Bias Reduction for Pricing American Options by Least-Squares Monte Carlo

Abstract

We derive an approximation to the bias in regression-based Monte Carlo estimators of American option values. This derivation holds for general asset-price processes of any dimensionality and for general pay-off structures. It uses the large sample properties of least-squares regression estimators. Bias-corrected estimators result by subtracting the bias approximation from the uncorrected estimator at each exercise opportunity. Numerical results show that the bias-corrected estimator outperforms its uncorrected counterpart across all combinations of number of exercise opportunities, option moneyness and sample size. Finally, the results suggest significant computational efficiency increases can be realized through trivial parallel implementations using the corrected estimator.     

Ruthenium-catalyzed asymmetric epoxidation of olefins using H2O2, part II: catalytic activities and mechanism

Asymmetric epoxidation of olefins with 30 % H2O2 in the presence of [Ru(pybox)(pydic)] 1 and [Ru(pyboxazine)(pydic)] 2 has been studied in detail (pybox = pyridine-2,6-bisoxazoline, pyboxazine = pyridine-2,6-bisoxazine, pydic = 2,6-pyridinedicarboxylate). 35 Ruthenium complexes with sterically and electronically different substituents have been tested in environmentally benign epoxidation reactions. Mono-, 1,1-di-, cis- and trans-1,2-di-, tri-, and tetra-substituted aromatic olefins with versatile functional groups can be epoxidized with this type of catalyst in good to excellent yields (up to 100 %) with moderate to good enantioselectivies (up to 84 % ee). Additive and solvent effects as well as the relative rate of reaction with different catalysts have been established. It is shown that the presence of weak organic acids or an electron-withdrawing group on the catalyst increases the reactivity. New insights on the reaction intermediates and reaction pathway of the ruthenium-catalyzed epoxidation are proposed on the basis of density functional theory calculation and experiments.     

Condition for the realization of a temperature-insensitive long-period waveguide grating

We analyze the condition for achieving a temperature-insensitive resonance wavelength of a long-period grating formed in a channel waveguide. We find that by controlling the waveguide cladding thickness, zero temperature sensitivity can be achieved with core and cladding materials that have significantly different thermo-optic coefficients. To verify our finding, we design a polymer long-period waveguide grating (LPWG) according to the zero-sensitivity condition, where the thermo-optic coefficient of the core is twice that of the cladding. The temperature sensitivity of the fabricated grating is within +/-0.15 nm/ degrees C over a temperature range of approximately 15 degrees C, which is more than an order of magnitude lower than those of previously reported LPWGs fabricated with the same materials.     

Optical and electroluminescent properties of 3,4,6-triphenyl-α-pyrone

The optical and electroluminescent properties of 3,4,6-triphenyl-α-pyrone (α-pyrone), a new blue fluoresce dye, are investigated using films prepared by wet and dry process and organic light-emitting diodes (OLEDs) fabricated with an α-pyrone-emitting layer. The optical properties of α-pyrone are found to be affected by its crystallinity. In the fabrication of OLEDs, wet processing (spin coating) is shown to be more suitable for preparation of the α-pyrone layer than dry processing (thermal evaporation). The best device performance is obtained for a device prepared using poly (n-vinylcarbazole) as the dye host, and a bathocuproine/tris-(8-hydroxyquinoline)aluminum bilayer as a hole-blocking and carrier-injection layer. The maximum luminance of this device is 3000 cd/m² at a current density of 0.2 A/cm², with a current efficiency of 1.8 cd/A at 0.02 A/cm².     

Layer-by-layer deposition of rhenium-containing hyperbranched polymers and fabrication of photovoltaic cells

Multilayer thin films were prepared by the layer-by-layer (LBL) deposition method using a rhenium-containing hyperbranched polymer and poly[2-(3-thienyl)ethoxy-4-butylsulfonate] (PTEBS). The radii of gyration of the hyperbranched polymer in solutions with different salt concentrations were measured by laser light scattering. A significant decrease in molecular size was observed when sodium trifluoromethanesulfonate was used as the electrolyte. The conditions of preparing the multilayer thin films by LBL deposition were studied. The growth of the multilayer films was monitored by absorption spectroscopy and spectroscopic ellipsometry, and the surface morphologies of the resulting films were studied by atomic force microscopy. When the pH of a PTEBS solution was kept at 6 and in the presence of salt, polymer films with maximum thickness were obtained. The multilayer films were also fabricated into photovoltaic cells and their photocurrent responses were measured upon irradiation with simulated air mass (AM) 1.5 solar light. The open-circuit voltage, short-circuit current, fill factor, and power conversion efficiency of the devices were 1.2 V, 27.1 mu A cm(-2), 0.19, and 6.1x10(-3) %, respectively. The high open-circuit voltage was attributed to the difference in the HOMO level of the PTEBS donor and the LUMO level of the hyperbranched polymer acceptor. A plot of incident photon-to-electron conversion efficiency versus wavelength also suggests that the PTEBS/hyperbranched polymer junction is involved in the photosensitization process, in which a maximum was observed at approximately 420 nm. The relatively high capacitance, determined from the measured photocurrent rise and decay profiles, can be attributed to the presence of large counter anions in the polymer film.     

Convenient method for epoxidation of alkenes using aqueous hydrogen peroxide

[reaction: see text] The complex [Ru(tpy)(pydic)] (1a) is an active catalyst for epoxidation of alkenes by aqueous 30% hydrogen peroxide in tertiary alcohols. The protocol is simple to operate and gives the corresponding epoxides in good to excellent yields. Chiral enantiopure [Ru(tpy)(pydic)] complexes have been synthesized and successfully applied in this procedure.