Review of modern numerical methods for a simple vanilla option pricing problem

Option pricing is a very attractive issue of financial engineering and optimization. The problem of determining the fair price of an option arises from the assumptions made under a given financial market model. The increasing complexity of these market assumptions contributes to the popularity of the numerical treatment of option valuation. Therefore, the pricing and hedging of plain vanilla options under the Black–Scholes model usually serve as a bench-mark for the development of new numerical pricing approaches and methods designed for advanced option pricing models. The objective of the paper is to present and compare the methodological concepts for the valuation of simple vanilla options using the relatively modern numerical techniques in this issue which arise from the discontinuous Galerkin method, the wavelet approach and the fuzzy transform technique. A theoretical comparison is accompanied by an empirical study based on the numerical verification of simple vanilla option prices. The resulting numerical schemes represent a particularly effective option pricing tool that enables some features of options that are depend-ent on the discretization of the computational domain as well as the order of the polynomial approximation to be captured better

Rigid multipodal platforms for metal surfaces

In this review the recent progress in molecular platforms that form rigid and well-defined contact to a metal surface are discussed. Most of the presented examples have at least three anchoring units in order to control the spatial arrangement of the protruding molecular subunit. Another interesting feature is the lateral orientation of these foot structures which, depending on the particular application, is equally important as the spatial arrangement of the molecules. The numerous approaches towards assembling and organizing functional molecules into specific architectures on metal substrates are reviewed here. Particular attention is paid to variations of both, the core structures and the anchoring groups. Furthermore, the analytical methods enabling the investigation of individual molecules as well as monomolecular layers of ordered platform structures are summarized. The presented multipodal platforms bearing several anchoring groups form considerably more stable molecule-metal contacts than corresponding monopodal analogues and exhibit an enlarged separation of the functional molecules due to the increased footprint, as well as restrict tilting of the functional termini with respect to the metal surface. These platforms are thus ideally suited to tune important properties of the molecule-metal interface. On a single-molecule level, several of these platforms enable the control over the arrangement of the protruding rod-type molecular structures (e.g., molecular wires, switches, rotors, sensors) with respect to the surface of the substrate

Self-Assembled Monolayers of Molecular Conductors with Terpyridine-Metal Redox Switching Elements: A Combined AFM, STM and Electrochemical Study

Self-assembled monolayers (SAMs) of terpyridine-based transition metal (ruthenium and osmium) complexes, anchored to gold substrate via tripodal anchoring groups, have been investigated as possible redox switching elements for molecular electronics. An electrochemical study was complemented by atomic force microscopy (AFM) and scanning tunneling microscopy (STM) methods. STM was used for determination of the SAM conductance values, and computation of the attenuation factor β from tunneling current–distance curves. We have shown that SAMs of Os-tripod molecules contain larger adlayer structures compared with SAMs of Ru-tripod molecules, which are characterized by a large number of almost evenly distributed small islands. Furthermore, upon cyclic voltammetric experimentation, Os-tripod films rearrange to form a smaller number of even larger islands, reminiscent of the Ostwald ripening process. Os-tripod SAMs displayed a higher surface concentration of molecules and lower conductance compared with Ru-tripod SAMs. The attenuation factor of Os-tripod films changed dramatically, upon electrochemical cycling, to a higher value. These observations are in accordance with previously reported electron transfer kinetics studies

Probabilistic mapping of single molecule junction configurations as a tool to achieve the desired geometry of asymmetric tripodal molecules

Four molecules containing identical tripodal anchors and p-oligophenylene molecular wires of increasing length were used to demonstrate tuning of the asymmetric molecular junction to the desired geometry by probabilistic mapping of single molecule junction configurations in a scanning tunnelling microscopy break junction experiment

Synthesis and Surface Behaviour of NDI Chromophores Mounted on a Tripodal Scaffold: Towards Self-Decoupled Chromophores for Single-Molecule Electroluminescence

This paper reports the efficient synthesis, absorption and emission spectra, and the electrochemical properties of a series of 2,6-disubstituted naphthalene-1,4,5,8-tetracarboxdiimide (NDI) tripodal molecules with thioacetate anchors for their surface investigations. Our studies showed that, in particular, the pyrrolidinyl group with its strong electron-donating properties enhanced the fluorescence of such core-substituted NDI chromophores and caused a significant bathochromic shift in the absorption spectrum with a correspondingly narrowed bandgap of 1.94 eV. Cyclic voltammetry showed the redox properties of NDIs to be influenced by core substituents. The strong electron-donating character of pyrrolidine substituents results in rather high HOMO and LUMO levels of -5.31 and -3.37 eV when compared with the parental unsubstituted NDI. UHV-STM measurements of a sub-monolayer of the rigid tripodal NDI chromophores spray deposited on Au(111) show that these molecules mainly tend to adsorb flat in a pairwise fashion on the surface and form unordered films. However, the STML experiments also revealed a few molecular clusters, which might consist of upright oriented molecules protruding from the molecular island and show electroluminescence photon spectra with high electroluminescence yields of up to 6×10$^{-3}$. These results demonstrate the promising potential of the NDI tripodal chromophores for the fabrication of molecular devices profiting from optical features of the molecular layer

Hot luminescence from single-molecule chromophores electrically and mechanically self-decoupled by tripodal scaffolds

Control over the electrical contact to an individual molecule is one of the biggest challenges in molecular optoelectronics. The mounting of individual chromophores on extended tripodal scaffolds enables both efficient electrical and mechanical decoupling of individual chromophores from metallic leads. Core-substituted naphthalene diimides fixed perpendicular to a gold substrate by a covalently attached extended tripod display high stability with well-defined and efficient electroluminescence down to the single-molecule level. The molecularly controlled spatial arrangement balances the electric conduction for electroluminescence and the insulation to avoid non-radiative carrier recombination, enabling the spectrally and spatially resolved electroluminescence of individual self-decoupled chromophores in a scanning tunneling microscope. Hot luminescence bands are even visible in single self-decoupled chromophores, documenting the mechanical decoupling between the vibrons of the chromophore and the substrate

Synthesis of modular components for molecular electronics.

UNIVERZITA KARLOVA PŘÍRODOVĚDECKÁ FAKULTA KATEDRA ORGANICKÉ A JADERNÉ CHEMIE CHARLES UNIVERSITY FACULTY OF SCIENCES DEPARTMENT OF ORGANIC AND NUCLEAR CHEMISTRY Praha / Prague 2010 AUTOREFERÁT DISERTAČNÍ PRÁCE / SUMMARY OF THE PHD THESIS PŘÍPRAVA MODULÁRNÍCH PRVKŮ PRO MOLEKULOVOU ELEKTRONIKU SYNTHESIS OF MODULAR COMPONENTS FOR MOLECULAR ELECTRONICS MICHAL VALÁŠEK Supervisors: Doc. RNDr. Václav Všetečka, CSc. RNDr. Jaroslav Pecka Obsah / Table of contents 1. Úvod / Introduction.............................................................................................................2 / 3 2. Cíle disertační práce / Aims of the work...........................................................................4 / 5 3. Výsledky a diskuse / Results and discussion...................................................................6 / 11 3.1 Příprava pyridiniových oligomerů / Preparation of pyridinium oligomers.......6 / 11 3.2 Molekulové izolátory / molecular isolators............................................................7 / 12 3.3 Molekulové diody / molecular diods ......................................................................7 / 12 3.4 Molekulové senzory / molecular sensors................................................................8 / 13 3.5 Samoskladné cyklobutadienové komplexy / Self-assembled..