC Ku Institute of Theoretical Physics and Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong, China Email: cho-hoi_hui{at}hkma.gov.hk Received on 31 July 2006. Accepted on 15 March 2007. This paper develops a valuation model of European options incorporatinga stochastic default barrier, which extends a constant defaultbarrier proposed in the Hull–White model. The defaultbarrier is considered as an option writer's liability. Closed-formsolutions of vulnerable European option values based on themodel are derived to study the impact of the stochastic defaultbarriers on option values. The numerical results show that negativecorrelation between the firm values and the stochastic defaultbarriers of option writers gives material reductions in optionvalues where the options are written by firms with leverageratios corresponding to BBB or BB ratings.     

Synthetic scope, computational chemistry and mechanism of a base induced 5-endo cyclization of benzyl alkynyl sulfides

We present an experimental and computational study of the reaction of aryl substituted benzyl 1-alkynyl sulfides with potassium alkoxide in acetonitrile, which produces 2-aryl 2,3-dihydrothiophenes in poor to good yields. The cyclization is most efficient with electron withdrawing groups on the aromatic ring. Evidence indicates there is rapid exchange of protons and tautomerism of the alkynyl unit prior to cyclization. Theoretical calculations were also conducted to help rationalize the base induced 5-endo cyclization of benzyl 1-propynyl sulfide (1a). The potential energy surface was calculated for the formation of 2,3-dihydrothiophene in a reaction of benzyl 1-propynyl sulfide (1a) with potassium methoxide. Geometries were optimized with CAM-B3LYP/6-311+G(d,p) in acetonitrile with the CPCM solvent model. It is significant that the benzyl propa-1,2-dien-1-yl sulfane (6) possessed a lower benzylic proton affinity than the benzyl prop-2-yn-1-yl sulfane (8) thus favoring the base induced reaction of the former. From benzyl(propa-1,2-dien-1-yl sulfane (6), 2,3-dihydrothiophene can be formed via a conjugate base that undergoes 5-endo-trig cyclization followed by a protonation step.     

Supramolecular Tetrad Featuring Covalently Linked Bis(porphyrin)–Phthalocyanine Coordinated to Fullerene: Construction and Photochemical Studies

A multimodular donor–acceptor tetrad featuring a bis(zinc porphyrin)–(zinc phthalocyanine) ((ZnP–ZnP)–ZnPc) triad and bis‐pyridine‐functionalized fullerene was assembled by a “two‐point” binding strategy, and investigated as a charge‐separating photosynthetic antenna‐reaction center mimic. The spectral and computational studies suggested that the mode of binding of the bis‐pyridine‐functionalized fullerene involves either one of the zinc porphyrin and zinc phthalocyanine (Pc) entities of the triad or both zinc porphyrin entities leaving ZnPc unbound. The binding constant evaluated by constructing a Benesi–Hildebrand plot by using the optical data was found to be 1.17×10⁵ M ^?1, whereas a plot of “mole‐ratio” method revealed a 1:1 stoichiometry for the supramolecular tetrad. The mode of binding was further supported by differential pulse voltammetry studies, in which redox modulation of both zinc porphyrin and zinc phthalocyanine entities was observed. The geometry of the tetrad was deduced by B3LYP/6‐31G* optimization, whereas the energy levels for different photochemical events was established by using data from the optical absorption and emission, and electrochemical studies. Excitation of the zinc porphyrin entity of the triad and tetrad revealed ultrafast singlet–singlet energy transfer to the appended zinc phthalocyanine. The estimated rate of energy transfer (k_ENT) in the case of the triad was found to be 7.5×10¹¹ s^?1 in toluene and 6.3×10¹¹ s^?1 in o‐dichlorobenzene, respectively. As was predicted from the energy levels, photoinduced electron transfer from the energy‐transfer product, that is, singlet‐excited zinc phthalocyanine to fullerene was verified from the femtosecond‐transient spectral studies, both in o‐dichlorobenzene and toluene. Transient bands corresponding to ZnPc ^{? +} in the 850 nm range and C₆₀ ^{? ?} in the 1020 nm range were clearly observed. The rate of charge separation, k_CS, and rate of charge recombination, k_CR, for the (ZnP–ZnP)–ZnPc ^{? +}:Py₂C₆₀ ^{? ?} radical ion pair (from the time profile of 849 nm peak) were found to be 2.20×10¹¹ and 6.10×10⁸ s^?1 in toluene, and 6.82×10¹¹ and 1.20×10⁹ s^?1 in o‐dichlorobenzene, respectively. These results revealed efficient energy transfer followed by charge separation in the newly assembled supramolecular tetrad.     

New deuterated oligo(ethylene glycol) building blocks and their use in the preparation of surface active lipids possessing labeled hydrophilic tethers

For the introduction of additional analysis protocols of tethered molecules, a method is presented to prepare functionalized, deuterated oligo(ethylene glycols) from ethylene glycol-d4. Partial oligomerization of ethylene glycol-d4 and conversion to ditosylates is accompanied by coupling reactions to prepare doubly benzyl protected oligo(ethylene glycols) with two to five repeating units. The tetramer bearing 16 deuteria was elaborated at both ends to eventually prepare 2,3-di-O-phytanyl-sn-glycerol-1-tetraethylene glycol-d,l-alpha-lipoic acid ester (DPTL), which bears a fully deuterated tetra(ethylene glycol) spacer group. Through linking of functionalized components, an analogue of DPTL possessing an octa(ethylene glycol) spacer group was prepared, both in deuterated and unlabeled form.     

Large scale polarizability calculations using the approximate coupled cluster model CC2 and MP2 combined with the resolution-of-the-identity approximation

We present an implementation of static and frequency-dependent polarizabilities for the approximate coupled cluster singles and doubles model CC2 and static polarizabilities for second-order Mo?ller-Plesset perturbation theory. Both are combined with the resolution-of-the-identity approximation for electron repulsion integrals to achieve unprecedented low operation counts, input-output, and disc space demands. To avoid the storage of double excitation amplitudes during the calculation of derivatives of density matrices, we employ in addition a numerical Laplace transformation for orbital energy denominators. It is shown that the error introduced by this approximation is negligible already with a small number of sampling points. Thereby an implementation of second-order one-particle properties is realized, which avoids completely the storage of quantities scaling with the fourth power of the system size. The implementation is tested on a set of organic molecules including large fused aromatic ring systems and the C(60) fullerene. It is demonstrated that exploiting symmetry and shared memory parallelization, second-order properties for such systems can be evaluated at the CC2 and MP2 level within a few hours of calculation time. As large scale applications, we present results for the 7-, 9-, and 11-ring helicenes.     

Lewis base stabilized phosphanylborane

The abstraction of the Lewis acid from [W(CO)(5)(PH(2)BH(2)NMe(3))] (1) by an excess of P(OMe(3))(3) leads to the quantitative formation of the first Lewis base stabilized monomeric parent compound of phosphanylborane [H(2)PBH(2)NMe(3)] 2. Density functional theory (DFT) calculations have shown a low energetic difference between the crystallographically determined antiperiplanar arrangement of the lone pair and the trimethylamine group relative to the P-B core and the synperiplanar conformation. Subsequent reactions with the main-group Lewis acid BH(3) as well as with an [Fe(CO)(4)] unit as a transition-metal Lewis acid led to the formation of [(BH(3))PH(2)BH(2)NMe(3)] (3), containing a central H(3)B-PH(2)-BH(2) unit, and [Fe(CO)(4)(PH(2)BH(2)NMe(3))] (4), respectively. In oxidation processes with O(2), Me(3)NO, elemental sulfur, and selenium, the boranylphosphine chalcogenides [H(2)P(Q)BH(2)NMe(3)] (Q = S 5 b; Se 5 c) as well as the novel boranyl phosphonic acid [(HO)(2)P(O)BH(2)NMe(3)] (6 a) are formed. All products have been characterized by spectroscopic as well as by single-crystal X-ray structure analysis.