Efficient pricing options under regime switching

In the paper, we propose two new efficient methods for pricing barrier option in wide classes of Lévy processes with/without regime switching. Both methods are based on the numerical Laplace transform inversion formulae and the Fast Wiener-Hopf factorization method developed in Kudryavtsev and Levendorski\v{i} (Finance Stoch. 13: 531--562, 2009). The first method uses the Gaver-Stehfest algorithm, the second one -- the Post-Widder formula. We prove the advantage of the new methods in terms of accuracy and convergence by using Monte-Carlo simulations.Lévy processes; barrier options;regime switching models; Wiener-Hopf factorization; Laplace transform; numerical methods; numerical transform inversion

An implementation of the Wiener-Hopf factorization into finite difference methods for option pricing under Lévy processes

In the paper, we consider the problem of pricing options in wide classes of Lévy processes. We propose a general approach to the numerical methods based on a finite difference approximation for the generalized Black-Scholes equation. The goal of the paper is to incorporate the Wiener-Hopf factorization into finite difference methods for pricing options in Lévy models with jumps. The method is applicable for pricing barrier and American options. The pricing problem is reduced to the sequence of linear algebraic systems with a dense Toeplitz matrix; then the Wiener-Hopf factorization method is applied. We give an important probabilistic interpretation based on the infinitely divisible distributions theory to the Laurent operators in the correspondent factorization identity. Notice that our algorithm has the same complexity as the ones which use the explicit-implicit scheme, with a tridiagonal matrix. However, our method is more accurate. We support the advantage of the new method in terms of accuracy and convergence by using numerical experiments.On considère le problème d'évaluation d'options pour une large classe de processus de Lévy. On propose une approche numérique basée sur une approximation par différences finies pour l'équation de Black-Scholes généralisée. Le but est d'introduire la factorisation de Wiener-Hopf dans la méthode de différences finies pour l'évaluation d'options dans des modèles de Lévy avec sauts. La méthode s'applique au cas des options barrières et les options américaines. Le problème d'évaluation se réduit à une suite de systèmes linéaires algébriques avec matrice dense de Toeplitz, pour laquelle la méthode de factorisation de Wiener-Hopf est appliquée. Nous donnons une interprétation probabiliste basée sur la théorie des distributions infiniment divisibles des opérateurs de Laurent de l'identité de factorisation correspondante. Notre algorithme a la même complexité que le shéma explicite avec matrice tridiagonale, mais est plus précis. Nous illustrons l'avantage de cette méthode en termes de précision et convergence, sur des expériences numériques

Efficient pricing options under regime switching

In the paper, we propose two new efficient methods for pricing barrier option in wide classes of Lévy processes with/without regime switching. Both methods are based on the numerical Laplace transform inversion formulae and the Fast Wiener-Hopf factorization method developed in Kudryavtsev and Levendorski\v{i} (Finance Stoch. 13: 531--562, 2009). The first method uses the Gaver-Stehfest algorithm, the second one -- the Post-Widder formula. We prove the advantage of the new methods in terms of accuracy and convergence by using Monte-Carlo simulations

Efficient pricing of swing options in Lévy-driven models

International audienceWe consider the problem of pricing swing options with multiple exercise rights in Lévy-driven models. We propose an efficient Wiener-Hopf factorisation method that solves multiple parabolic partial integro-differential equations associated with the pricing problem. We compare the proposed method with a finite difference algorithm. Both proposed deterministic methods are related to the dynamic programming principle and lead to the solution of a multiple optimal stopping problem. Numerical examples illustrate the efficiency and the precision of the proposed methods

Efficient pricing options under regime switching

In the paper, we propose two new efficient methods for pricing barrier option in wide classes of Lévy processes with/without regime switching. Both methods are based on the numerical Laplace transform inversion formulae and the Fast Wiener-Hopf factorization method developed in Kudryavtsev and Levendorski\v{i} (Finance Stoch. 13: 531--562, 2009). The first method uses the Gaver-Stehfest algorithm, the second one -- the Post-Widder formula. We prove the advantage of the new methods in terms of accuracy and convergence by using Monte-Carlo simulations

The extraordinary complex magnetic field of the helium-strong star HD 37776

The early-type chemically peculiar stars often show strong magnetic fields on their surfaces. These magnetic topologies are organized on large scales and are believed to be close to an oblique dipole for most of the stars. In a striking exception to this general trend, the helium-strong star HD 37776 shows an extraordinary double-wave rotational modulation of the longitudinal magnetic field measurements, indicating a topologically complex and, possibly, record strong magnetic field. Here we present a new investigation of the magnetic field structure of HD 37776, using both simple geometrical interpretation of the longitudinal field curve and detailed modeling of the time-resolved circular polarization line profiles with the help of magnetic Doppler imaging technique. We derive a model of the magnetic field structure of HD 37776, which reconciles for the first time all magnetic observations available for this star. We find that the local surface field strength does not exceed ~30 kG, while the overall field topology of HD 37776 is dominated by a non-axisymmetric component and represents by far the most complex magnetic field configuration found among early-type stars.Comment: 9 pages, 8 figures; accepted for publication in The Astrophysical Journa

Level increase of competitive readiness of elite judokas in the weight category ofup to 60 kg (as an example is the national team of Kyrgyzstan)

The aim of the research is to find the new methods of the judoists’ preparation for the competitive activity. Actually the participants of the researches are the men (n=20) and they are the members of Kyrgyzstan national judo team. Moreover, the median age was 22,8 years. The research period was 1 year. It was revealed that the blocks of coordination and speed-power exercises jointly with the improvement of the technical base of the wrestlers were added in the program of the athletes’ preparation of the experimental group (n=10). Besides, the tests were used to determine the level of different motor skills of the athletes to assess the obtained data. Attention should also be paid to the calculation of the values of the competitive coefficients (CC) of the athletes which was made. Besides, the statistical analysis of the data was carried out using Mann–Whitney U–test. Indeed, the test results revealed a significant (P<0,05) advantage of the athletes from the experimental group in the speed running, strength training and running 1 mile. Fortunately, CC data of the athletes showed a significant (P<0,05) discrepancy in the volume of the effective equipment (Nage-waza) and a significant (P<0,01) difference in the intervals between the attacks (Nage-waza) in favor of the athletes from the experimental group. Accordingly, the use of coordination blocks and speed-power exercises in the structure of a year cycle of the athletes’ preparation allows to increase the development indicators of the motor skills and technical activity of the judoists during the competitive matches significantly

РЕАЛИЗАЦИЯ ФИЛЬТРА КАЛМАНА ПРИ ОБРАБОТКЕ ДАННЫХ ОТ ДАТЧИКА УРОВНЯ ТОПЛИВА С ИСПОЛЬЗОВАНИЕМ ДОПОЛНИТЕЛЬНОЙ ИНФОРМАЦИИ ОТ НАВИГАЦИОННО-СВЯЗНОГО ТЕРМИНАЛА

All measuring instruments have a certain error, the components of which can be external and internal effects. This leads to the fact that the information read from the measuring devices is highly distorted. The noisier the data, the more difficult it is to rely on it. One of the tasks of monitoring vehicles is to measure the fuel level in the tank, determine fueling and discharges, and calculate fuel consumption. In this article, we’ll look at the data from the fuel level sensor and then process it to remove the noise.Purpose: the goal is to obtain reliable fuel level values in the tank of vehicles using the Kalman filter.Methodology in the article proposes a method for filtering fuel level data, which implies the use of data from fuel sensors and additional information from navigation and communication terminals.Results: the most accurate values of fuel level in the tank of vehicles are obtained.Practical implications: it is advisable to use the results obtained in motor transport enterprises to control the fuel consumption of vehicles.Все измерительные приборы обладают некоторой погрешностью, составляющими которой могут быть внешние и внутренние воздействия. Это приводит к тому, что информация, считываемая с измерительных устройств, оказывается искаженной. Чем сильнее зашумлены данные, тем сложнее их обрабатывать. Одной из задач мониторинга параметров работы транспортных средств является измерение уровня топлива в баке, определение заправок и сливов, а также расчет расхода топлива. В данной статье рассматриваются данные от датчика уровня топлива с последующей обработкой этих данных.Цель – получение достоверных значений уровня топлива в баке транспортных средств с использованием фильтра Калмана.Метод или методология проведения исследования: в статье предложен метод фильтрации данных уровня топлива, подразумевающий использование данных от датчика топлива и дополнительной информации от навигационно-связного терминала.Результаты: получены отфильтрованные значения уровня топлива в баке транспортных средств.Область применения результатов: полученные результаты целесообразно применять в автотранспортных предприятиях для контроля расхода топлива транспортных средств

Minerals of Rare Earth Elements in High-Phosphorus Ooidal Ironstones of the Western Siberia and Turgai Depression

The aim of this research was to study the rare earth (REE) minerals in ooidal ironstone deposits of the West Siberian basin and the Turgai depression. Authigenic minerals (monazite and cerite) were described, and their main mineral form was identified as light rare earth element phosphate (LREE-phosphate) in this study. LREE-phosphate is included in ferruginous ooids, peloids, and oncoids and forms a consistent mineral association with Fe-hydroxides (goethite and its hydrated amorphous derivatives) and Fe-rich layered silicates (Fe-illite-smectite, chamosite, berthierine). The constancy of the mineral association in two deposits of different ages indicates a general mechanism behind the formation of these minerals. LREE-phosphates (authigenic monazite) are characterized by microscopic sizes (up to 24 ?m), diverse morphology (mainly spherical or xenomorphic), and occupy spaces between the micro-cortex in ferruginous spheroids. This mineral can be found in other deposits of ooidal ironstone. According to its mineralogical and chemical characteristics, LREE-phosphate mainly belongs to the authigenic (nodular or “gray”) monazite. However, the incomplete (not 100%) correspondence of Kikuchi bands with the reference monazite does not allow its reliable identification. Based on its small size, chemical leaching or bacterial interaction is recommended to extract REE from ooidal ironstone while predicting the associated removal of phosphorus from iron ore due to its dominant phosphate mineral form. Ooidal ironstone should be considered a complex deposit and an unconventional natural type of REE ores as an example of the largest Bakchar and Lisakovsk deposits