arXiv subjects
Publications and source records attributed to V. M. Belyaev.
Here we demonstrate how we can use Small Volatility Approximation in calibration of Multi-Factor HJM model with deterministic correlations, factor volatilities and mean reversals. It is noticed that quality of this calibration is very good and it does not depend on number of factors.
Local Volatility (LV) is a powerful tool for market modeling, enabling the generation of arbitrage-free scenarios calibrated to all European options. To implement LV, we need to interpolate and extrapolate option prices. This approach is significantly faster and more accurate than any parameterized model. The implementation is demonstrated specifically for interest rate swaptions and caplets. A key component of this method is the Small Volatility Approximation within the HJM interest rate model, which is used to calculate sensitivity of forward bond volatility. These calculations are deterministic and fast, with excellent calibration accuracy. A detailed description of the calibration procedure is provided.
Closed form formulas for swaption prices in HJM model are derived. These formulas are used for nonparametric fit of deterministic forward volatility. It is demonstrated that this formula and non-parametric fit works very well and can be used to identify arbitrage opportunities
Variable annuities (VA) are popular insurance products. VAs provides the insured with a guaranteed accumulation rate on their premium at maturity. In addition, the insured may receive extra benefit if returns of underlying funds are high enough. Here we consider a special case of VA with high-water mark feature and Guaranteed Minimum payment reset. In Black-Scholes model for underlying fund we derive explicit pricing formula for this type of contract. The value of VA contracts depends on the time between observation dates. Corrections due to this effect are calculated and compared with Monte-Carlo results. Good agreement between analytical formula and numerical calculations of VA values is demonstrated.
Cumulant expansion is used to derive accurate closed-form approximation for Monthly Sum Options in case of constant volatility model. Payoff of Monthly Sum Option is based on sum of $N$ caped (and probably floored) returns. It is noticed, that $1/\sqrt{N}$ can be used as a small parameter in Edgeworth expansion. First two leading terms of this expansion are calculated here. It is shown that the suggest closed-form approximation is in a good agreement with numerical results for typical mode parameters.
The role of Z_N symmetry in gauge theories at finite temperatures is discussed. This symmetry is studied in terms of A_0-effective potential. We consider two- and four-dimensional models where the question on physical interpretation of minima of $A_0$-effective potential can be considered exactly. It is shown that the correct result for the partition function can be obtained by summation of contributions near all minima of the $A_0$-effective potential.
We discuss a relation between the light-front quark model and QCD. We argue that this model can be used for an evaluation of the light-cone wave functions for moderate values of "u", but that it is inapplicable for this purpose in the region near the ends points u=0,1. We find additional support for a recent analysis in which it was claimed that the twist-two pion wave function attains its asymptotic form. The asymptotic twist-four two-particle wave function is also in good agreement with the light-front quark model.
We present an analysis of the existing constraints for the twist-2 light-cone pion wave function. We find that existing information on the pion wave function does not exclude the possibility that the pion wave function attains its asymptotic form. New bounds on the parameters of the pion wave function are presented.
A method for calculating the pion structure function directly in terms of light-cone wave functions is suggested. Taking twist-2 and twist-4 pion light-cone wave functions into account, it is shown that the QCD sum rule prediction is in agreement with quark distribution obtained from analysis of the Drell-Yan process. Twist-4 quark-gluon light-cone wave functions give a large positive contribution to the pion structure function for x_B<0.2. A new constraint on the twist-2 pion light-cone wave function is obtained. We argue that the leading twist pion wave function ϕ_π(u) \simeq 1 for u=0.3 with an accuracy of about 20-30%.
We consider the procedure of determination of induced quark condensates in the QCD sum rule approach. It is noted that the previous estimations of this value were very rough. It is shown, that the detailed analyses of this parameter of QCD vacuum leads to the conclusion that the value of the tensor susceptibility has opposite sign and much larger than estimations which were obtained before. The reason of this contradiction is discussed. It is noted that naive ways of determination of induced condensates may lead to wrong results. The case of tensor susceptibility is the example demonstrating the importance of the procedure which is applied for calculation of such condensates. New results for the nucleon tensor charge are presented. The tensor charge is related to the first momentof the transversity distribution function $h_1(x)$.
In the framework of light-cone QCD sum rules, we study the valence quark distribution function $q(x_B)$ of a pion for moderate $x_B$. The sum rule with the leading twist-2 wave function gives $q(x_B)=φ_π(x_B)$. Twist-4 wave functions give about 30\% for $x_B\sim 0.5$. It is shown that QCD sum rule predictions, with the asymptotic pion wave function, are in good agreement with experimental data. We found that a two-hump profile for the twist-2 wave function leads to a valence quark disribution function that contradicts experimental data.
The purely nonperturbative soft contribution to the $γ^* p \to Δ^+$ transition form factors is estimated using the local quark-hadron duality approach. Our results show that the soft contribution is dominated by the magnetic transition: the ratio $G_E^*(Q^2)/G_M^*(Q^2)$ is small for all accessible $Q^2$, in contrast to pQCD expectations that $G_E^*(Q^2) \to -G_M^*(Q^2)$. We also found that the soft contribution to the magnetic form factor is large enough to explain the magnitude of existing experimental data.
We use local quark-hadron duality to estimate the purely nonperturbative soft contribution to the $γ^* p \to Δ$ form factors. Our results are in agreement with existing experimental data. We predict that the ratio $G_E^*(Q^2)/G_M^*(Q^2)$ is small for all accessible $Q^2$, in contrast to the pQCD expectations that $G_E^*(Q^2) \to -G_M^*(Q^2)$.
We use local quark-hadron duality to estimate the purely nonperturbative soft contribution to the $γ^*p\to Δ$ form factors. Our results are in agreement with existing experimental data. We predict that the ratio $G_E^*(Q^2)/G_M^*(Q^2)$ is small for all accessible $Q^2$, in contrast to the pQCD expectations that $G_E^*(Q^2)\to -G_M^*(Q^2)$.
We consider a nonlocal lattice action for fermions fermion doubling in lattice theories. It is shown, that it is possible to avoid the fermionic doubling in the case of free fermions, but this approach does not reproduce results for the effective action for gauge fields in the continuum theory, because the high frequency fermion modes have a strong dependence on the gauge field.
We calculate the $D^*Dπ$ and $B^*Bπ$ couplings using QCD sum rules on the light-cone. In this approach, the large-distance dynamics is incorporated in a set of pion wave functions. We take into account two-particle and three-particle wave functions of twist 2, 3 and 4. The resulting values of the coupling constants are $g_{D^*Dπ}= 12.5\pm 1$ and $g_{B^*Bπ}= 29\pm 3 $. From this we predict the partial width $ Γ(D^{*+} \ra D^0 π^+ )=32 \pm 5~ keV $. We also discuss the soft-pion limit of the sum rules which is equivalent to the external axial field approach employed in earlier calculations. Furthermore, using $g_{B^*Bπ}$ and $g_{D^*Dπ}$ the pole dominance model for the $ B \ra π$ and $D\ra π$ semileptonic form factors is compared with the direct calculation of these form factors in the same framework of light-cone sum rules.
Electromagnetic form factors of the transition $π+γ_{virt.}\ra A_1$ are calculated by QCD sum rules technique with the description of the pion in terms of the set of wave functions of increasing twist. Obtained results are compared with standard QCD sum rule calculations.
We investigate path integral formalism for continuum theory. It is shown that the path integral for the soft modes can be represented in the form of a lattice theory. Kinetic term of this lattice theory has a standard form and potential term has additional nonlocal terms which contributions should tend to zero in the limit of continuum theory. Contributions of these terms can be estimated. It is noted that this representation of path integral may be useful to improve lattice calculations taking into account hard modes contribution by standard perturbative expansion. We discuss translation invariance of correlators and the possibility to construct a lattice theory which keeps rotary invariance also.