An efficient and accurate lattice for pricing derivatives under a jump-diffusion process

Derivatives are popular financial instruments whose values depend on other more fundamental financial assets (called the underlying assets). As they play essential roles in financial markets, evaluating them efficiently and accurately is critical. Most derivatives have no simple valuation formulas; as a result, they must be priced by numerical methods such as lattice methods. In a lattice, the prices of the derivatives converge to theoretical values when the number of time steps increases. Unfortunately, the nonlinearity error introduced by the nonlinearity of the option value function may cause the pricing results to converge slowly or even oscillate significantly. The lognormal diffusion process, which has been widely used to model the underlying asset’s price dynamics, does not capture the empirical findings satisfactorily. Therefore, many alternative processes have been proposed, and a very popular one is the jump-diffusion process. This paper proposes an accurate and efficient lattice for the jump-diffusion process. Our lattice is accurate because its structure can suit the derivatives’ specifications so that the pricing results converge smoothly. To our knowledge, no other lattices for the jump-diffusion process have successfully solved the oscillation problem. In addition, the time complexity of our lattice is lower than those of existing lattice methods by at least half an order. Numerous numerical calculations confirm the superior performance of our lattice to existing methods in terms of accuracy, speed, and generality.     

On the structure of digital explicit nonlinear and inversive pseudorandom number generators

We analyze the lattice structure and distribution of the digital explicit inversive pseudorandom number generator introduced by Niederreiter and Winterhof as well as of a general digital explicit nonlinear generator. In particular, we extend a lattice test designed for this class of pseudorandom number generators to parts of the period and arbitrary lags and prove that these generators pass this test up to very high dimensions. We also analyze the behavior of digital explicit inversive and nonlinear generators under another very strong lattice test which in its easiest form can be traced back to Marsaglia and provides a complexity measure essentially equivalent to linear complexity.     

Lattice based extended formulations for integer linear equality systems

We study different extended formulations for the set with in order to tackle the feasibility problem for the set Pursuing the work of Aardal, Lenstra et al. using the reformulation , our aim is to derive reformulations of the form with 0  ≤  s ≤ n − m where preferably all the coefficients of P are small compared to the coefficients of A and T. In such cases the new variables μ appear to be good branching directions, and in certain circumstances permit one to deduce rapidly that the instance is infeasible. We give a polynomial time algorithm for identifying such P, T if possible, and for the case that A has one row a we analyze the reformulation when s = 1, that is, one μ-variable is introduced. In particular, we determine the integer width of the extended formulations in the direction of the μ-variable, and derive a lower bound on the Frobenius number of a. We conclude with some preliminary tests to see if the reformulations are effective when the number s of additional constraints and variables is limited. This work was partly carried out within the framework of ADONET, a European network in Algorithmic Discrete Optimization, contract no. MRTN-CT-2003-504438. The first author is financed in part by the Dutch BSIK/BRICKS project. The research was carried out in part while the second author visited CWI, Amsterdam with the support of the NWO visitor grant number B 61-556.     

On the combinatorics of Galois numbers

We define interval decompositions of the lattice of subspaces of a finite-dimensional vector space. We show that such a decomposition exists if and only if there exists a family of linear forms with certain properties. As applications we prove that all finite-dimensional real vector spaces admit an interval decomposition, while GF(2)ⁿ has an interval decomposition if and only if n≤4. On the other hand, we present an interval decomposition of GF(3)⁵. This partially answers a question of Faigle and Kruse (2004) [1] and [4].     

Heterogeneous reaction mechanism of elemental mercury oxidation by oxygen species over MnO2 catalyst

MnO₂-based catalysts have attracted great attention in the field of elemental mercury (Hg⁰) catalytic oxidation because of their superior catalytic performance and wide temperature window. Quantum chemistry calculations based on density functional theory (DFT) combined with periodic slab models were carried out to investigate the heterogeneous mechanism of Hg⁰ oxidation by oxygen species (gas-phase O₂, chemisorbed oxygen, and lattice oxygen) on MnO₂ surface. The results indicate that Hg⁰ and HgO are chemically adsorbed on MnO₂ surface with the adsorption energies of ?69.50 and ?226.48?kJ/mol, respectively. The adsorption of O₂ on MnO₂ surface belongs to chemisorption. O₂ can decompose on MnO₂ surface with an energy barrier of 97.46?kJ/mol to produce two atomic adsorbed oxygen. The perpendicular adsorbed O₂ and dissociative adsorbed O₂ are more favorable for Hg⁰ catalytic oxidation than lattice oxygen, and perpendicular adsorbed O₂ is the most active oxygen for Hg⁰ oxidation. The reaction pathway of Hg⁰ oxidation by perpendicular adsorbed O₂ includes three reaction steps: Hg⁰?→?Hg(ads)?→?HgO(ads)?→?HgO. The third step (HgO(ads)?→?HgO) is endothermic by 168.17?kJ/mol with an energy barrier of 179.48?kJ/mol, and it is the rate-limiting step of the whole Hg⁰ oxidation reaction.     

固体酸WO3/TiO2负载锂锰催化剂组成对其甲烷氧化偶联反应性能的影响

The selective oxidation of methane to basic petrochemicals (ethylene and ethane) is desirable and has attracted extensive research attention. The oxidative coupling of methane (OCM) is considered a promising one-step route for the production of C₂ compounds (ethylene and ethane) from methane, and has been the focus of industrial and fundamental studies. It is widely accepted that the composition is a crucial factor governing the activity of a catalyst system. It was found that the phase structures, basicity, existing status and distribution of the active components, oxygen species, and chemical states of the catalyst were influenced by the composition and ratio, resulting in different catalytic performances for the OCM. In this study, a series of solid acid WO₃/TiO₂-supported lithium-manganese oxide catalysts for OCM were synthesized via the impregnation method. The impacts of diverse compositions, such as the individual contents (Li and Mn) and dual contents (Li-Mn), on the OCM were investigated in detail, using inductively coupled plasma optical emission spectrometry, X-ray diffraction, high-resolution transmission electron microscopy, CO₂-temperature-programmed desorption, O₂-temperature-programmed desorption, H₂-temperature-programmed reduction, Raman spectroscopy, X-ray photoelectron spectroscopy, and CH₄-temperature-programmed surface reaction. The addition of Li content to the catalyst not only led to the anatase-to-rutile crystal structure transformation of TiO₂, and the reduction of the high-valence-state Mn species to low-valence-state Mn, but also increased the content of surface lattice oxygen and decreased the surface basicity. The observed effects on the structures and catalytic performance suggest that the Li content is helpful in suppressing the formation of completely oxidized CO₂, and increases the C₂ selectivity. Moreover, increasing the Li content of the catalyst facilitated the mobility of the lattice oxygen, which triggered the promotion of CH₄ activation, thereby enhancing the OCM catalytic performance. The Mn content acted as the active sites for OCM; therefore, the performance of the catalyst was closely related to the Mn concentration and valence state. However, the WO₃/TiO₂-supported catalyst with excessive Mn content exhibited a high surface basicity, high valence state of Mn, and low abundant lattice oxygen, which was unfavorable for C₂ selectivity. The Raman spectroscopy results revealed that MnTiO₃ was formed due to the co-existence of Li and Mn on WO₃/TiO₂, and played an essential role in improving the low-temperature OCM performance. There was a synergic effect of the Li and Mn components on the OCM. The optimal performance (16.3% C₂ yield) was achieved over the WO₃/TiO₂-supported lithium-manganese catalyst with n(Li) : n(Mn) = 2 : 1 at 750 ℃.     

Lattice self-assembly of cyclodextrin complexes and beyond

While lipids form soft, fluidic membranes (soft assembly), proteins can readily assemble into rigid, crystalline structures such as viral capsids and bacterial compartments (lattice assembly). The key difference has to do with the driving forces, where the former is driven by the weak, directionless hydrophobic effect and the latter, by a combination of relatively strong, directional intermolecular interactions. In synthetic systems, the lipid assembly has been massively replicated but the protein assembly has been rarely rivaled. Herein, we briefly review these two kinds of assemblies with special emphasis on a recently reported lattice self-assembly system of cyclodextrin complexes. The complexes arrange themselves into an in-plane, rhombic lattice that develops into lamellar, tubular, and polygonal structures depending on concentration. We will then cover the formation mechanisms, driving forces, and an application of the tubes in particle encapsulation. We hope that this short review would draw people's attention to this emerging field of lattice self-assembly.     

Lattice Boltzmann simulation for hydrothermal analysis of free convection within dumbbell-shaped heat exchanger

The lattice Boltzmann simulation of nanofluid flow and heat transfer during natural convection within a dumbbell-shaped heat exchanger is carried out. The heat exchanger is filled with CuO–water. The KKL model is employed to predict the thermo-physical properties of nanofluid. In order to perform a comprehensive hydrothermal investigation, different post-processing approaches such as heatline visualization, total entropy generation, local entropy generation based on local fluid friction irreversibility and heat transfer irreversibility, average and local Nusselt variation are employed. In the present investigation, it is tried to present the impact of different influential parameters like Rayleigh number, solid volume fraction of nanofluid and thermal arrangement of internal fins-bodies on the fluid flow, heat transfer rate and entropy generation.     

Static potentials for quarkonia at finite temperatures

We review non-perturbative static potentials commonly used in potential models for quarkonia at finite T. Potentials derived from Polyakov loop correlators are shown to be inappropriate for this purpose. The free energy is physical but has the wrong spatial decay and perturbative limit. The so-called singlet free energy is gauge dependent and unphysical. An appropriate static real time potential can be defined through a generalisation of pNRQCD to finite T. In perturbation theory, its real part reproduces the Debye-screened potential, its imaginary part accounts for Landau damping. Possibilities for its non-perturbative evaluation are discussed.     

Quantum gravity on the lattice

I review the lattice approach to quantum gravity, and how it relates to the non-trivial ultraviolet fixed point scenario of the continuum theory. After a brief introduction covering the general problem of ultraviolet divergences in gravity and other non-renormalizable theories, I discuss the general methods and goals of the lattice approach. An underlying theme is the attempt at establishing connections between the continuum renormalization group results, which are mainly based on diagrammatic perturbation theory, and the recent lattice results, which apply to the strong gravity regime and are inherently non-perturbative. A second theme in this review is the ever-present natural correspondence between infrared methods of strongly coupled non-abelian gauge theories on the one hand, and the low energy approach to quantum gravity based on the renormalization group and universality of critical behavior on the other. Towards the end of the review I discuss possible observational consequences of path integral quantum gravity, as derived from the non-trivial ultraviolet fixed point scenario. I argue that the theoretical framework naturally leads to considering a weakly scale-dependent Newton’s constant, with a scaling violation parameter related to the observed scaled cosmological constant (and not, as naively expected, to the Planck length). Invited lecture presented at the conference “Quantum Gravity: Challenges and Perspectives”, Bad Honnef, 14–16 April 2008. To appear in the proceedings edited by Hermann Nicolai.