Conditional Extremes in Asymmetric Financial Markets

<p>The global financial crisis of 2007–2009 revealed the great extent to which systemic risk can jeopardize the stability of the entire financial system. An effective methodology to quantify systemic risk is at the heart of the process of identifying the so-called systemically important financial institutions for regulatory purposes as well as to investigate key drivers of systemic contagion. The article proposes a method for dynamic forecasting of CoVaR, a popular measure of systemic risk. As a first step, we develop a semi-parametric framework using asymptotic results in the spirit of extreme value theory (EVT) to model the conditional probability distribution of a bivariate random vector given that one of the components takes on a large value, taking into account important features of financial data such as asymmetry and heavy tails. In the second step, we embed the proposed EVT method into a dynamic framework via a bivariate GARCH process. An empirical analysis is conducted to demonstrate and compare the performance of the proposed methodology relative to a very flexible fully parametric alternative.</p

β‑Diketiminate Germylene-Supported Pentafluorophenylcopper(I) and -silver(I) Complexes [LGe(Me)(CuC₆F₅)_<i>n</i>]₂ (<i>n</i> = 1, 2), LGe[C(SiMe₃)N₂]AgC₆F₅, and {LGe[C(SiMe₃)N₂](AgC₆F₅)₂}₂ (L = HC[C(Me)N-2,6‑<i>i</i>Pr₂C₆H₃]₂): Synthesis and Structural Characterization

Reactions of LGeMe (L = HC­[C­(Me)­N-2,6-<i>i</i>Pr₂C₆H₃]₂) with 0.25 or 0.5 equiv of (CuC₆F₅)₄ gave the products [LGe­(Me)­CuC₆F₅]₂ (<b>1</b>) and [LGe­(Me)­(CuC₆F₅)₂]₂ (<b>2</b>), respectively. In situ formed <b>1</b> reacted with 0.5 equiv of (CuC₆F₅)₄ to give <b>2</b> on the basis of NMR (¹H and ¹⁹F) spectral measurements. Conversely, <b>2</b> was converted into <b>1</b> by treatment with 2 equiv of LGeMe. Reactions of LGeC­(SiMe₃)­N₂ with 1 or 2 equiv of AgC₆F₅·MeCN produced the corresponding compounds LGe­[C­(SiMe₃)­N₂]­AgC₆F₅ (<b>3</b>) and {LGe­[C­(SiMe₃)­N₂]­(AgC₆F₅)₂}₂ (<b>4</b>). Similarly, <b>3</b> was converted into <b>4</b> by treatment with 1 equiv of AgC₆F₅·MeCN and <b>4</b> converted into <b>3</b> by reaction with 2 equiv of LGeC­(SiMe₃)­N₂. X-ray crystallographic studies showed that <b>1</b> contains a rhombically bridged (CuC₆F₅)₂, while <b>2</b> has a chain-structurally aggregated (CuC₆F₅)₄, both supported by LGeMe. Correspondingly, <b>3</b> showed a terminally bound AgC₆F₅ and <b>4</b> a chain-structurally aggregated (AgC₆F₅)₄, both supported by LGeC­(SiMe₃)­N₂. Photophysical studies proved that the Ge–Cu metal–metalloid donor–acceptor bonding persists in solutions of <b>1</b> and <b>2</b> and Ge–Ag donor–acceptor bonding in solutions of <b>3</b> and <b>4</b> as a result of the clear migration of their emission bands compared to those of the corresponding starting materials. Low-temperature (−50 °C) ¹⁹F NMR spectral measurements detected dissociation of <b>1</b>, <b>2</b>, and <b>4</b> by the aggregation part of the CuC₆F₅ or AgC₆F₅ entities in solution. These results provide good support for pentafluorophenylcopper­(I) or -silver­(I) species having β-diketiminate germylene as a donor because of its remarkably electronic and steric character

β‑Diketiminate Germylene-Supported Pentafluorophenylcopper(I) and -silver(I) Complexes [LGe(Me)(CuC₆F₅)_<i>n</i>]₂ (<i>n</i> = 1, 2), LGe[C(SiMe₃)N₂]AgC₆F₅, and {LGe[C(SiMe₃)N₂](AgC₆F₅)₂}₂ (L = HC[C(Me)N-2,6‑<i>i</i>Pr₂C₆H₃]₂): Synthesis and Structural Characterization

Reactions of LGeMe (L = HC­[C­(Me)­N-2,6-<i>i</i>Pr₂C₆H₃]₂) with 0.25 or 0.5 equiv of (CuC₆F₅)₄ gave the products [LGe­(Me)­CuC₆F₅]₂ (<b>1</b>) and [LGe­(Me)­(CuC₆F₅)₂]₂ (<b>2</b>), respectively. In situ formed <b>1</b> reacted with 0.5 equiv of (CuC₆F₅)₄ to give <b>2</b> on the basis of NMR (¹H and ¹⁹F) spectral measurements. Conversely, <b>2</b> was converted into <b>1</b> by treatment with 2 equiv of LGeMe. Reactions of LGeC­(SiMe₃)­N₂ with 1 or 2 equiv of AgC₆F₅·MeCN produced the corresponding compounds LGe­[C­(SiMe₃)­N₂]­AgC₆F₅ (<b>3</b>) and {LGe­[C­(SiMe₃)­N₂]­(AgC₆F₅)₂}₂ (<b>4</b>). Similarly, <b>3</b> was converted into <b>4</b> by treatment with 1 equiv of AgC₆F₅·MeCN and <b>4</b> converted into <b>3</b> by reaction with 2 equiv of LGeC­(SiMe₃)­N₂. X-ray crystallographic studies showed that <b>1</b> contains a rhombically bridged (CuC₆F₅)₂, while <b>2</b> has a chain-structurally aggregated (CuC₆F₅)₄, both supported by LGeMe. Correspondingly, <b>3</b> showed a terminally bound AgC₆F₅ and <b>4</b> a chain-structurally aggregated (AgC₆F₅)₄, both supported by LGeC­(SiMe₃)­N₂. Photophysical studies proved that the Ge–Cu metal–metalloid donor–acceptor bonding persists in solutions of <b>1</b> and <b>2</b> and Ge–Ag donor–acceptor bonding in solutions of <b>3</b> and <b>4</b> as a result of the clear migration of their emission bands compared to those of the corresponding starting materials. Low-temperature (−50 °C) ¹⁹F NMR spectral measurements detected dissociation of <b>1</b>, <b>2</b>, and <b>4</b> by the aggregation part of the CuC₆F₅ or AgC₆F₅ entities in solution. These results provide good support for pentafluorophenylcopper­(I) or -silver­(I) species having β-diketiminate germylene as a donor because of its remarkably electronic and steric character

Reactivity Studies of (Phenylethynyl)germylene LGeCCPh (L = HC[C(Me)N-2,6‑<i>i</i>Pr₂C₆H₃]₂) toward Pentafluorophenylcopper(I), -silver(I), and -gold(I) Complexes

Reactions of (phenylethynyl)­germylene LGeCCPh (L = HC­[C­(Me)­N-2,6-<i>i</i>Pr₂C₆H₃]₂) with 0.25 equiv of (CuC₆F₅)₄, 1 equiv of AgC₆F₅·MeCN, and 1 equiv of AuC₆F₅·SC₄H₈, respectively, yielded LGe­(CCPh)­CuC₆F₅ (<b>1</b>), [(LGeCCPh)₂Ag]⁺[Ag­(C₆F₅)₂]⁻ (<b>2</b>), and LGe­(CCPh)­AuC₆F₅ (<b>3</b>). Complexes <b>1</b>–<b>3</b> were characterized by IR and NMR spectroscopy and X-ray crystallography. Compound <b>1</b> shows a bonding pattern of the CuC₆F₅ entity by both the phenylethynyl CC linkage and the L ligand backbone of the γ-C atom, while <b>3</b> exhibits a bonding mode of the AuC₆F₅ entity at the germylene center. Compound <b>2</b> is an ionic derivative featuring the Ge–Ag donor–acceptor bond formed under redistribution of the AgC₆F₅ entity. Further reactions of <b>1</b> with (CuC₆F₅)₄, AgC₆F₅·MeCN, and AuC₆F₅·SC₄H₈ afforded the complexes LGe­(CCPh)­(CuC₆F₅)­(MC₆F₅) (M = Cu (<b>4</b>), Ag (<b>5</b>), Au (<b>6</b>)). Compounds <b>4</b>–<b>6</b> were characterized by IR and NMR spectroscopy, and <b>5</b> and <b>6</b> were further investigated by X-ray crystallography. Compounds <b>4</b>–<b>6</b> all show an additional bonding of the respective MC₆F₅ moiety at the germylene center of <b>1</b>. These studies reveal a multiple donor reactivity of LGeCCPh. The slightly different Lewis acidic properties of the congeneric pentafluorophenylcopper­(I), -silver­(I), and -gold­(I) complexes as acceptors are thus disclosed

Reactivity Studies of (Phenylethynyl)germylene LGeCCPh (L = HC[C(Me)N-2,6‑<i>i</i>Pr₂C₆H₃]₂) toward Pentafluorophenylcopper(I), -silver(I), and -gold(I) Complexes

Reactions of (phenylethynyl)­germylene LGeCCPh (L = HC­[C­(Me)­N-2,6-<i>i</i>Pr₂C₆H₃]₂) with 0.25 equiv of (CuC₆F₅)₄, 1 equiv of AgC₆F₅·MeCN, and 1 equiv of AuC₆F₅·SC₄H₈, respectively, yielded LGe­(CCPh)­CuC₆F₅ (<b>1</b>), [(LGeCCPh)₂Ag]⁺[Ag­(C₆F₅)₂]⁻ (<b>2</b>), and LGe­(CCPh)­AuC₆F₅ (<b>3</b>). Complexes <b>1</b>–<b>3</b> were characterized by IR and NMR spectroscopy and X-ray crystallography. Compound <b>1</b> shows a bonding pattern of the CuC₆F₅ entity by both the phenylethynyl CC linkage and the L ligand backbone of the γ-C atom, while <b>3</b> exhibits a bonding mode of the AuC₆F₅ entity at the germylene center. Compound <b>2</b> is an ionic derivative featuring the Ge–Ag donor–acceptor bond formed under redistribution of the AgC₆F₅ entity. Further reactions of <b>1</b> with (CuC₆F₅)₄, AgC₆F₅·MeCN, and AuC₆F₅·SC₄H₈ afforded the complexes LGe­(CCPh)­(CuC₆F₅)­(MC₆F₅) (M = Cu (<b>4</b>), Ag (<b>5</b>), Au (<b>6</b>)). Compounds <b>4</b>–<b>6</b> were characterized by IR and NMR spectroscopy, and <b>5</b> and <b>6</b> were further investigated by X-ray crystallography. Compounds <b>4</b>–<b>6</b> all show an additional bonding of the respective MC₆F₅ moiety at the germylene center of <b>1</b>. These studies reveal a multiple donor reactivity of LGeCCPh. The slightly different Lewis acidic properties of the congeneric pentafluorophenylcopper­(I), -silver­(I), and -gold­(I) complexes as acceptors are thus disclosed

Determining the Conformational Landscape of σ and π Coupling Using <i>para</i>-Phenylene and “Aviram–Ratner” Bridges

The torsional dependence of donor–bridge–acceptor (D–B–A) electronic coupling matrix elements (<i><b>H</b></i>_{<i><b>DA</b></i>}, determined from the magnetic exchange coupling, <i><b>J</b></i>) involving a spin S_D = 1/2 metal semiquinone (Zn-<b>SQ</b>) donor and a spin S_A = 1/2 nitronylnitroxide (<b>NN</b>) acceptor mediated by the σ/π-systems of <i>para</i>-phenylene and methyl-substituted <i>para</i>-phenylene bridges and by the σ-system of a bicyclo[2.2.2]­octane (<b>BCO</b>) bridge are presented and discussed. The positions of methyl group(s) on the phenylene bridge allow for an experimentally determined evaluation of conformationally dependent (π) and conformationally independent (σ) contributions to the electronic and magnetic exchange couplings in these D–B–A biradicals at parity of D and A. The trend in the experimental magnetic exchange couplings are well described by CASSCF calculations. The torsional dependence of the pairwise exchange interactions are further illuminated in three-dimensional, “Ramachandran-type” plots that relate D–B and B–A torsions to both electronic and exchange couplings. Analysis of the magnetic data shows large variations in magnetic exchange (<i><b>J</b></i> ≈ 1–175 cm^–1) and electronic coupling (<i><b>H</b></i>_{<i><b>DA</b></i>} ≈ 450–6000 cm^–1) as a function of bridge conformation relative to the donor and acceptor. This has allowed for an experimental determination of both the σ- and π-orbital contributions to the exchange and electronic couplings

Determining the Conformational Landscape of σ and π Coupling Using <i>para</i>-Phenylene and “Aviram–Ratner” Bridges

The torsional dependence of donor–bridge–acceptor (D–B–A) electronic coupling matrix elements (<i><b>H</b></i>_{<i><b>DA</b></i>}, determined from the magnetic exchange coupling, <i><b>J</b></i>) involving a spin S_D = 1/2 metal semiquinone (Zn-<b>SQ</b>) donor and a spin S_A = 1/2 nitronylnitroxide (<b>NN</b>) acceptor mediated by the σ/π-systems of <i>para</i>-phenylene and methyl-substituted <i>para</i>-phenylene bridges and by the σ-system of a bicyclo[2.2.2]­octane (<b>BCO</b>) bridge are presented and discussed. The positions of methyl group(s) on the phenylene bridge allow for an experimentally determined evaluation of conformationally dependent (π) and conformationally independent (σ) contributions to the electronic and magnetic exchange couplings in these D–B–A biradicals at parity of D and A. The trend in the experimental magnetic exchange couplings are well described by CASSCF calculations. The torsional dependence of the pairwise exchange interactions are further illuminated in three-dimensional, “Ramachandran-type” plots that relate D–B and B–A torsions to both electronic and exchange couplings. Analysis of the magnetic data shows large variations in magnetic exchange (<i><b>J</b></i> ≈ 1–175 cm^–1) and electronic coupling (<i><b>H</b></i>_{<i><b>DA</b></i>} ≈ 450–6000 cm^–1) as a function of bridge conformation relative to the donor and acceptor. This has allowed for an experimental determination of both the σ- and π-orbital contributions to the exchange and electronic couplings

Water-Soluble Polythiophene for Two-Photon Excitation Fluorescence Imaging and Photodynamic Therapy of Cancer

Positively charged water-soluble polythiophene (<b>PT0</b>) that could self-assemble into nanoparticles in pure water solution was designed and synthesized. <b>PT0</b> exhibited high photostabilities and pH stabilities, excellent biocompatibility, strong ¹O₂ generation capability, and large two-photon absorption cross sections. Moreover, we showed that the fluorescence of <b>PT0</b> was unaffected by the interference of biomolecules and metal ions. As an example application, <b>PT0</b> was demonstrated to be capable of simultaneous cell imaging and photodynamic therapy under either one-photon or two-photon excitation modes