Option Pricing in Illiquid Markets with Jumps

ABSTRACT

The classical linear Black–Scholes model for pricing derivative securities is a popular model in the financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the assumption on the underlying asset price dynamics following a geometric Brownian motion. The main purpose of this paper is to generalize the classical Black–Scholes model for pricing derivative securities by taking into account feedback effects due to an influence of a large trader on the underlying asset price dynamics exhibiting random jumps. The assumption that an investor can trade large amounts of assets without affecting the underlying asset price itself is usually not satisfied, especially in illiquid markets. We generalize the Frey–Stremme nonlinear option pricing model for the case the underlying asset follows a Lévy stochastic process with jumps. We derive and analyze a fully nonlinear parabolic partial-integro differential equation for the price of the option contract. We propose a semi-implicit numerical discretization scheme and perform various numerical experiments showing the influence of a large trader and intensity of jumps on the option price.     

Delocalization-to-localization charge transition in diferrocenyl-oligothienylene-vinylene molecular wires as a function of the size by Raman spectroscopy

In going from short to large size thienylene-vinylene diferrocenyl cations, the transition from a charge delocalized to a localized state is addressed by resonance Raman spectroscopy and supported by theoretical model chemistry. The shorter members, dimer and tetramer, display conjugated structures near the cyanine limit of bond length equalization as a result of the strong interferrocene charge resonance, producing a full charge delocalized mixed valence system. In the longest octamer, charge resonance vanishes and the cation is localized at the bridge center (the mixed valence property disappears). The hexamer is at the delocalized-to-localized turning point. Solvent and variable-temperature Raman measurements highlight this borderline property. A detailed structure-property correlation of bond length alternation data and Raman frequencies is proposed to account for the whole set of spectroscopic properties, with emphasis on the changes observed with the size of the molecular wire.     

Asymmetric organocatalytic formal [2 + 2]-cycloadditions via bifunctional H-bond directing dienamine catalysis

A new concept in organocatalysis allowing for the construction of cyclobutanes with four contiguous stereocenters with complete diastereo- and enantiomeric control by a formal [2 + 2]-cycloaddition is presented. The concept is based on simultaneous dual activation of α,β-unsaturated aldehydes and nitroolefins by amino- and hydrogen-bonding catalysis, respectively. A new bifunctional squaramide-based aminocatalyst has been designed and synthesized in order to enable such an activation strategy. The potential and scope of the reaction are demonstrated, and computational studies which account for the stereochemical outcome are presented.     

Raman spectroscopic detection of Nickel impact on single Streptomyces cells – possible bioindicators for heavy metal contamination

Heavy metal contamination of soil has an immense impact on the surrounding environment, such as the ground water, and hence, has become an important issue within bioremediation. Therefore, heavy metal contamination has to be determined preferably cost‐efficiently, rapidly, and reliably. Here, soil bacteria of the genus Streptomyces are used as bioindicators for heavy metal contamination investigated via micro‐Raman spectroscopy. A single cell approach is studied to avoid time‐consuming culturing and plate counting. Bacteria of Streptomyces galilaeus were incubated in Ni²⁺ enriched media and single cell spectra were recorded. Supervised statistics linear discriminant analysis was used to evaluate the influence of the culture age and the anion on bacterial cells, which has been determined to be minor compared with the spectral impact of Ni²⁺. The identification of the Raman spectra according to different Ni²⁺ concentration ranges is accomplished with a prediction accuracy of about 88%. Therefore, we conclude that Streptomyces can be used as a bioindicator to predict Ni²⁺ concentrations in the micromolar range. Copyright © 2011 John Wiley & Sons, Ltd.     

The set of numerical semigroups of a given genus

In this paper we present a new approach to construct the set of numerical semigroups with a fixed genus. Our methodology is based on the construction of the set of numerical semigroups with fixed Frobenius number and genus. An equivalence relation is given over this set and a tree structure is defined for each equivalence class. We also provide a more efficient algorithm based on the translation of a numerical semigroup to its so-called Kunz-coordinates vector.     

The role of iron in neurodegeneration--M?ssbauer spectroscopy, electron microscopy, enzyme-linked immunosorbent assay and neuroimaging studies

The possible role of iron in neurodegeneration was studied by various techniques: electron microscopy, enzyme-linked immunosorbent assay, M?ssbauer spectroscopy, atomic absorption, ultrasonography and magnetic resonance imaging. The measurements were made on human tissues extracted from liver and from brain structures involved in diseases of the human brain: substantia nigra (Parkinson's, PD), hippocampal cortex (Alzheimer's, AD) and globus pallidus (progressive supranuclear palsy, PSP). The sizes of the iron cores of ferritin, the main iron storage compound in tissues, were found to be smaller in brain than in liver. Brain ferritin has a higher proportion of H to L chains compared to liver. A significant decrease of the concentration of L chains in PD compared to control was found. No increase in the concentration of iron in PD versus control was detected; however, there was an increase of labile iron, which constitutes only 2‰ of brain iron. In AD an increase in the concentration of ferritin was noticed, without a significant increase in iron concentration. In PSP an increase of total iron was observed. Our findings suggest that the mechanisms leading to the death of nerve cells in these three diseases may be different, although all may be related to iron mediated oxidative stress.     

Morphometric partitioning of the respiratory surface area and diffusion capacity of the gills and swim bladder in juvenile Amazonian air-breathing fish, Arapaima gigas

The gills and the respiratory swim bladders of juvenile specimens (mean body mass 100 g) of the basal teleost Arapaima gigas (Cuvier 1829) were evaluated using stereological methods in vertical sections. The surface areas, harmonic mean barrier thicknesses and morphometric diffusing capacities for oxygen and carbon dioxide were estimated. The average respiratory surface area of the swim bladder (2173 cm² kg^?1) exceeded that of the gills (780 cm² kg^?1) by a factor of 2.79. Due to the extremely thin air–blood barrier in the swim bladder (harmonic mean 0.22 μm) and the much thicker water–blood barrier of the gills (9.61 μm), the morphometric diffusing capacity for oxygen and carbon dioxide was 88 times greater in the swim bladder than in the gills. These data clearly indicate the importance of the swim bladder, even in juvenile A. gigas that still engage in aquatic respiration. Because of the much greater diffusion constant of CO₂ than O₂ in water, the gills also remain important for CO₂ release.     

Optical band gap of semiconductive type II Si clathrate purified by centrifugation

The optical properties of Si clathrate, which is believed to have potential as a new Si-based material for optical devices, were investigated in this study. Si clathrates with type II structure (Na_xSi₁₃₆) with low Na content (x = 1.3, 2.0) were synthesized by thermal decomposition of NaSi. The synthesized samples were purified by centrifugation using a solution of CH₂Br₂–C₂Cl₄ to remove impurities. Using the obtained high purity samples (Na_1.3Si₁₃₆, 93 wt.%; Na_2.0Si₁₃₆, 90 wt.%), the optical absorption spectra of Na_xSi₁₃₆ were clarified, for the first time, from diffuse reflection measurements. The inclusion of Na in Si₁₃₆ was found to cause free carrier absorption in the infrared region but had little effect on the fundamental absorption edge found in the visible region.     

In vitro metabolic fate of alizapride: evidence for the formation of reactive metabolites based on liquid chromatography-tandem mass spectrometry

The study of the formation of reactive metabolites during drug metabolism is one of the major areas of research in drug development since the link between reactive metabolites and drug adverse effects was well recognized. In particular, it has been shown that acrolein, a reactive carbonyl species sharing carbonylating and alkylating properties, binds covalently to nucleophilic sites in proteins, causing cellular damage. Alizapride, (±)-6-methoxy-N-{[1-(prop-2-en-1-yl)-pyrrolidin-2-yl]methyl}-1H-benzotriazole-5-carboxamide, is a N-allyl containing dopamine antagonist with antiemetic properties for which no data concerning its metabolic fate are so far reported. The study of the in vitro metabolism of alizapride showed the formation of acrolein during the oxidative N-deallylation. Moreover, the formation of an epoxide metabolite has been also described suggesting its role as a putative structural alert. The reactivity of the acrolein and the epoxide generated in alizapride metabolism was demonstrated by the formation of the corresponding adducts with nucleophilic thiols. Overall, ten metabolites have been identified and characterized by electrospray ionization tandem mass spectrometry analysis allowing to propose an in vitro metabolic scheme for alizapride. At the best of our knowledge, this is the second case of a drug involved in the generation of acrolein during its metabolism being the first represented by cyclophosphamide.     

Iron in the brain

The results of our studies of iron in three brain structures, substantia nigra (SN), globus pallidus (GP), and hippocampus (Hip), are presented. Mössbauer spectroscopy, electron microscopy and ELISA (enzyme-linked immuno-absorbent assay) were applied. Mössbauer studies show that most of the iron in the brain is ferritin-like. The concentration of iron is similar in SN and GP, but less than half of this in Hip. ELISA studies showed that the H/L ratio of ferritin in SN and GP is also similar, but is about three times higher in Hip. These results suggest that the role of iron in SN and GP may be different from that in Hip. Electron microscopy shows that the diameters of the ferritin iron cores in the brain are smaller that in the liver (3.5 ± 0.5 nm vs. 6.0 ± 0.5 nm). Mössbauer studies yield the ratio between the concentration of iron in control and parkinsonian SN as 1.00 ± 0.13.