Robustness of Gaussian Hedges and the Hedging of Fixed Income Derivatives

The effect of model and parameter misspecification on the effectiveness of Gaussian hedging strategies for derivative financial instrumens is analyzed, showing that Gaussian hedges in the "natural" hedging instruments are particularly robust. This is true for all models that imply Balck/Scholes - type formulas for option prices and hedging strategies. In this paper we focus on the hedging of fixed income derivatives and show how to apply these results both within the framework of Gaussian term structure models as well as the increasingly popular market models where the prices for caplets and swaptions are given by the corresponding Black formulas. By explicitly considering the behaviour of the hedging strategy under misspecification we also derive the El Karoui, Jeanblanc-Picque and Shreve (1995, 1998) and Avellaneda, Levy and Paras (1995) results that a superhedge is obtained in the Black/Scholes model if the misspecified volatility dominates the true volatility. Furthermore, we show that the robustness and superhedging result do not hold if the natural hedging instruments are unavailable. In this case, we study criteria for the optimal choice from the instruments that are available.

Single-Site Vanadyl Species Isolated within Molybdenum Oxide Monolayers in Propane Oxidation

The cooperation of metal oxide subunits in complex mixed metal oxide catalysts for selective oxidation of alkanes still needs deeper understanding to allow for a rational tuning of catalyst performance. Herein we analyze the interaction between vanadium and molybdenum oxide species in a monolayer supported on mesoporous silica SBA-15. Catalysts with variable Mo/V ratio between 10 and 1 were studied in the oxidation of propane and characterized by FTIR, Raman, and EPR spectroscopies, temperature-programmed reduction, UV/vis spectroscopy in combination with DFT calculations, and time-resolved experiments to analyze the redox properties of the catalysts. Molybdenum oxide (sub)monolayers on silica contain mainly dioxo (Si–O−)2Mo(═O)2 species. Dilution of silica-supported vanadium oxide species by (Si–O−)2Mo(═O)2 prevents the formation of V–O–V bonds, which are abundant in the pure vanadium oxide catalyst that predominantly contains two-dimensional vanadium oxide oligomers. Existing single vanadyl (Si–O−)3V(═O) sites and neighboring (Si–O−)2Mo(═O)2 sites do not strongly interact. The rates of reduction in propane and of oxidation in oxygen are lower for single metal oxide sites compared to those for oligomers. The rate of propane oxidation correlates with the overall redox rates of the catalysts but not linearly with the chemical composition. Retarded redox behavior facilitates selectivity toward acrolein on single-site catalysts. The abundance of M–O–M bonds is more important in terms of activity and selectivity compared to the nature of the central atom (molybdenum versus vanadium)

The role of sub-surface oxygen in the silver-catalyzed, oxidative coupling of methane

The silver-catalyzed, oxidative coupling of methane to C2 hydrocarbons (OCM) is shown to be an extremely structure-sensitive reaction. Reaction-induced changes in the silver morphology lead to changes in the nature and extent of formation of various bulk and surface-terminating crystal structures. This, in-turn, impacts the adsorption properties and diffusivity of oxygen in silver which is necessary to the formation of sub-surface oxygen. A strongly-bound, Lewis-basic, oxygen species which is intercalated in the silver crystal structure is formed as a result of these diffusion processes. This species is referred to as Og and acts as a catalytically active site for the direct dehydrogenation of a variety of organic reactants. It is found that the activation energy for methane coupling over silver of 138 kJ/mol is nearly identical to the value of 140 kJ/mol for oxygen diffusion in silver measured under similar conditions. This correlation between the diffusion kinetics of bulk-dissolved oxygen and the reaction kinetics of the oxidative coupling of methane to C2 hydrocarbons suggests that the reaction is limited by the formation of Og via surface segregation of bulk dissolved oxygen. Catalysis over fresh silver catalysts indicates an initially preferential oxidation of CH4 to complete oxidation products. This is a result of the reaction of methane with surface bound atomic oxygen which forms preferentially on high-index terminating crystalline planes. Reaction-induced facetting of the silver results in a restructuring of the catalyst from one which initially catalyzes the complete oxidation of methane to COx and water to a catalyst which preferentially catalyzes the formation of coupling products. This represents an extremely dynamic situation in which a solid-state restructuring of the catalyst results in the formation of a Lewis-basic, silver-oxygen species which preferentially catalyzes the dehydrogenation of organic molecules

Carbon accumulation, deactivation and reactivation of Pt catalysts upon exposure to hydrocarbons

The formation and catalytic effect of carbonaceous deposits was studied on monofunctional Pt catalysts: Pt black (PtN, i.e., reduced with hydrazine), Pt/SiO2 (EUROPT-1), Pt on “herringbone” graphite nanofiber (Pt/GNF-H, GNF being able to store hydrogen) and Pt/CeO2 (ceria tending to consume spilt over hydrogen). They were exposed to hexane or t,t-hexa-2,4-diene between 483 and 663 K, with or without H2. Hydrocarbon transformations during these deactivating exposures as well as in subsequent standard test reaction with hexane in hydrogen excess were studied. Carbon accumulation on Pt black after analogous deactivating treatments was also examined by electron spectroscopy (XPS and UPS). The abundance of hydrogen on Pt sites controlled the activity and selectivity containing much PtC species. The amount of surface C could reach 45% causing almost total activity loss, but even 30% C on Pt blacks decreased markedly the catalytic activity, due to massive 3D deposits. “Disordered” carbon selectively poisoned the formation of saturated C6 products and fragmentation. The yield of dehydrogenation to hexenes was a good universal indicator of deactivation for each catalyst. Four regions weredistinguished: “beneficial”, “selective”, “non-selective” and “severe” deactivation