We suggest two new fast and accurate methods, Fast Wiener-Hopf method (FWH-method) and Iterative Wiener-Hopf method (IWH-method), for pricing barrier options for a wide class of Lévy processes. Both methods use the Wiener-Hopf factorization and Fast Fourier Transform algorithm. Using an accurate albeit relatively slow finite-difference algorithm developed in (FDS-method), we demonstrate the accuracy and fast convergence of the two methods for processes of finite variation. We explain that the convergence of the methods must be better for processes of infinite variation, and, as a certain supporting evidence, demonstrate with numerical examples that the results obtained by two methods are in extremely good agreement. Finally, we use FDS, FWH and IWH-methods to demonstrate that Cont and Volchkova method (CV-method), which is based on the approximation of small jumps by an additional diffusion, may lead to sizable relative errors, especially near the barrier and strike. The reason is that CV-method presumes that the option price is of class C 2 up to the barrier, whereas for processes without Gaussian component, it is typically not of class C 1 at the barrier. (2006) (FDS-method), on démontre la précision et la convergence rapide des deux méthodes pour des processusà variation finie. On explique que la convergence des méthodes doitêtre meilleure pour des processusà variation infinie et on montre sur des exemples numériques la cohérence des résultats obtenus par les deux méthodes. Finalement on utilise les méthodes FDS, FWH and IWHmethods pour montrer que la méthode de Cont and Volchkova (CV-method), qui est basée sur l'approximation des petits sauts par une diffusion additionnelle peut entrainer des erreurs relativement importantes notamment près de la barrière et du strike. Cela s'explique par le fait que cette méthode présuppose que le prix de l'option est de classe C 2 jusqu'à la barrière, alors que pour des processus sans composante gaussienne, il n'est en général pas de classe C 1à la barrière.

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The high‐pressure and high‐temperature technique is the most promising for mass production of ultra‐small diamond nanoparticles of perfect structure. In the present work, this technique was successfully used for the synthesis of nanodiamonds from their molecular analogue, adamantane. A minimum size of synthesized diamond crystals of about 3 nm was reached. It was found that the decisive condition for the stable production of nanodiamonds from adamantane under pressures below the limit value required for direct conversion of graphite into diamond is the minimization of the carbon sample loss during the synthesis. The possibility of doping such diamonds with optically active impurities is demonstrated by the synthesis of submicron diamonds, containing nitrogen‐related centers, from a mixture of adamantane and adamantane carbonitrile.

The first application of the high-pressure-high-temperature (HPHT) technique for direct production of doped ultrasmall diamonds starting from a one-component organic precursor is reported. Heavily boron-doped diamond nanoparticles with a size below 10 nm are produced by HPHT treatment of 9-borabicyclo [3,3,1]nonane dimer molecules.