An Evaluation of Multi-Factor CIR Models Using LIBOR, Swap Rates, and Cap and Swaption Prices

We evaluate the classical Cox, Ingersoll and Ross (1985) (CIR) model using data on LIBOR, swap rates and caps and swaptions. With three factors the CIR model is able to fit the term structure of LIBOR and swap rates rather well. The model is able to match the hump shaped unconditional term structure of volatility in the LIBOR-swap market. However, statistical tests indicate that the model is misspecified. In particular the pricing errors are related to the slope of the swap yield curve. The economic importance of these shortcomings is highlighted when the model is confronted with data on cap and swaption prices. Pricing errors are large relative to the bid-ask spread in these markets. The model tends to overvalue shorter maturity caps and undervalue longer maturity caps. With only one or two factors, the model also tends to undervalue swaptions. Our findings point out the need for evaluating term structure models using data on derivative prices.

Generation of X-rays by electrons recycling through thin internal targets of cyclic accelerators

The use of thin (< 10{−3} radiation length) internal targets in cyclic accelerators leads to multiple passes (recycling effect) of electrons through them. The multiplicity of electron passes (M) is determined by the electron energy, accelerator parameters, the thickness, structure and material of a target and leads to an increase in the effective target thickness and the efficiency of radiation generation. The increase of M leads to the increase in the emittance of electron beams which can change the characteristics of radiation processes. The experimental results obtained using the Tomsk synchrotron and betatron showed the possibility of increasing the yield and brightness of coherent X-rays generated by the electrons passing (recycling) through thin crystals and periodic multilayers placed into the chambers of accelerators, when the recycling effect did not influence on the spectral and angular characteristics of generated X-rays

Radiation of the magneto-crystalline undulator

The radiation at grazing incidence of relativistic positively charged particles on the crystal surface in the presence of magnetic field is studied theoretically. The magnetic field is supposed to be parallel to the surface. Dependent on the initial conditions the particle can be captured in the channeling mode and perform periodic oscillations along the surface of the crystal. The spectrum, angular distribution and polarization of radiation are calculated. The emission spectrum of a single particle is discrete and it extends up to very large numbers of harmonics. If the magnetic field is much weaker than the electric field of atoms, the frequency range of radiation of the particle beam does not depend on magnetic field and is defined solely by the energy of the particles and by the surface averaged potential, though the frequency of the first harmonic is defined only by the magnetic field. In case of channeled positrons the characteristic energy of the emitted photons is of order 10?3/2 (eV), where ? is the particle relativistic factor. The main part of radiation is bound to a narrow cone and is polarized largely orthogonal to the surface of the crystal

X-ray Cherenkov radiation under conditions of grazing incidence of relativistic electrons onto a target surface

X-ray Cherenkov radiation in the vicinity of the photoabsorption edge of a target is considered in this workyesBelgorod State Universit