Efficient numerical methods for pricing American options under stochastic volatility

Five numerical methods for pricing American put options under Heston's stochastic volatility model are described and compared. The option prices are obtained as the solution of a two‐dimensional parabolic partial differential inequality. A finite difference discretization on nonuniform grids leading to linear complementarity problems with M‐matrices is proposed. The projected SOR, a projected multigrid method, an operator splitting method, a penalty method, and a componentwise splitting method are considered. The last one is a direct method while all other methods are iterative. The resulting systems of linear equations in the operator splitting method and in the penalty method are solved using a multigrid method. The projected multigrid method and the componentwise splitting method lead to a sequence of linear complementarity problems with one‐dimensional differential operators that are solved using the Brennan and Schwartz algorithm. The numerical experiments compare the accuracy and speed of the considered methods. The accuracies of all methods appear to be similar. Thus, the additional approximations made in the operator splitting method, in the penalty method, and in the componentwise splitting method do not increase the error essentially. The componentwise splitting method is the fastest one. All multigrid‐based methods have similar rapid grid independent convergence rates. They are about two or three times slower that the componentwise splitting method. On the coarsest grid the speed of the projected SOR is comparable with the multigrid methods while on finer grids it is several times slower. ©John Wiley & Sons, Inc. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Monochromatic,Cicularly Polarized Resonant Radiation in the Investigation of Magnetic Materials

Monochromatic, circularly polarized radiation brings useful information on orientations of hyperfine fields in investigation of magnetic materials. This information can be extracted even from poorly resolved spectra by a model free method. In particular, the z-component of the average hyperfine magnetic field is given simply by a “center of gravity” of the difference between the spectra measured with two opposite polarizations. The efficiency of such an approach is demonstrated on the example of the ⁵⁷Fe h.m.f. in bcc Cr–Fe–Mn alloys. This revised version was published online in September 2006 with corrections to the Cover Date.     

Quadrupole moments of highly deformed structures in the A approximately 135 region: probing the single-particle motion in a rotating potential

The latest generation gamma-ray detection system, GAMMASPHERE, coupled with the Microball charged-particle detector, has made possible a new class of nuclear lifetime measurement. For the first time differential lifetime measurements free from common systematic errors for over 15 different nuclei ( >30 rotational bands in various isotopes of Ce, Pr, Nd, Pm, and Sm) have been extracted at high spin within a single experiment. This comprehensive study establishes the effective single-particle transition quadrupole moments in the A approximately 135 light rare-earth region. Detailed comparisons are made with theoretical calculations using the self-consistent cranked mean-field theory which convincingly demonstrates the validity of the additivity of single-particle quadrupole moments in this mass region.     

Continuous-wave light source at 317 nm based on frequency doubling of a diode laser

Received: 16 October 1997     

Limits of applicability of the classical field concept in Mössbauer spectroscopy

We show that the classical model widely employed for the field radiated by an excited Mössbauer nucleus predicts an enhanced rate of coincidences for two detectors. This contradicts our experiment. We discuss the limits of applicability of the classical field concept for various experimental conditions.     

Low-loss photon-to-electron conversion

Silicon photodiodes with induced junction structure can reach low-loss photon-to-electron conversion. The calculated conversion efficiency in the visible wavelength range typically deviates less than 10 ppm from unity and its uncertainty is about 100 ppm at room temperature or as low as 1 ppm at 78 K. Here we show experimentally that our dedicated induced junction photodiodes indeed have very low conversion losses when they are assembled in a light trapping structure as provided by, for example, the predictable quantum efficient detector (PQED). It is concluded that the remaining measured losses, if any, are probably due to surface recombination of electrons and holes close to the silicon/silicon dioxide interface of the photodiode.     

Computer simulations of stretching and collapse of polymer molecules in solution

Computer simulations are reported for system of linear polymer molecules, diblock copolymer and dendrimer in dilute solution without and with elongational flow. The effect of fluctuating hydrodynamics interactions (HI) on the coil-stretch transition of linear polymers and dendrimers in elongational flow is studied. The process of coiling of homo- and blockcopolymer from completely extended state is also simulated.