Computation of Greeks in LIBOR models driven by time–inhomogeneous Lévy processes

The aim of this article is to compute Greeks, i.e. price sensitivities in the framework of the Lévy LIBOR model. Two approaches are discussed. The first approach is based on the integration-by-parts formula, which lies at the core of the application of the Malliavin calculus to finance. The second approach consists of using Fourier-based methods for pricing derivatives. We illustrate the result by applying the formula to a caplet price where the jump part of the driving process of the underlying model is given by a time–inhomogeneous Gamma process and alternatively by a Variance Gamma process.     

侧链键合水杨醛型双齿席夫碱配基的功能化聚砜的合成及其稀土离子配合物的光致发光性能

通过氯甲基化聚砜(CMPSF)与4-羟基水杨醛(HSA)的亲核取代反应,将水杨醛(SA)基团键合在聚砜侧链,制得改性聚砜PSF-SA;再经PSF-SA的醛基分别与苯胺(AN)和环己胺(CA)发生席夫碱反应,获得了两种侧链键合了水杨醛型双齿席夫碱配基的功能化聚砜PSF-SAN和PSF-SCA,产物的结构由红外光谱和核磁共振氢谱表征。以两种功能化聚砜为大分子配体,与Tb(Ⅲ)离子及Eu(Ⅲ)离子分别配位,制得了二元高分子-稀土配合物,初步探索了配合物的光致发光性能。本文重点研究了功能化聚砜PSF-SAN和PSFSCA的制备反应,考察与分析了主要因素对CMPSF与HSA之间亲核取代反应的影响规律。结果表明,对于该亲核取代反应,适宜的溶剂为极性较强的N,N-二甲基乙酰胺,80℃为适宜的反应温度。大分子配体PSFSAN对Eu(Ⅲ)离子的荧光发射产生强烈的敏化作用,配合物PSF-(SAN)_3-Eu(Ⅲ)发射红光;大分子配体PSF-SCA对Tb(Ⅲ)离子的荧光发射也产生敏化作用,配合物PSF-(SCA)_3-Tb(Ⅲ)发射绿光。     

Different two-dimensional metal-organic frameworks through ligand modification

Through ligand modification, we have replaced the central benzene ring of H₂TDBA ([1,1′:3′,1″-terphenyl]-4,4″-dicarboxylic acid) with the pyridine structurally related ligand H₂PDDA (4,4′-(pyridine-2,6-diyl)dibenzoic acid), which makes the central pyridine ring of H₂PDDA more coplanar with two benzene rings on both sides of the ligand. The modification results in a dramatically different linkage configuration, thereby allowing structural changes to the metal-organic frameworks (MOFs). Two 2-D MOFs, [Cu(TDBA)(DMA)₂]·H₂O (BUT-221, DMA = N,N-dimethylacetamide), and [Cu₃(PDDA)₃(DMA)₂(H₂O)]·5H₂O (BUT-223) have been synthesized through reactions of two ditopic carboxylate ligands with Cu(NO₃)₂·3H₂O under solvothermal conditions, and characterized by single-crystal X-ray diffraction, powder X-ray diffraction, thermogravimetric analysis and infrared spectroscopy. Topological analysis shows that BUT-221 is a twofold parallel interpenetrating 4⁴ 2-D network with a skl topology, while BUT-223 is a 2-D network with a kgm topology.     

Co−MOFs with 1,1′-(5-methyl-1,3-phenylene)bis(1H-imidazole) and aromatic carboxylates as coligands: synthesis,structure, and spectroscopic and thermal characterizations

Four cobalt(II) compounds, [Co(Bim)(IA)(H₂O)₂]_n·0.5nH₂O (1), [Co(Bim)(MA)(H₂O)₂]_n (2), [Co₂(Bim)₂(MA)₂]_n·nH₂O (3), and [Co₃(Bim)₄(TA)₂(H₂O)₂]_n·2.5nH₂O (4), have been synthesized by solvothermal reactions of cobalt(II) salts with 1,1′-(5-methyl-1,3-phenylene)bis(1H-imidazole) [Bim] and aromatic polycarboxylic acids (H₂IA = isophthalic acid, H₂MA = 5-methylisophthalic acid, and H₃TA = trimesic acid) as coligands. The four complexes were characterized by IR and UV?vis spectra, elemental analyses, X-ray powder and single-crystal diffractions, and thermogravimetric analyses (TGAs). 1 features a zigzag polymeric macrocycle chain containing a nanotubular channel, which is constructed by bridging the folded 20-membered macrocyclic [Co₂(Bim)₂] subunits with IA ligands. 2 represents a double-chain structure containing 18-membered macrocyclic [Co₂(Bim)(MA)] subunits. Both 3 and 4 are 2-D porous coordination polymers but have different architectures. In 3, cage-like [Co₄(Bim)₂(MA)₄] subunits are 4-connected nodes that are further bridged by another half-set of Bim ligands to form a 2-D helical structure containing one-dimensional achiral channels and alternately arranged left- and right-handed helical tubular channels. In 4, Bim ligands bridge three crystallographically independent Co centers into sharply distorted left- and right-handed helices which are further connected by TA ligands to form a meso layer about 3.0 nm monolayer thickness with a unique (3,4)-connected topology. The structural diversities of coordination polymers 1–4 are tuned by the flexible coordination number of Co and coligand polycarboxylates. Thermal analyses show that the main frameworks of all compounds remain stable to 352 °C. Moreover, the interesting color changes of crystals 1–4, varying from pink to purple and dark blue, result from the d → d* transitions of chromophoric Co²⁺ in different coordination geometries as determined by the UV–vis spectra in combination with crystal structure analyses.     

A crystallographic and DFT study on a NHC complex of niobium oxide trifluoride

The complex [NbOF₃(Ipr)]₂, 1, was afforded in crystalline form by reaction of NbF₅ with the bulky NHC ligand 1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene (IPr) in toluene by slow contact with moisture air. The molecular structure of 1 was ascertained by X-ray diffraction, providing the first example of a dinuclear NbOF₃ derivative and also a rare case of niobium compound with a monodentate NHC. A DFT investigation has shown that the Nb–C bond consists of a weak NHC to Nb σ donation, reinforced by an electrostatic contribution presumably favored by the presence of the ancillary fluoride ligands. The computed enthalpy for the dissociation of one Ipr from 1 is ca. 36 kcal mol^?1. The presence of bulky 2,6-diisopropylphenyl substituents on the carbene ligand has negligible influence on the Nb–C bond, as highlighted by DFT analyses on simplified models.     

Mononuclear,homo- and hetero-binuclear complexes of 1-(5-(1-(2-aminophenylimino)ethyl)-2,4-dihydroxyphenyl)ethanone: synthesis,magnetic, spectral,antimicrobial, antioxidant,and antitumor studies

A new Schiff base, H₂L, was prepared by condensation of 4,6-diacetylresorcinol with o-phenylenediamine in molar ratio 1?:?1. The ligand reacted with copper(II), nickel(II), cobalt(II), iron(III), zinc(II), oxovanadium(IV), and dioxouranium(VI) ions in the absence and presence of LiOH to yield mononuclear and homobinuclear complexes. The mononuclear dioxouranium(VI) complex [(HL)-(UO₂)(OAc)(H₂O)]·5H₂O was used to synthesize heterobinuclear complexes. The ligand and its metal complexes were characterized by elemental analyses, IR, ¹H-, and ¹³C-NMR, electronic, ESR and mass spectra, conductivity, and magnetic susceptibility measurements as well as thermal analysis. In the absence of LiOH, mononuclear complexes (1, 4, and 9) were obtained; in the presence of LiOH, binuclear complexes (3, 5, 7, and 10) as well as mononuclear complexes (2, 6, and 8) were obtained. In the mononuclear complexes, the coordinating sites are the phenolic oxygen, azomethine nitrogen, and amino nitrogen. In addition to these coordinating sites, the free carbonyl and phenolic OH are involved in coordination in binuclear complexes. The metal complexes exhibited octahedral, tetrahedral, and square planar geometries while the uranium is seven-coordinate. The antimicrobial and antioxidant activities of the ligand and its complexes were investigated. The ligand and the metal complexes showed antitumor activity against Ehrlich Acites Carcinoma.     

Synthesis and DFT calculations of oxido and phenylimido-rhenium(V) complexes incorporating the N,O donor ligand 2-[(2-hydroxyethylimino)methyl]phenol

The reactions of equimolar amounts of trans-[ReOC1₃(PPh₃)₂] or trans-[Re(NPh)(PPh₃)₂Cl₃] with a Schiff base formed by condensation of 2-hydroxy-4-methoxybenzaldehyde and ethanolamine (H₂L) result in the formation of cis-[ReO(HL)PPh₃Cl₂] (1a) and trans-[Re(NPh)(HL)(PPh₃)Cl₂] (2b), respectively, in good yields. 1a and 2b have been characterized by a range of spectroscopic and analytical techniques. The X-ray crystal structures of 1a and 2b reveal that 1a is an octahedral cis-Cl,Cl oxorhenium(V) complex, while 2b is a trans-Cl,Cl phenylimidorhenium(V) complex. The complexes are weakly emissive at room temperature with quantum yields of 10^?4. Density functional theory calculations of the electronic properties of the complexes were performed and are in agreement with the experimental results. The complexes display quasi-reversible Re(V)/Re(VI) redox couples in acetonitrile. There is reasonable agreement between the experimental and calculated redox potentials of 1a and 2b.     

Construction of Mononuclear Copper(II) and Trinuclear Cobalt(II) Complexes Based on Asymmetric Salamo‐Type Ligands

Mononuclear copper(II) and trinuclear cobalt(II) complexes, namely [Cu(L¹)]₂ · CH₂Cl₂ and [{Co(L²)(EtOH)}₂Co(H₂O)] · EtOH {H₂L¹ = 4,6‐dichloro‐6′‐methyoxy‐2,2′‐[1,1′‐(ethylenedioxydinitrilo)dimethylidyne]diphenol and H₃L² = 6‐ethyoxy‐6′‐hydroxy‐2,2′‐[1,1′‐(ethylenedioxydinitrilo)dimethylidyne]diphenol}, were synthesized and characterized by elemental analyses, IR and UV/Vis spectroscopy, and single‐crystal X‐ray diffraction. In the Cu^II complex, the Cu^II atom is four‐coordinate, with a N₂O₂ coordination sphere, and has a slightly distorted square‐planar arrangement. Interestingly, the obtained trinuclear Co^II complex is different from the common reported 2:3 (L:Co^II) salamo‐type Co^II complexes. Infinite 2D layer supramolecular structures are formed via abundant intermolecular hydrogen bonding and π ··· π stacking interactions in the Cu^II and Co^II complexes.