Scaling and long-range dependence in option pricing I: Pricing European option with transaction costs under the fractional Black–Scholes model

This paper deals with the problem of discrete time option pricing by the fractional Black–Scholes model with transaction costs. By a mean self-financing delta-hedging argument in a discrete time setting, a European call option pricing formula is obtained. The minimal price of an option under transaction costs is obtained as timestep , which can be used as the actual price of an option. In fact, is an adjustment to the volatility in the Black–Scholes formula by using the modified volatility to replace the volatility σ, where is the Hurst exponent, and k is a proportional transaction cost parameter. In addition, we also show that timestep and long-range dependence have a significant impact on option pricing.     

Dynamics of implied volatility surfaces from random matrix theory

We analyze the dynamics of the implied volatility surface of KOSPI 200 futures options from random matrix theory. To extract the informative data, we use random matrix criteria. Implied volatility data have a colossal eigenvalue, and the order of eigenvalues in a noisy regime is distinguishably smaller than a random matrix theory prediction. We discern the marketwide knowledge of the implied volatility surface movement such as the level, skew, and smile effect. These dynamics has the ergodic property and long range autocorrelation. We also study the relationship between the three implied volatility surface dynamics and the underlying asset dynamics, and confirm the existence of leverage effect even in the short time interval.     

Scaling and long-range dependence in option pricing V: Multiscaling hedging and implied volatility smiles under the fractional Black-Scholes model with transaction costs

This paper deals with the problem of discrete time option pricing using the fractional Black-Scholes model with transaction costs. Through the ‘anchoring and adjustment’ argument in a discrete time setting, a European call option pricing formula is obtained. The minimal price of an option under transaction costs is obtained. In addition, the relation between scaling and implied volatility smiles is discussed.     

A delay financial model with stochastic volatility; martingale method

In this paper, we extend a delayed geometric Brownian model by adding a stochastic volatility term, which is driven by a hidden process of fast mean reverting diffusion, to the delayed model. Combining a martingale approach and an asymptotic method, we develop a theory for option pricing under this hybrid model. The core result obtained by our work is a proof that a discounted approximate option price can be decomposed as a martingale part plus a small term. Subsequently, a correction effect on the European option price is demonstrated both theoretically and numerically for a good agreement with practical results.     

Visible to NIR absorbing C–N and C–C bonding squaraines: A computational study

We report a comparative computational study of 2 series of molecules with C–N bonding squaraines (NSQ) and C–C bonding squaraines (CSQ), having absorption from visible to near infrared region (350‐800 nm). The NSQ are considered as molecules with break‐in conjugation, and CSQ are considered as molecules with complete conjugation in molecular backbone. The lowest electronic excitations in CSQ molecules are always having around 200 nm red shifted absorption than its corresponding NSQ molecules. The reason for this drastic red shift in CSQ series than NSQ has been systematically studied by density functional theory, time‐dependent density functional theory, and symmetry adopted cluster configuration interaction methods. The CSQ series are showing less charge transfer than NSQ, but having small diradical character. This study may be helpful in design and synthesis of new squaraine dyes, which are useful in materials applications.     

Improvement of superconducting properties of old Y–Ba–Cu–O specimens by high-energy heavy ion irradiation

Superconducting parameters of different, almost 20 years old Y–Ba–Cu–O samples, prepared in 1987–1988 are investigated. The aim of this research is to find out how a heavy ion beam can enhance the superconducting features of very old and originally not always perfect Y-based specimens. As is observed, their electrical and magnetic characteristics are very sensitive to high-energy Bi-ion irradiation, which results in significant increase of the superconducting parameters. The most important one of them is the global critical current density which is calculated with the help of a new method on the basis of experiments. It can be increased by 18–39%, depending on the original, starting conditions of the samples before the irradiation. At the same time, the average values of intragrain critical current density grows by 37–51%. A slight increase in the critical temperature of 1–2 K was also observed. The experiments on AC susceptibility demonstrate that this irradiation causes to develop faster the total diamagnetic state and decreases the loss. The reason of these effects can be found in the better orientation of crystals, enlargement of microcrystalline aggregates, higher homogenization of the material, thus, in the increase of the superconducting component of samples due to the irradiation.     

A note on regularization methods in Kaluza–Klein theories

We comment on the presence of power-like divergences in Kaluza–Klein theories with supersymmetry breaking à la Scherk–Schwarz. By introducing a SUSY preserving regulator, we show that, in the context of a recently model proposed by Barbieri, Hall and Nomura, the Higgs mass is finite and unambiguously defined. The same result applies to similar models.     

A new form of the Sutton–Chen potential for the Cu–Ag alloys

The analytic construction of a many-body potential inspired from the Sutton–Chen parametrization is presented for copper and silver. A new approach is used to model the cross interaction for the Cu–Ag alloys. The parameters are fitted to first principles calculations based on the full potential linear plane wave method. The structural properties of the order and disorder Cu–Ag alloys in the B₂and fcc structures are presented for different concentration.     

Annealing effects on the magnetization of Co–Ni–B amorphous nanoparticles

Chemically prepared (Co_xNi_1−x)_1−yB_y (x=0.5, 0.75, 1; y≈0.4) amorphous fine particles were characterized by X-ray diffraction, DTA and TGA, and in situ magnetic measurement as a function of annealing temperature in an inert atmosphere. Magnetic measurement performed in as-prepared and 150°C annealed samples shows an increase of the saturation magnetization and magnetic moment after thermal treatment. Room temperature magnetization increases by factors of 3.5, 1.8, and 1.5, for x=0.5, 0.75, and 1, respectively. These measurements may indicate a local re-ordering of the amorphous phase at temperatures much lower than the full crystallization temperature.     

Note on spin–orbit interactions in nuclei and hypernuclei

A detailed comparison is made between the spin–orbit interactions in Λ hypernuclei and ordinary nuclei. We argue that there are three major contributions to the spin–orbit interaction: (1) a short-range component involving scalar and vector mean fields; (2) a “wrong-sign” spin–orbit term generated by the pion exchange tensor force in second order; and (3) a three-body term induced by two-pion exchange with excitation of virtual Δ(1232)-isobars (à la Fujita–Miyazawa). For nucleons in nuclei the long-range pieces related to the pion-exchange dynamics tend to cancel, leaving room dominantly for spin–orbit mechanisms of short-range origin (parametrized, e.g., in terms of relativistic scalar and vector mean fields terms). In contrast, the absence of an analogous 2π-exchange three-body contribution for Λ hyperons in hypernuclei leads to an almost complete cancellation between the short-range (relativistic mean-field) component and the “wrong-sign” spin–orbit interaction generated by second order π-exchange with an intermediate Σ hyperon. These different balancing mechanisms between short- and long-range components are able to explain simultaneously the very strong spin–orbit interaction in ordinary nuclei and the remarkably weak spin–orbit splitting in Λ hypernuclei.     

Anti-self-dual Yang–Mills equations on noncommutative space–time

By replacing the ordinary product with the so-called -product, one can construct an analog of the anti-self-dual Yang–Mills (ASDYM) equations on the noncommutative . Many properties of the ordinary ASDYM equations turn out to be inherited by the -product ASDYM equation. In particular, the twistorial interpretation of the ordinary ASDYM equations can be extended to the noncommutative , from which one can also derive the fundamental structures for integrability such as a zero-curvature representation, an associated linear system, the Riemann–Hilbert problem, etc. These properties are further preserved under dimensional reduction to the principal chiral field model and Hitchin’s Higgs pair equations. However, some structures relying on finite dimensional linear algebra break down in the -product analogs.     

A note on Chern–Simons solitons—A type III vortex from the wall vortex

We study some properties of topological Chern–Simons vortices in 2+1 dimensions. As has already been understood in the past, in the large magnetic flux limit, they are well described by a Chern–Simons domain wall, which has been compactified on a circle with the symmetric phase inside and the asymmetric phase on the outside.Our goal is two-fold. First we want to explore how the tension depends on the magnetic flux discretized by the integer n. The BPS case is already known, but not much has been explored about the non-BPS potentials. A generic renormalizable potential has two dimensionless parameters that can be varied. Variation of only one of them leads to a type I and type II vortex, very similar to the Abrikosov–Nielsen–Olesen (ANO) case. Variation of both the parameters leads to a much richer structure. In particular we have found a new type of vortex, which is type I-like for small flux and then turns type II-like for larger flux. We could tentatively denote it a type III vortex. This results in a stable vortex with number of fluxes which can be greater than one.Our second objective is to study the Maxwell–Chern–Simons theory and understand how the large n limit of the CS vortex is smoothly connected with the large n limit of the ANO vortex.     

A new configuration of the Moxon–Rae detector based on Si detector

A new Moxon–Rae detector configuration based on Si semiconductor detector was proposed in this paper. Three γ-ray sources, ¹³⁷Cs, ⁶⁰Co, and ²⁴Na, were employed to make actual measurements using the new Moxon–Rae detector. The measured pulse height spectra and detection efficiencies were compared with the EGS4 simulated values. The results revealed that the proposed new configuration is indeed a successful method and specially a useful technique for higher energy γ-ray measurement.     

Spacelike hypersurfaces with constant higher order mean curvature in Minkowski space–time

In this paper, we develop a series of general integral formulae for compact spacelike hypersurfaces with hyperplanar boundary in the (n+1)-dimensional Minkowski space–time . As an application of them, we prove that the only compact spacelike hypersurfaces in having constant higher order mean curvature and spherical boundary are the hyperplanar balls (with zero higher order mean curvature) and the hyperbolic caps (with nonzero constant higher order mean curvature). This extends previous results obtained by the first author, jointly with Pastor, for the case of constant mean curvature [J. Geom. Phys. 28 (1998) 85] and the case of constant scalar curvature [Ann. Global Anal. Geom. 18 (2000) 75].     

A hodograph transformation which applies to the Boyer–Finley equation

A hodograph transformation for a wide family of multidimensional nonlinear partial differential equations is presented. It is used to derive solutions of the Boyer–Finley equation (dispersionless Toda equation), which are not group invariant, and the corresponding family of explicit ultra-hyperbolic selfdual vacuum spaces.     

A note on Δn ≠ 0 Stark transitions in hydrogenlike atoms

In a gaseous helium or hydrogen target slow muons or antiprotons are captured into orbits with a high principal quantum number (n = 15 to 50) to form (μ^? α)⁺ ions, (p α)⁺ ions, or (p p) atoms respectively. In the subsequent deexcitation process Stark mixing of the intermediary states plays an important role. The successful Mainz Cascade Model assumed Δn = 0 for the Stark transitions, although formally no such selection rule exists. This note examines the reasons why Δn ≠ 0 Stark transitions play only a negligible role in the deexcitation cascade.     

Characterization of metal/GaN Schottky interfaces based on I–V–T characteristics

Interface properties of metal/n- and p-GaN Schottky diodes are studied by I–V–T and C–V–T measurements, and simulation of their characteristics. On the basis of the previously proposed “surface patch” model, the gross behavior of I–V–T characteristics, which includes Richardson plots together with temperature dependence of the effective Schottky barrier heights (SBHs) and n-values, can be well reproduced. Furthermore, the dependence of the true SBH on the metal work function was also deduced from high-temperature I–V curves, giving S-values of 0.28 and 0.20 for n- and p-GaN samples, respectively, and the interface Fermi level tends to be pinned at a characteristic energy of about two-third of the bandgap.     

A direct measurement of g-factors in II–VI and III–V core–shell nanocrystals

This study describes a direct measurement of spectroscopic g-factors of photo-generated carriers in InP/ZnS and HgTe/Hg_xCd_1−xTe(S) core–shell nanocrystals. The g-factor of trapped electrons and their spin-lattice versus radiative relaxation ratio (T₁/τ) were measured by the use of continuous-wave and time-resolved optically detected magnetic resonance (ODMR) spectroscopy. The g-factors of excitons and donor–hole pairs were derived by the use of field-induced circular-polarized photoluminescence (CP-PL) spectroscopy. The combined information enabled to determine the g-factors of the individual band-edge electrons and holes. The results suggested an increase of the g-factor of the exciton and conduction electron with a decrease of the nanocrystal size.