Implied volatility and state price density estimation: arbitrage analysis

This paper deals with implied volatility (IV) estimation using no-arbitrage techniques. The current market practice is to obtain IV of liquid options as based on Black–Scholes (BS type hereafter) models. Such volatility is subsequently used to price illiquid or even exotic options. Therefore, it follows that the BS model can be related simultaneously to the whole set of IVs as given by maturity/moneyness relation of tradable options. Then, it is possible to get IV curve or surface (a so called smile or smirk). Since the moneyness and maturity of IV often do not match the data of valuated options, some sort of estimating and local smoothing is necessary. However, it can lead to arbitrage opportunity if no-arbitrage conditions on state price density (SPD) are ignored. In this paper, using option data on DAX index, we aim to analyse the behavior of IV and SPD with respect to different choices of bandwidth parameter h, time to maturity and kernel function. A set of bandwidths which violates no-arbitrage conditions is identified. We document that the change of h implies interesting changes in the violation interval of moneyness. We also perform the analysis after removing outliers, in order to show that not only outliers cause the violation of no-arbitrage conditions. Moreover, we propose a new measure of arbitrage which can be considered either for the SPD curve (arbitrage area measure) or for the SPD surface (arbitrage volume measure). We highlight the impact of h on the proposed measures considering the options on a German stock index. Finally, we propose an extension of the IV and SPD estimation for the case of options on a dividend-paying stock.     

The classic differential evolution algorithm and its convergence properties

Differential evolution algorithms represent an up to date and efficient way of solving complicated optimization tasks. In this article we concentrate on the ability of the differential evolution algorithms to attain the global minimum of the cost function. We demonstrate that although often declared as a global optimizer the classic differential evolution algorithm does not in general guarantee the convergence to the global minimum. To improve this weakness we design a simple modification of the classic differential evolution algorithm. This modification limits the possible premature convergence to local minima and ensures the asymptotic global convergence. We also introduce concepts that are necessary for the subsequent proof of the asymptotic global convergence of the modified algorithm. We test the classic and modified algorithm by numerical experiments and compare the efficiency of finding the global minimum for both algorithms. The tests confirm that the modified algorithm is significantly more efficient with respect to the global convergence than the classic algorithm.     

Oxidative Catalysis Using the Stoichiometric Oxidant as a Reagent: An Efficient Strategy for Single‐Electron‐Transfer‐Induced Tandem Anion–Radical Reactions

Oxidative single‐electron transfer‐catalyzed tandem reactions consisting of a conjugate addition and a radical cyclization are reported, which incorporate the mandatory terminal oxidant as a functionality into the product.     

Diethyl Fluoronitromethylphosphonate: Synthesis and Application in Nucleophilic Fluoroalkyl Additions

Diethyl fluoronitromethylphosphonate ( 3 ), a previously unknown compound, was synthesized by electrophilic fluorination of diethyl nitromethylphosphonate with Selectfluor. Base‐induced decomposition of 3 was studied by NMR spectroscopy, which identified diethyl fluorophosphate and fluoronitromethane as the main decomposition products. C?H acidities [pK_a values in dimethyl sulfoxide (DMSO)] of 3 , 1‐fluoro‐1‐phenylsulfonylmethanephosphonate ( 1 ; McCarthy’s reagent), tetraethyl fluoromethylenebisphosphonate ( 2 ), and some nonfluorinated phosphonates were computed, and a good correlation between calculated and experimental pK_a values was found. The calculated C?H acidities increased in the sequence 2 < 1 < 3 . Diethyl fluoronitromethylphosphonate ( 3 ) was applied in the Horner–Wadsworth–Emmons reaction with aldehydes and trifluoromethyl ketones to provide new 1‐fluoro‐1‐nitroalkenes with good to high stereoselectivities. Alkylation of 3 was successful only with iodomethane, however, conjugate additions of 3 to Michael acceptors such as α,β‐unsaturated carbonyl compounds, sulfones, and nitro compounds allowed access to variously modified diethyl 1‐fluoro‐1‐nitrophosphonates.     

Highly Functionalized and Potent Antiviral Cyclopentane Derivatives Formed by a Tandem Process Consisting of Organometallic,Transition‐Metal‐Catalyzed,and Radical Reaction Steps

A simple modular tandem approach to multiply substituted cyclopentane derivatives is reported, which succeeds by joining organometallic addition, conjugate addition, radical cyclization, and oxygenation steps. The key steps enabling this tandem process are the thus far rarely used isomerization of allylic alkoxides to enolates and single‐electron transfer to merge the organometallic step with the radical and oxygenation chemistry. This controlled lineup of multiple electronically contrasting reactive intermediates provides versatile access to highly functionalized cyclopentane derivatives from very simple and readily available commodity precursors. The antiviral activity of the synthesized compounds was screened and a number of compounds showed potent activity against hepatitis C and dengue viruses.     

Design of Stereoelectronically Promoted Super Lewis Acids and Unprecedented Chemistry of Their Complexes

A new family of stereoelectronically promoted aluminum and scandium super Lewis acids is introduced on the basis of state‐of‐the‐art computations. Structures of these molecules are designed to minimize resonance electron donation to central metal atoms in the Lewis acids. Acidity of these species is evaluated on the basis of their fluoride‐ion affinities relative to the antimony pentafluoride reference system. It is demonstrated that introduced changes in the stereochemistry of the designed ligands increase acidity considerably relative to Al and Sc complexes with analogous monodentate ligands. The high stability of fluoride complexes of these species makes them ideal candidates to be used as weakly coordinating anions in combination with highly reactive cations instead of conventional Lewis acid–fluoride complexes. Further, the interaction of all designed molecules with methane is investigated. All studied acids form stable pentavalent‐carbon complexes with methane. In addition, interactions of the strongest acid of this family with very weak bases, namely, H₂, N₂, carbon oxides, and noble gases were investigated; it is demonstrated that this compound can form considerably stable complexes with the aforementioned molecules. To the best of our knowledge, carbonyl and nitrogen complexes of this species are the first hypothetical four‐coordinated carbonyl and nitrogen complexes of aluminum. The nature of bonding in these systems is studied in detail by various bonding analysis approaches.