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C W Oosterlee - One of the best experts on this subject based on the ideXlab platform.

  • Fast valuation and calibration of credit default swaps under Lévy dynamics
    Journal of Computational Finance, 2020
    Co-Authors: Fang Fang, C W Oosterlee, Henrik Jönsson, Wim Schoutens
    Abstract:

    In this paper we address the issue of finding an efficient and flexible numerical approach for calculating survival/default probabilities and pricing Credit Default Swaps under advanced jump dynamics. We have chosen to use the firm’s value approach, modeling the firm’s value by an exponential Levy model. For this approach the default event is defined as a first passage of a barrier and it is therefore possible to exploit a numerical technique developed to price barrier options under Levy models to calculate the default probabilities. The method presented is based on the Fourier-Cosine Series expansion of the underlying model’s density function.

  • A Fourier-Based Valuation Method for Bermudan and Barrier Options under Heston's Model
    Siam Journal on Financial Mathematics, 2020
    Co-Authors: Fang Fang, C W Oosterlee
    Abstract:

    We develop an efficient Fourier-based numerical method for pricing Bermudan and discretely monitored barrier options under the Heston stochastic volatility model. The two-dimensional pricing problem is dealt with by a combination of a Fourier Cosine Series expansion, as in [F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826-848, F. Fang and C. W. Oosterlee, Numer. Math., 114 (2009), pp. 27-62], and high-order quadrature rules in the other dimension. Error analysis and experiments confirm a fast error convergence.

  • A Fourier Cosine Method for an Efficient Computation of Solutions to BSDEs
    SIAM Journal on Scientific Computing, 2015
    Co-Authors: Marjon Ruijter, C W Oosterlee
    Abstract:

    We develop a Fourier method to solve backward stochastic differential equations (BSDEs). A general theta-discretization of the time-integrands leads to an induction scheme with conditional expectations. These are approximated by using Fourier Cosine Series expansions, relying on the availability of a characteristic function. The method is applied to BSDEs with jumps. Numerical experiments demonstrate the applicability of BSDEs in financial and economic problems and show fast convergence of our efficient probabilistic numerical method.

  • on the Fourier Cosine Series expansion method for stochastic control problems
    Numerical Linear Algebra With Applications, 2013
    Co-Authors: Marjon Ruijter, C W Oosterlee, R F T Aalbers
    Abstract:

    SUMMARY We develop a method for solving stochastic control problems under one-dimensional Levy processes. The method is based on the dynamic programming principle and a Fourier Cosine expansion method. Local errors in the vicinity of the domain boundaries may disrupt the algorithm. For efficient computation of matrix–vector products with Hankel and Toeplitz structures, we use a fast Fourier transform algorithm. An extensive error analysis provides new insights based on which we develop an extrapolation method to deal with the propagation of local errors. Copyright © 2013 John Wiley & Sons, Ltd.

  • two dimensional Fourier Cosine Series expansion method for pricing financial options
    SIAM Journal on Scientific Computing, 2012
    Co-Authors: Marjon Ruijter, C W Oosterlee
    Abstract:

    The COS method for pricing European and Bermudan options with one underlying asset was developed in [F. Fang and C. W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826--848] and [F. Fang and C. W. Oosterlee, Numer. Math., 114 (2009), pp. 27--62]. In this paper, we extend the method to higher dimensions, with a multidimensional asset price process. The algorithm can be applied to, for example, pricing two-color rainbow options but also to pricing under the popular Heston stochastic volatility model. For smooth density functions, the resulting method converges exponentially in the number of terms in the Fourier Cosine Series summations; otherwise we achieve algebraic convergence. The use of an FFT algorithm, for asset prices modeled by Levy processes, makes the algorithm highly efficient. We perform extensive numerical experiments.

F Fang - One of the best experts on this subject based on the ideXlab platform.

  • pricing options under stochastic volatility with Fourier Cosine Series expansions
    2010
    Co-Authors: F Fang, C. W. Oosterlee
    Abstract:

    An option pricing method for European options based on the FourierCosine Series, called the COS method, is presented. It can cover underlying asset processes for which the characteristic function is known, and in this paper, in particular, we consider stochastic volatility dynamics.

  • pricing early exercise and discrete barrier options by Fourier Cosine Series expansions
    Numerische Mathematik, 2009
    Co-Authors: F Fang, C W Oosterlee
    Abstract:

    We present a pricing method based on Fourier-Cosine expansions for early-exercise and discretely-monitored barrier options. The method works well for exponential Levy asset price models. The error convergence is exponential for processes characterized by very smooth ($${{\rm{C}}^{\infty}[a,b]\in\mathbb {R}}$$) transitional probability density functions. The computational complexity is O((M − 1)N log N) with N a (small) number of terms from the Series expansion, and M, the number of early-exercise/monitoring dates. This paper is the follow-up of (Fang and Oosterlee in SIAM J Sci Comput 31(2):826–848, 2008) in which we presented the impressive performance of the Fourier-Cosine Series method for European options.

  • Pricing early-exercise and discrete barrier options by Fourier-Cosine Series expansions
    Numerische Mathematik, 2009
    Co-Authors: F Fang, C. W. Oosterlee
    Abstract:

    We present a pricing method based on Fourier-Cosine expansions for early-exercise and discretely-monitored barrier options. The method works well for exponential Lévy asset price models. The error convergence is exponential for processes characterized by very smooth ( $${{\rm{C}}^{\infty}[a,b]\in\mathbb {R}}$$ ) transitional probability density functions. The computational complexity is O (( M − 1) N log N ) with N a (small) number of terms from the Series expansion, and M , the number of early-exercise/monitoring dates. This paper is the follow-up of (Fang and Oosterlee in SIAM J Sci Comput 31(2):826–848, 2008) in which we presented the impressive performance of the Fourier-Cosine Series method for European options.

  • a novel pricing method for european options based on Fourier Cosine Series expansions
    SIAM Journal on Scientific Computing, 2008
    Co-Authors: F Fang, C W Oosterlee
    Abstract:

    Here we develop an option pricing method for European options based on the Fourier-Cosine Series and call it the COS method. The key insight is in the close relation of the characteristic function with the Series coefficients of the Fourier-Cosine expansion of the density function. In most cases, the convergence rate of the COS method is exponential and the computational complexity is linear. Its range of application covers underlying asset processes for which the characteristic function is known and various types of option contracts. We will present the method and its applications in two separate parts. The first one is this paper, where we deal with European options in particular. In a follow-up paper we will present its application to options with early-exercise features.

  • on an option pricing method based on Fourier Cosine Series expansions
    Reports of the Department of Applied Mathematical Analysis, 2008
    Co-Authors: F Fang, C W Oosterlee
    Abstract:

    Here we develop an option pricing method for European options based on the Fourier-Cosine Series, and call it the COS method. The convergence rate of the COS method is exponential and the computational complexity is linear. It has a wide range of applicability for different underlying dynamics, including Levy processes and Heston’s stochastic volatility model, and for various types of option contracts. We will present the method and its applications in two separate parts. The first one is this paper, where we deal in particular with European options. In a follow-up paper, part II, we will present its application to options with early-exercise features.

D.h. Werner - One of the best experts on this subject based on the ideXlab platform.

  • An exact integration procedure for vector potentials of thin circular loop antennas
    IEEE Transactions on Antennas and Propagation, 1996
    Co-Authors: D.h. Werner
    Abstract:

    A direct integration procedure for far-zone vector potentials of thin circular loop antennas has been known for many years. This method is general in the sense that it leads to simple integrals which have closed form solutions for most commonly assumed loop current distributions. However, a comparable integration technique has not been available for evaluating the more complicated near-zone vector potentials. This paper introduces a systematic approach for the exact integration of general near-zone vector potentials associated with current-carrying circular loop antennas. A particular example is considered where this new integration technique is used to find exact solutions to the vector potential and electromagnetic field integrals for loops with a Fourier Cosine-Series expansion of the current. The observation is made that degenerate forms of these exact representations lead to simplified expressions for the important special cases of a uniform and cosinusoidal current loop. Two equivalent forms of exact Series expansions are derived for the uniform current vector potential and field integrals. It is shown that the familiar small-loop approximations, as well as the classical far-field expressions, may be obtained as limiting cases of the more general exact Series representations for the uniform current loop obtained in this paper. Convenient asymptotic far-field expansions are derived for the loop with a cosinusoidal current distribution. Finally, the far-field analysis for the cosinusoidal loop is generalized to loops having an arbitrary current represented by a Fourier Cosine Series.

Le-wei Li - One of the best experts on this subject based on the ideXlab platform.

  • Fast full-wave analysis of a cylindrical antenna using a single integral with an exact kernel
    IEEE Antennas and Wireless Propagation Letters, 2002
    Co-Authors: Le-wei Li, Er-ping Li
    Abstract:

    This paper presents a fast approach in the method-of-moments (MoM) analysis so as to obtain the nonuniform current distributions of cylindrical antennas with electrically large radii. An oblique incident field in its general form and a delta-gap source are considered in the formulation of nonuniform current distributions. In the Galerkin's MoM procedure, the Fourier Cosine Series is considered as the entire domain basis function Series. In this formulation, the kernel is represented by a Series of weighted spherical Hankel functions of the second kind and the convergence of this Series is fast. As the result, the computation time is short. The Mathematica package is used to obtain and plot the current distributions along the cylindrical antennas.

  • Fast full wave analysis of a cylindrical antenna using a single integral with an exact kernel
    2002 3rd International Conference on Microwave and Millimeter Wave Technology 2002. Proceedings. ICMMT 2002., 2002
    Co-Authors: Le-wei Li, Er-ping Li
    Abstract:

    This paper presents a fast approach in the method of moments (MoM) analysis so as to obtain the non-uniform current distributions of cylindrical antennas with electrically large radii. An oblique incident field in its general form and a delta-gap source are considered in the formulation of non-uniform current distributions. In the Galerkin's MoM procedure, the Fourier Cosine Series is considered as the entire domain basis function Series. In this formulation, the kernel is represented by a Series of weighted spherical Hankel functions of the second kind and the convergence of this Series is fast. As a result, the computation time is short. The Mathematica package is used to obtain and plot the current distributions along the cylindrical antennas.

  • Method of moments analysis of electrically large circular-loop antennas: non-uniform currents
    IEEE Antennas and Propagation Society International Symposium. 1999 Digest. Held in conjunction with: USNC URSI National Radio Science Meeting (Cat. N, 1999
    Co-Authors: Le-wei Li, Mook-seng Leong
    Abstract:

    In this paper, a method of moments analysis is carried out so as to obtain in closed form the non-uniform current distributions, and their resulted radiation patterns in both the near and far zones, of circular loop antennas with electrically larger circumferences. An oblique incident field in its general form is considered in the formulation of the non-uniform current distributions. In the Galerkin's method of moment analysis, the Fourier Cosine Series is considered as the full-domain basis function Series. As a result, the current distributions along the circular loops are expressed analytically in terms of the azimuth angle for various diameters of large loops. Finally, the radiated electromagnetic (EM) fields and their power pattern in both the near and far zones are determined by applying the dyadic Green's function (DGF) in spherical coordinates and plotted with the Mathematica package, respectively.

  • Method-of-moments analysis of electrically large circular-loop antennas: nonuniform currents
    IEE Proceedings - Microwaves Antennas and Propagation, 1999
    Co-Authors: Le-wei Li, Mook-seng Leong
    Abstract:

    A method-of-moments analysis is carried out so as to obtain, in closed form, the nonuniform current distributions, and their resulted radiation patterns in both near and far zones, of circular loop antennas with electrically larger circumferences. An oblique incident field in its general form is considered in the formulation of the nonuniform current distributions. In Galerkin's method-of-moments analysis, the Fourier Cosine Series is considered as the full-domain basis-function Series. As a result, the current distributions along the circular loops are expressed analytically in terms of the azimuth angle for various diameters of large loops. Finally, the radiated electromagnetic (EM) fields and their power pattern in both near and far zones are determined by applying the dyadic Green's function (DGF) in spherical co-ordinates and plotted using a commercial software package respectively.

Mook-seng Leong - One of the best experts on this subject based on the ideXlab platform.

  • Method of moments analysis of electrically large circular-loop antennas: non-uniform currents
    IEEE Antennas and Propagation Society International Symposium. 1999 Digest. Held in conjunction with: USNC URSI National Radio Science Meeting (Cat. N, 1999
    Co-Authors: Le-wei Li, Mook-seng Leong
    Abstract:

    In this paper, a method of moments analysis is carried out so as to obtain in closed form the non-uniform current distributions, and their resulted radiation patterns in both the near and far zones, of circular loop antennas with electrically larger circumferences. An oblique incident field in its general form is considered in the formulation of the non-uniform current distributions. In the Galerkin's method of moment analysis, the Fourier Cosine Series is considered as the full-domain basis function Series. As a result, the current distributions along the circular loops are expressed analytically in terms of the azimuth angle for various diameters of large loops. Finally, the radiated electromagnetic (EM) fields and their power pattern in both the near and far zones are determined by applying the dyadic Green's function (DGF) in spherical coordinates and plotted with the Mathematica package, respectively.

  • Method-of-moments analysis of electrically large circular-loop antennas: nonuniform currents
    IEE Proceedings - Microwaves Antennas and Propagation, 1999
    Co-Authors: Le-wei Li, Mook-seng Leong
    Abstract:

    A method-of-moments analysis is carried out so as to obtain, in closed form, the nonuniform current distributions, and their resulted radiation patterns in both near and far zones, of circular loop antennas with electrically larger circumferences. An oblique incident field in its general form is considered in the formulation of the nonuniform current distributions. In Galerkin's method-of-moments analysis, the Fourier Cosine Series is considered as the full-domain basis-function Series. As a result, the current distributions along the circular loops are expressed analytically in terms of the azimuth angle for various diameters of large loops. Finally, the radiated electromagnetic (EM) fields and their power pattern in both near and far zones are determined by applying the dyadic Green's function (DGF) in spherical co-ordinates and plotted using a commercial software package respectively.