Pricing derivatives with stochastic volatility

This Ph.D. thesis contains 4 essays in mathematical finance with a focus on pricing Asian option (Chapter 4), pricing futures and futures option (Chapter 5 and Chapter 6) and time dependent volatility in futures option (Chapter 7). In Chapter 4, the applicability of the Albrecher et al.(2005)'s comonotonicity approach was investigated in the context of various benchmark models for equities and com- modities. Instead of classical Levy models as in Albrecher et al.(2005), the focus is the Heston stochastic volatility model, the constant elasticity of variance (CEV) model and the Schwartz (1997) two-factor model. It is shown that the method delivers rather tight upper bounds for the prices of Asian Options in these models and as a by-product delivers super-hedging strategies which can be easily implemented. In Chapter 5, two types of three-factor models were studied to give the value of com- modities futures contracts, which allow volatility to be stochastic. Both these two models have closed-form solutions for futures contracts price. However, it is shown that Model 2 is better than Model 1 theoretically and also performs very well empiri- cally. Moreover, Model 2 can easily be implemented in practice. In comparison to the Schwartz (1997) two-factor model, it is shown that Model 2 has its unique advantages; hence, it is also a good choice to price the value of commodity futures contracts. Fur- thermore, if these two models are used at the same time, a more accurate price for commodity futures contracts can be obtained in most situations. In Chapter 6, the applicability of the asymptotic approach developed in Fouque et al.(2000b) was investigated for pricing commodity futures options in a Schwartz (1997) multi-factor model, featuring both stochastic convenience yield and stochastic volatility. It is shown that the zero-order term in the expansion coincides with the Schwartz (1997) two-factor term, with averaged volatility, and an explicit expression for the first-order correction term is provided. With empirical data from the natural gas futures market, it is also demonstrated that a significantly better calibration can be achieved by using the correction term as compared to the standard Schwartz (1997) two-factor expression, at virtually no extra effort. In Chapter 7, a new pricing formula is derived for futures options in the Schwartz (1997) two-factor model with time dependent spot volatility. The pricing formula can also be used to find the result of the time dependent spot volatility with futures options prices in the market. Furthermore, the limitations of the method that is used to find the time dependent spot volatility will be explained, and it is also shown how to make sure of its accuracy.

Changes in physical and chemical parameters of the traditional portuguese product água-mel during the production process

Changes in physical and chemical parameters (viscosity, total soluble solids and Hunter color parameters L*, a*, b*, chroma and hue angle) of água-mel were investigated throughout processing. Kinetic parameters for color change of heatprocessed água-mel were monitored. A zero-order kinetic model was applied to changes in L* and b*, while a* and C* were described using a first-order kinetic model. The heating process changed all three color parameters (L*, a*, b*), causing a shift toward the darker colors. Parameters L* decreased, while a*, b*, C* and hue angle (°h) increased during heating. Regarding changes in total soluble solids and in apparent viscosity, both fitted first-order kinetics. A direct relationship was found between the changes in these two parameters. The increase in both total soluble solids and viscosity affected a*, b* and C*. In addition, a flow diagram for the Portuguese água-mel production process has been established.

Caractérisation pharmacocinétique et pharmacodynamique de la lidocaïne avec ou sans adrénaline lors d’un bloc paravertébral du plexus brachial chez le chien

Au cours des vingt dernières années, l’anesthésie régionale est devenue, autant en médecine vétérinaire qu’humaine, un outil essentiel à l’élaboration de protocoles analgésiques péri-opératoires. Parmi l’éventail de techniques mises au point en anesthésie canine, le bloc paravertébral du plexus vertébral (PBPB) et sa version modifiée sont d’un grand intérêt pour toute procédure du membre thoracique, dans sa portion proximale. Toutefois, l’essentiel des données publiées à ce jour provient d’études colorimétriques, sans évaluation clinique, et peu d’information est disponible sur les techniques de localisation nerveuse envisageables à ce site. Notre étude visait à décrire une approche échoguidée du PBPB modifié, puis à caractériser ses paramètres pharmacocinétiques et pharmacodynamiques après administration de lidocaïne (LI) ou lidocaïne adrénalinée (LA). Huit chiens ont été inclus dans un protocole prospectif, randomisé, en aveugle et croisé, réparti sur trois périodes. L’impact pharmacodynamique du bloc effectué avec LI ou LA a été évalué régulièrement pour 180 min suivant son exécution. Le traitement à l’adrénaline n’a pas démontré d’impact significatif (P = 0,845) sur la durée du bloc sensitif, tel qu’évalué par un stimulus douloureux mécanique appliqué aux dermatomes ciblés. À l’opposé, l’atteinte proprioceptive évaluée par la démarche a été trouvée prolongée (P = 0,027) et le bloc moteur mesuré par le pic de force verticale (PVF) au trot sur la plaque de force s’est avéré plus marqué (PVF réduit; P = 0,007) sous LA. À l’arrêt comme au trot, le nadir de la courbe PVF-temps a été trouvé retardé (P < 0,005) et la pente ascendante de retour aux valeurs normales adoucie (P = 0,005). Parallèlement aux évaluations cliniques, des échantillons plasmatiques ont été collectés régulièrement afin de quantifier et décrire le devenir pharmacocinétique de la lidocaïne. Parmi les trois élaborés, un modèle bi-compartimental doté d’une double absorption asynchrone d’ordre zéro a finalement été sélectionné et appliqué aux données expérimentales. Sous LA, la Cmax a été trouvée significativement diminuée (P < 0,001), les phases d’absorption prolongées [P < 0,020 (Dur1) et P < 0,001 (Dur2)] et leurs constantes réduites [P = 0,046(k01) et P < 0,001 (k02)], le tout en concordance avec les effets proprioceptifs et moteurs rapportés. Bien que l’extrapolation du dosage soit maintenant théoriquement envisageable à partir du modèle mis en lumière ici, des études supplémentaires sont encore nécessaires afin d’établir un protocole de PBPB d’intérêt clinique. L’analyse sur plaque de force pourrait alors devenir un outil de choix pour évaluer l’efficacité du bloc dans un cadre expérimental.

Caractérisation pharmacocinétique et pharmacodynamique de la lidocaïne avec ou sans adrénaline lors d’un bloc paravertébral du plexus brachial chez le chien

Au cours des vingt dernières années, l’anesthésie régionale est devenue, autant en médecine vétérinaire qu’humaine, un outil essentiel à l’élaboration de protocoles analgésiques péri-opératoires. Parmi l’éventail de techniques mises au point en anesthésie canine, le bloc paravertébral du plexus vertébral (PBPB) et sa version modifiée sont d’un grand intérêt pour toute procédure du membre thoracique, dans sa portion proximale. Toutefois, l’essentiel des données publiées à ce jour provient d’études colorimétriques, sans évaluation clinique, et peu d’information est disponible sur les techniques de localisation nerveuse envisageables à ce site. Notre étude visait à décrire une approche échoguidée du PBPB modifié, puis à caractériser ses paramètres pharmacocinétiques et pharmacodynamiques après administration de lidocaïne (LI) ou lidocaïne adrénalinée (LA). Huit chiens ont été inclus dans un protocole prospectif, randomisé, en aveugle et croisé, réparti sur trois périodes. L’impact pharmacodynamique du bloc effectué avec LI ou LA a été évalué régulièrement pour 180 min suivant son exécution. Le traitement à l’adrénaline n’a pas démontré d’impact significatif (P = 0,845) sur la durée du bloc sensitif, tel qu’évalué par un stimulus douloureux mécanique appliqué aux dermatomes ciblés. À l’opposé, l’atteinte proprioceptive évaluée par la démarche a été trouvée prolongée (P = 0,027) et le bloc moteur mesuré par le pic de force verticale (PVF) au trot sur la plaque de force s’est avéré plus marqué (PVF réduit; P = 0,007) sous LA. À l’arrêt comme au trot, le nadir de la courbe PVF-temps a été trouvé retardé (P < 0,005) et la pente ascendante de retour aux valeurs normales adoucie (P = 0,005). Parallèlement aux évaluations cliniques, des échantillons plasmatiques ont été collectés régulièrement afin de quantifier et décrire le devenir pharmacocinétique de la lidocaïne. Parmi les trois élaborés, un modèle bi-compartimental doté d’une double absorption asynchrone d’ordre zéro a finalement été sélectionné et appliqué aux données expérimentales. Sous LA, la Cmax a été trouvée significativement diminuée (P < 0,001), les phases d’absorption prolongées [P < 0,020 (Dur1) et P < 0,001 (Dur2)] et leurs constantes réduites [P = 0,046(k01) et P < 0,001 (k02)], le tout en concordance avec les effets proprioceptifs et moteurs rapportés. Bien que l’extrapolation du dosage soit maintenant théoriquement envisageable à partir du modèle mis en lumière ici, des études supplémentaires sont encore nécessaires afin d’établir un protocole de PBPB d’intérêt clinique. L’analyse sur plaque de force pourrait alors devenir un outil de choix pour évaluer l’efficacité du bloc dans un cadre expérimental.

Fractional order modelling of zero length column desorption response for adsorbents with variable particle sizes

This manuscript analyses the data generated by a Zero Length Column (ZLC) diffusion experimental set-up, for 1,3 Di-isopropyl benzene in a 100% alumina matrix with variable particle size. The time evolution of the phenomena resembles those of fractional order systems, namely those with a fast initial transient followed by long and slow tails. The experimental measurements are best fitted with the Harris model revealing a power law behavior.

Band-edge states of the zero(th)-order gap in quasi-periodic photonic superlattices

The photonic modes of Thue-Morse and Fibonacci lattices with generating layers A and B, of positive and negative indices of refraction, are calculated by the transfer-matrix technique. For Thue-Morse lattices, as well for periodic lattices with AB unit cell, the constructive interference of reflected waves, corresponding to the zero(th)-order gap, takes place when the optical paths in single layers A and B are commensurate. In contrast, for Fibonacci lattices of high order, the same phenomenon occurs when the ratio of those optical paths is close to the golden ratio. In the long wavelength limit, analytical expressions defining the edge frequencies of the zero(th) order gap are obtained for both quasi-periodic lattices. Furthermore, analytical expressions that define the gap edges around the zero(th) order gap are shown to correspond to the = 0 and = 0 conditions.

Higher order spectral analysis of Chua's circuit

Higher order spectral analysis is used to investigate nonlinearities in time series of voltages measured from a realization of Chua's circuit. For period-doubled limit cycles, quadratic and cubic nonlinear interactions result in phase coupling and energy exchange between increasing numbers of triads and quartets of Fourier components as the nonlinearity of the system is increased. For circuit parameters that result in a chaotic Rossler-type attractor, bicoherence and tricoherence spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. When the circuit exhibits a double-scroll chaotic attractor the bispectrum is zero, but the tricoherences are high, consistent with the importance of higher-than-second order nonlinear interactions during chaos associated with the double scroll.

Effectiveness factor for zeroth-order catalytic reactions with volume change and nonuniform catalyst activity profiles

Analytical solutions are presented for the effectiveness factor of a zeroth-order reaction with volume change and nonuniform catalyst activity profile in slab, cylinder and spherical pellets. The possibility of shape normalization is considered for a variety of activity profiles and pellet shapes. When the catalyst activity at the external surface of the pellet is non-zero, shape normalization is obtained, which makes the asymptotic behavior of the effectiveness factor identical for small and large values of Thiele modulus, however, the normalization can lead to significant errors, particularly for the case of activity profiles decreasing towards the outer surface of the catalyst.

Shape-Dependent Confinement in Ultrasmall Zero-, One-, and Two-Dimensional PbS Nanostructures

Spatial dimensionality affects the degree of confinement when an electron-hole pair is squeezed from one or more dimensions approaching the bulk exciton Bohr radius (alpha(B)) limit. The etectron-hole interaction in zero-dimensional (0D) dots, one-dimensional (1D) rods/wires, and two-dimensional (2D) wells/sheets should be enhanced by the increase in confinement dimensions in the order 0D > 1D > 2D. We report the controlled synthesis of PbS nanomateriats with 0D, 1D, and 2D forms retaining at least one dimension in the strongly confined regime far below alpha(B) (similar to 10 nm for PbS) and provide evidence through varying the exciton-phonon coupling strength that the degree of confinement is systematically weakened by the loss of confinement dimension. Geometry variations show distinguishable far-field optical polarizations, which could find useful applications in polarization-sensitive devices.

Zero-crossings in turbulent signals

A primary motivation for this work arises from the contradictory results obtained in some recent measurements of the zero-crossing frequency of turbulent fluctuations in shear flows. A systematic study of the various factors involved in zero-crossing measurements shows that the dynamic range of the signal, the discriminator characteristics, filter frequency and noise contamination have a strong bearing on the results obtained. These effects are analysed, and explicit corrections for noise contamination have been worked out. New measurements of the zero-crossing frequency N0 have been made for the longitudinal velocity fluctuation in boundary layers and a wake, for wall shear stress in a channel, and for temperature derivatives in a heated boundary layer. All these measurements show that a zero-crossing microscale, defined as Λ = (2πN0)−1, is always nearly equal to the well-known Taylor microscale λ (in time). These measurements, as well as a brief analysis, show that even strong departures from Gaussianity do not necessarily yield values appreciably different from unity for the ratio Λ/λ. Further, the variation of N0/N0 max across the boundary layer is found to correlate with the familiar wall and outer coordinates; the outer scaling for N0 max is totally inappropriate, and the inner scaling shows only a weak Reynolds-number dependence. It is also found that the distribution of the interval between successive zero-crossings can be approximated by a combination of a lognormal and an exponential, or (if the shortest intervals are ignored) even of two exponentials, one of which characterizes crossings whose duration is of the order of the wall-variable timescale ν/U2*, while the other characterizes crossings whose duration is of the order of the large-eddy timescale δ/U[infty infinity]. The significance of these results is discussed, and it is particularly argued that the pulse frequency of Rao, Narasimha & Badri Narayanan (1971) is appreciably less than the zero-crossing rate.

Induced higher-order aberrations after laser in situ keratomileusis (LASIK) performed with wavefront-guided IntraLase femtosecond laser in moderate to high astigmatism

Background Wavefront-guided Laser-assisted in situ keratomileusis (LASIK) is a widespread and effective surgical treatment for myopia and astigmatic correction but whether it induces higher-order aberrations remains controversial. The study was designed to evaluate the changes in higher-order aberrations after wavefront-guided ablation with IntraLase femtosecond laser in moderate to high astigmatism. Methods Twenty-three eyes of 15 patients with moderate to high astigmatism (mean cylinder, −3.22 ± 0.59 dioptres) aged between 19 and 35 years (mean age, 25.6 ± 4.9 years) were included in this prospective study. Subjects with cylinder ≥ 1.5 and ≤2.75 D were classified as moderate astigmatism while high astigmatism was ≥3.00 D. All patients underwent a femtosecond laser–enabled (150-kHz IntraLase iFS; Abbott Medical Optics Inc) wavefront-guided ablation. Uncorrected (UDVA), corrected (CDVA) distance visual acuity in logMAR, keratometry, central corneal thickness (CCT) and higher-order aberrations (HOAs) over a 6 mm pupil, were assessed before and 6 months, postoperatively. The relationship between postoperative change in HOA and preoperative mean spherical equivalent refraction, mean astigmatism, and postoperative CCT were tested. Results At the last follow-up, the mean UDVA was increased (P < 0.0001) but CDVA remained unchanged (P = 0.48) and no eyes lost ≥2 lines of CDVA. Mean spherical equivalent refraction was reduced (P < 0.0001) and was within ±0.50 D range in 61 % of eyes. The average corneal curvature was flatter by 4 D and CCT was reduced by 83 μm (P < 0.0001, for all), postoperatively. Coma aberrations remained unchanged (P = 0.07) while the change in trefoil (P = 0.047) postoperatively, was not clinically significant. The 4th order HOAs (spherical aberration and secondary astigmatism) and the HOA root mean square (RMS) increased from −0.18 ± 0.07 μm, 0.04 ± 0.03 μm and 0.47 ± 0.11 μm, preoperatively, to 0.33 ± 0.19 μm (P = 0.004), 0.21 ± 0.09 μm (P < 0.0001) and 0.77 ± 0.27 μm (P < 0.0001), six months postoperatively. The change in spherical aberration after the procedure increased with an increase in the degree of preoperative myopia. Conclusions Wavefront-guided IntraLASIK offers a safe and effective option for vision and visual function improvement in astigmatism. Although, reduction of HOA is possible in a few eyes, spherical-like aberrations are increased in majority of the treated eyes.

Rough Justice or Zero Tolerance? - Reassessing the Nature of Copyright in Light of Collective Licensing (Part I)

Starting point in the European individualistic copyright ideology is that an individual author creates a work and controls the use of it. However, this paper argues that it is (and has always been) impossible to control the use of works after their publication. This has also been acknowledged by the legislator, who has introduced collective licensing agreements because of this impossibility. Since it is impossible to rigorously control the use of works this writing "Rough Justice or Zero Tolerance - Reassessing the Nature of Copyright in Light of Collective Licensing" examines what reality of copyright is actually about. Finding alternative (and hopefully more "true") ways to understand copyright helps us to create alternative solutions in order to solve possible problems we have as it comes e.g. to use of content in online environment. The paper makes a claim that copyright is actually about defining negotiation points for different stakeholders and that nothing in the copyright reality prevents us from defining e.g. a new negotiation point where representatives of consumers would meet representatives of right holders in order to agree on the terms of use for certain content types in online environment.

Reactivation kinetics of boron acceptors in hydrogenated silicon during zero bias anneal

The reactivation kinetics of passivated boron accepters in hydrogenated silicon during zero bias annealing in the temperature range of 65-130 degrees C are reported, For large annealing times and high annealing temperatures, the reactivation process follows second-order kinetics and is rate limited by a thermally activated <(H)over tilde (2)> complex formation process, For short annealing times and low annealing temperatures, the reactivation rate is found to be larger than that due to <(H)over tilde (2)> complex formation alone. We conclude that the faster reactivation is caused by the diffusion of the liberated hydrogen atoms into the bulk as well as <(H)over tilde (2)> complex formation. The effective diffusion coefficient of hydrogen is measured and found to obey the Arrhenius relation with an activation energy (1.41 +/- 0.1) eV. (C) 1997 American Institute of Physics.

On the diversity and complexity of Zero Forcing receivers for MIMO Zero Padded systems

Zero padded systems with linear receivers are shown to be robust and amenable to fast implementations in single antenna scenarios. In this paper, properties of such systems are investigated when multiple antennas are present at both ends of the communication link. In particular, their diversity and complexity are evaluated for precoded transmissions. The linear receivers are shown to exploit multipath and receive diversities, even in the absence of any coding at the transmitter. Use of additional redundancy to improve performance is considered and the effect of transmission rate on diversity order is analyzed. Low complexity implementations of Zero Forcing receivers are devised to further enhance their applicability.

Adaptive window zero-crossing-based instantaneous frequency estimation

We address the problem of estimating instantaneous frequency (IF) of a real-valued constant amplitude time-varying sinusoid. Estimation of polynomial IF is formulated using the zero-crossings of the signal. We propose an algorithm to estimate nonpolynomial IF by local approximation using a low-order polynomial, over a short segment of the signal. This involves the choice of window length to minimize the mean square error (MSE). The optimal window length found by directly minimizing the MSE is a function of the higher-order derivatives of the IF which are not available a priori. However, an optimum solution is formulated using an adaptive window technique based on the concept of intersection of confidence intervals. The adaptive algorithm enables minimum MSE-IF (MMSE-IF) estimation without requiring a priori information about the IF. Simulation results show that the adaptive window zero-crossing-based IF estimation method is superior to fixed window methods and is also better than adaptive spectrogram and adaptive Wigner-Ville distribution (WVD)-based IF estimators for different signal-to-noise ratio (SNR).