empirical investigation of a field theory formula and black s formula for the price of an interest rate caplet abstract the industry standard for pricing an interest rate caplet is black s formula another distinct price of the same caplet can be derived using a quantum field theory model of the forward interest rates an empirical study is carried out to compare the two caplet pricing formulae historical volatility and correlation of forward interest rates are used to generate the field theory caplet price another approach is to fit a parametric formula for the effective volatility using market caplet price the study shows that the field theory model generates the price of a caplet and cap fairly accurately black s formula for a caplet is compared with field theory pricing formula it is seen that the field theory formula for caplet price has many advantages over black s formula

efficient calculation of the green s function for multilayered planar periodic structures an efficient calculation scheme is presented for the periodic green s function in planar multilayered structures the proposed method is based on the static complex image conversion and the ewald sum technique and it converts the slowly convergent green s function into the sum of two rapidly convergent series

a comparison of acceleration procedures for the two dimensional periodic green s function alternate acceleration procedures are evaluated for the two dimensional free space periodic green s function two of these techniques yield exponential convergence rates and are preferable if high accuracies are required numerical aspects of these procedures are described

efficient computation of the 2 d green s function for 1 d periodic structures using the ewald method the ewald method is applied to accelerate the evaluation of the green s function of an infinite periodic phased array of line sources the ewald representation for a cylindrical wave is obtained from the known representation for the spherical wave and a systematic general procedure is applied to extend previous results only a few terms are needed to evaluate ewald sums which are cast in terms of error functions and exponential integrals to high accuracy singularities and convergence rates are analyzed and a recipe for selecting the ewald splitting parameter spl epsiv is given to handle both low and high frequency ranges indeed it is shown analytically that the choice of the standard optimal splitting parameter spl epsiv sub 0 will cause overflow errors at high frequencies numerical examples illustrate the results and the sensitivity of the ewald representation to the splitting parameter spl epsiv

an efficient numerical evaluation of the green s function for the helmholtz operator on periodic structures abstract numerical methods which are based on boundary integral formulations require the numerical evaluation of the green s function associated with the problem in the case of periodic structures the green s function is often an infinite series this infinite series may converge slowly making numerical evaluation expensive here we present a practical computer implementation of a technique which dramatically speeds up the convergence of the infinite series green s function associated with the helmholtz operator to show the consequences of using this technique we include some numerical examples

computations of the complex error function rational expansions for computing the complex error function w z e z 2 text erfc iz are presented these expansions have the following attractive properties 1 they can be evaluated using a polynomial evaluation routine such as homer s method 2 the polynomial coefficients can be computed once and for all by a single fast fourier transform fft and 3 high accuracy is achieved uniformly in the complex plane with only a small number of terms comparisons reveal that in some parts of the complex plane certain competitors may be more efficient however the difference in efficiency is never great and the new algorithms are simpler than existing ones a complete program takes eight lines of matlab code

accelerating the convergence of series representing the free space periodic green s function a method for improving the convergence of the series representing the doubly periodic free space green s function is presented the method consists of successively applying three different transformations to the green s function spectral representation kummer s transformation is first applied to convert the slowly converging spectral representation into the sum of a rapidly converging series and a slowly converging series the latter series is recognized as the spectral representation of the original periodic source distribution radiating in a medium with an imaginary wavenumber application of the poisson transformation to this series renders it exponentially convergent since it effectively represents propagation of point source contributions through a medium with imaginary wavenumber finally shanks transform is plotted versus the number of terms taken in the series numerical results confirm that an improvement in the convergence rate of the series is achieved for a particular convergence criterion

a one sided version of the poisson sum formula for semi infinite array green s functions the poisson sum formula provides an efficient method for transforming many slowly converging infinite summations into equivalent but more rapidly converging infinite summations electromagnetic applications for this result come in the analysis of infinite arrays of periodic scatterers such as frequency selective surfaces however in some applications such as when one desires the radiation of a semi infinite array of periodically spaced currents the original form of the poisson sum formula is inappropriate for such applications we derive a one sided version of the formula and apply it to the radiation from a semi infinite array of line sources with currents dictated by floquet s theorem the one sided poisson sum transformation yields enhanced convergence characteristics for certain regions of application as a result of the inverse bandwidth relationship between fourier transform pairs the application of it to a semi infinite line source array also provides a plane wave representation for the fields which makes for an extension of the solution to geometries with stratified dielectric media

a novel approach for the efficient computation of 1 d and 2 d summations a novel computational method is proposed to evaluate 1 d and 2 d summations and integrals which are relatively difficult to compute numerically the method is based on applying a subspace algorithm to the samples of partial sums and approximating them in terms of complex exponentials for a convergent summation the residue of the exponential term with zero complex pole of this approximation corresponds to the result of the summation since the procedure requires the evaluation of relatively small number of terms the computation time for the evaluation of the summation is reduced significantly in addition by using the proposed method very accurate and convergent results are obtained for the summations which are not even absolutely convergent the efficiency and accuracy of the method are verified by evaluating some challenging 1 d and 2 d summations and integrals

rapidly convergent representations for periodic green s functions of a linear array in layered media green s function representations are presented to rapidly compute the fields resulting from a linear 1d periodic array of dipole current sources on or near a planarly layered medium in 2d and 3d space the representation is formulated as spectral integral which accounts for the reflected continuous spectrum of fields and a series that accounts for the discrete spectrum of guided modes it is exponentially convergent for observation points on and near the array axis and surface and for complex phase shifts between periodic unit cells it can be defined on alternate riemann sheets with respect to any of the diffraction modes characterizing the array a complete dyadic green s function is derived to fully account for the reflected fields for all source current orientations this green s function representation can greatly accelerate the simulation of printed 1d periodic structures in optics and microwave engineering

an integral representation of the green function for a linear array of acoustic point sources we present a new algorithm for the evaluation of the quasi periodic green function for a linear array of acoustic point sources such as those arising in the analysis of line array loudspeakers a variety of classical algorithms based on spatial and spectral representations ewald transformation etc have been implemented in the past to evaluate these acoustic fields however as we show these methods become unstable and or impractically expensive as the frequency of use of the sources increases here we introduce a new numerical scheme that overcomes some of these limitations allowing for simulations at unprecedentedly large frequencies the method is based on a new integral representation derived from the classic spatial form and on suitable further manipulations of the relevant integrands to render the integrals amenable to efficient and accurate approximations through standard quadrature formulas we include a variety of numerical results that demonstrate that our algorithm compares favorably with several classical methods both for points close to the line where the poles are located and at high frequencies while remaining competitive with them in every other instance

reply to comments on comparative analysis of acceleration techniques for 2 d and 3 d green s functions in periodic structures along one and two directions the authors wish to thank dr skobelev for his interesting remark about the acceleration technique for the three dimensional 3 d green s function of a two dimensional 2 d array first proposed by ivanishin it basically consists of a kummer s decomposition of higher order with respect to those presented the possibility of obtaining similar decompositions is mentioned where details are shown only about the lowest order extraction and it has also been recalled in our paper in connection with the first presented geometry 2 d green s function of a one dimensional array

the sensitivity analysis of propagator for path independent quantum finance model abstract quantum finance successfully implements the imperfectly correlated fluctuation of forward interest rates at different maturities by replacing the wiener process with a two dimensional quantum field interest rate derivatives can be priced at a more realistic value under this new framework the quantum finance model requires three main ingredients for pricing the initial forward interest rates the volatility of forward interest rates and the correlation of forward interest rates at different maturities however the hedging strategy only focused on fluctuation of forward interest rates this hedging method is based on the assumption that the propagator the covariance of forward interest rates has an ergodic property since inserting the propagator is the main characteristic that distinguishes quantum finance from the libor market model lmm and the heath jarrow and morton hjm model understanding the impact of propagator dynamics on the price of interest rate derivatives is crucial this research is the first step in developing a hedge strategy with respect to the evolution of the propagator we analyze the dynamics of the propagator from libor futures data and the integrated propagator from zero coupon bond rate data then we study the sensitivity of the implied volatility of caplets and swaptions according to the three dominant dynamics of the propagator and the change of the zero coupon bond option price according to the two dominant dynamics of the integrated propagator

efficient calculation of the free space periodic green s function electromagnetic scattering from periodic structures can be formulated in terms of an integral equation that has as its kernel a periodic green s function the periodic green s function can be derived as a response to an array of line point sources spatial domain or as a response to series of current sheets spectral domain these responses are a fourier transform pair and are slowly convergent summations the convergence problems in each domain arise from unavoidable singularities in the reciprocal domain a method is discussed to overcome the slow convergence by using the poisson summation formula and summing in a combination of spectral and spatial domains a parameter study is performed to determine an optimum way to weigh the combination of domains simple examples of scattering from a one dimensional array of strips and two dimensional array of plates are used to illustrate the concepts

a novel efficient technique for the calculation of the green s functions in rectangular waveguides based on accelerated series decomposition a new efficient technique for computing the green s functions inside rectangular waveguides is presented after a summary of the classical approaches and their difficulties a new strategy is proposed based on the decomposition of the main spectral series into simpler terms although the resulting series present better convergence rate several acceleration techniques are combined to further improve the efficiency several results are presented to demonstrate the improvements in convergence rates obtained using the new decomposition

quasi 3 d mixed potential integral equation formulation for periodic structures this paper introduces the use of the quasi 3 d mixed potential integral equation formulation for structures with a periodicity in two dimensions the quasi 3 d formulation allows to use both horizontal and vertical conductors and dielectric inclusions the key innovation is the use of an effective algorithm to calculate periodic green s functions pgfs for vertical currents in the planar multilayered background medium this algorithm retains the same scheme as for a single source green s function gf in both cases the gfs are calculated via an inverse fourier transform of the gfs in the spectral domain which are known in closed form in order to remedy the poor convergence for small source observation distances an asymptotic extraction is used yielding a very compact algorithm and acceleration techniques are applied simple guidelines are proposed to construct asymptotes having the required leading terms and a good convergence it is shown that many acceleration algorithms widely used in literature are actually able to perform well only in specific circumstances as far as the authors can see there is still no general and robust technique yielding highly accurate results under all circumstances several examples illustrate the efficiency of the technique

on the use of rho algorithm in series acceleration the rho algorithm a nonlinear transformation is shown to be applicable to monotonic series the results of applying the algorithm to a series involving the zeroth order hankel function of the second kind and its associated fourier transform are given it is shown that the algorithm performs better than the epsilon algorithm derived from shanks transform 1955 numerical results include a relative error measure versus number of terms taken in the series

fast and accurate mom analysis of periodic arrays of multilayered stacked rectangular patches with application to the design of reflectarray antennas the scattering of plane waves by periodic arrays of stacked rectangular patches in multilayered substrates is a problem that has to be solved many times when designing reflectarray antennas made of those patches under the local periodicity assumption the solution to the periodic multilayered problem has been traditionally carried out by means of the galerkin s version of the method of moments mom in the spectral domain this approach involves the computation of double infinite summations and whereas some of these summations converge very fast some other converge very slowly in this paper the slowly convergent summations are computed by making use of an enhanced mixed potential integral equation mpie formulation of the mom in the spatial domain this enhanced formulation is based on the interpolation of the multilayered periodic green s functions and on the efficient computation of the four dimensional 4 d integrals leading to the mom matrix entries both the novel hybrid spectral spatial mom code and the standard spectral domain mom code have been used for the design of a contoured beam reflectarray antenna it has been verified that the spectral spatial mom code requires cpu times that are typically 30 times smaller than those required by the pure spectral domain mom code

scattering and radiation from by 1 d periodic metallizations residing in layered media an efficient technique is proposed to compute the scattering or radiation from by 1 d periodic structures residing in a layered background medium the technique is based on a mixed potential integral equation mpie combined with the method of moments mom solving for the unknown current density flowing within a unit cell of the periodic structure the formalism requires the knowledge of the pertinent layered medium green s functions with 1 d periodicity here these green s functions are derived in closed form by invoking the perfectly matched layer pml paradigm the stationary phase method is applied to determine the far field of the infinite periodic structure leading to a series of floquet modes in addition approximating this series leads to an efficient technique to estimate the scattering or radiation from by large but finite periodic structures with a 1 d periodic character the theory is illustrated and validated by means of various examples stemming from scattering and radiation applications from by antenna arrays residing on microstrip substrates the efficiency of the method is also demonstrated

a new acceleration technique with exponential convergence rate to evaluate periodic green functions we propose a new approach to compute the dynamic potential green function from two and three dimensional periodic arrays of point sources in a three dimensional space the method has at least exponential convergence rate in some cases it has gaussian convergence rate the convergence rate is independent of the position of the observation point in the unit cell the proposed approach can also be used to calculate the derivatives of the green function very efficiently

comparative analysis of acceleration techniques for 2 d and 3 d green s functions in periodic structures along one and two directions the problem of accelerating the calculation of the periodic green s function is addressed here for both 3 d and 2 d free space configurations in the 3 d case periodicity is considered both along one axis and along two generally skew axes a comprehensive review of the existing methods is first presented and some extensions are developed the possibility of treating the case of complex phase shifts between unit cells necessary for the study of complex modes in periodic structures is also investigated comparisons among the various acceleration methods are performed thus providing fundamental information on their actual efficiency in typical problems

quantum field theory of forward rates with stochastic volatility in a recent formulation of a quantum field theory of forward rates the volatility of the forward rates was taken to be deterministic the field theory of the forward rates is generalized to the case of stochastic volatility two cases are analyzed first when volatility is taken to be a function of the forward rates and second when volatility is taken to be an independent quantum field since volatility is a positive valued quantum field the full theory turns out to be an interacting nonlinear quantum field theory in two dimensions the state space and hamiltonian for the interacting theory are obtained and shown to have a nontrivial structure due to the manifold moving with a constant velocity the no arbitrage condition is reformulated in terms of the hamiltonian of the system and then exactly solved for the nonlinear interacting case

efficient algorithms for adaptive capon and apes spectral estimation in this paper fast algorithms for adaptive capon and amplitude and phase estimation apes methods for spectral analysis of time varying signals are derived fast stable nonrecursive formulae are derived based on time shifting properties of the pertinent variables as a consequence efficient frequency domain recursive least squares rls based as well as fast rls based algorithms for the adaptive estimation of the power spectra are developed stability issues of the frequency domain estimators are considered and stabilization procedures are proposed the computational complexity of the proposed algorithms is lower than relevant existing methods the performance of the proposed algorithms is demonstrated through extensive simulations