Zero-Coupon Bond

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Robert A. Jarrow - One of the best experts on this subject based on the ideXlab platform.

  • Liquidity risk and the term structure of interest rates
    Mathematics and Financial Economics, 2015
    Co-Authors: Robert A. Jarrow, Alexandre F. Roch
    Abstract:

    This paper develops an arbitrage-free pricing theory for a term structure of fixed income securities that incorporates liquidity risk. In our model, there is a quantity impact on the term structure of Zero-Coupon Bond prices from the trading of any single Zero-Coupon Bond. We derive a set of conditions under which the term structure evolution is arbitrage-free. These no arbitrage conditions constrain both the risk premia and the term structure’s volatility. In addition, we also provide conditions under which the market is complete, and we show that the replication cost of an interest rate derivative is the solution to a backward stochastic differential equation.

  • Information reduction via level crossings in a credit risk model
    Finance and Stochastics, 2007
    Co-Authors: Robert A. Jarrow, Philip Protter, A. Deniz Sezer
    Abstract:

    This paper provides an alternative credit risk model based on information reduction where the market only observes the firm’s asset value when it crosses certain levels, interpreted as changes significant enough for the firm’s management to make a public announcement. For a class of diffusion processes we are able to provide explicit expressions for the firm’s default intensity process and its Zero-Coupon Bond prices.

  • Risky coupon Bonds as a portfolio of Zero-Coupon Bonds
    Finance Research Letters, 2004
    Co-Authors: Robert A. Jarrow
    Abstract:

    This paper characterizes conditions under which a risky coupon Bond is equivalent to a portfolio of risky Zero-Coupon Bonds. This characterization is extended to enable the estimation of firm specific Zero-Coupon Bond prices from risky coupon Bond prices for the determination of firm specific credit risk curves.

  • pricing treasury inflation protected securities and related derivatives using an hjm model
    Journal of Financial and Quantitative Analysis, 2003
    Co-Authors: Robert A. Jarrow, Yildiray Yildirim
    Abstract:

    This paper uses an HJM model to price TIPS and related derivative securities. First, using the market prices of TIPS and ordinary U.S. Treasury securities, both the real and nominal Zero-Coupon Bond price curves are obtained using standard coupon Bond price stripping procedures. Next, a three-factor arbitrage-free term structure model is fit to the time-series evolutions of the CPI-U and the real and nominal Zero-Coupon Bond price curves. Then, using these estimated term structure parameters, the validity of the HJM model for pricing TIPS is confirmed via its hedging performance. Lastly, the usefulness of the pricing model is illustrated by valuing call options on the inflation index.

  • Finance - Chapter 8 Pricing interest rate options
    Handbooks in Operations Research and Management Science, 1995
    Co-Authors: Robert A. Jarrow
    Abstract:

    Publisher Summary This chapter reviews the various approaches to pricing interest rate options. The review has concentrated on a discrete time, discrete state space model and the continuous time analogues. The two problems are described in the chapter to which the interest rate option pricing theory is applied. The first problem is to value the entire zero coupon Bond price curve, given the prices of only a few Bonds (one, two or three) thatlie upon it. The second problem is to price contingent claims (options) on the zero coupon Bond price curve. The chapter presents the identification of a theoretical difference between the model structures used to solve these two different problems. The distinction relates to the manner in which the spot-rate process' parameters are specified within the model. Zero curve arbitrage models require an exogenous specification of the spot-rate process. In option pricing models, however, the spot rate process is endogenously determined by an exogenous specification of the evolution of the entire zero coupon Bond price curve. This distinction is important in the subsequent analysis.

Stefano Taddei - One of the best experts on this subject based on the ideXlab platform.

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

  • Liquidity risk and the term structure of interest rates
    Mathematics and Financial Economics, 2015
    Co-Authors: Robert A. Jarrow, Alexandre F. Roch
    Abstract:

    This paper develops an arbitrage-free pricing theory for a term structure of fixed income securities that incorporates liquidity risk. In our model, there is a quantity impact on the term structure of Zero-Coupon Bond prices from the trading of any single Zero-Coupon Bond. We derive a set of conditions under which the term structure evolution is arbitrage-free. These no arbitrage conditions constrain both the risk premia and the term structure’s volatility. In addition, we also provide conditions under which the market is complete, and we show that the replication cost of an interest rate derivative is the solution to a backward stochastic differential equation.

Marco Rosaclot - One of the best experts on this subject based on the ideXlab platform.

Radoslav L. Valkov - One of the best experts on this subject based on the ideXlab platform.

  • Analysis of a finite volume element method for a degenerate parabolic equation in the Zero-Coupon Bond pricing
    Computational and Applied Mathematics, 2014
    Co-Authors: Tatiana P. Chernogorova, Radoslav L. Valkov
    Abstract:

    We construct and analyze a stable exponentially fitted numerical scheme for a degenerate parabolic equation in the Zero-Coupon Bond pricing. Introducing weighted Sobolev spaces, we present the Garding coercivity and the weak maximum principle for the differential solution. The differential problem is discretized by a fitted finite volume element method resolving the degeneration. We derive coercivity of the discrete bilinear form as we also show that the fully discrete system matrix is essentially of positive type which implies the maximum principle for the implicit time stepping. Numerical experiments validate the theoretical results.

  • Finite Volume Difference Scheme for a Degenerate Parabolic Equation in the Zero-Coupon Bond Pricing
    arXiv: Numerical Analysis, 2013
    Co-Authors: Tatiana P. Chernogorova, Radoslav L. Valkov
    Abstract:

    In this paper we solve numerically a degenerate parabolic equation with dynamical boundary conditions of Zero-Coupon Bond pricing. First, we discuss some properties of the differential equation. Then, starting from the divergent form of the equation we implement the finite-volume method of S. Wang [16] to discretize the differential problem. We show that the system matrix of the discretization scheme is a M-matrix, so that the discretization is monotone. This provides the non-negativity of the price with respect to time if the initial distribution is nonnegative. Numerical experiments demonstrate the efficiency of our difference scheme near the ends of the interval where the degeneration occurs.

  • LSSC - Petrov-Galerkin analysis for a degenerate parabolic equation in Zero-Coupon Bond pricing
    Large-Scale Scientific Computing, 2012
    Co-Authors: Radoslav L. Valkov
    Abstract:

    A degenerate parabolic equation in the Zero-Coupon Bond pricing (ZCBP) is studied. First, we analyze the time discretization of the equation. Involving weighted Sobolev spaces, we develop a variational analysis to describe qualitative properties of the solution. On each time-level we formulate a Petrov-Galerkin FEM, in which each of the basis functions of the trial space is determined by the finite volume difference scheme in [2, 3]. Using this formulation, we establish the stability of the method with respect to a discrete energy norm and show that the error of the numerical solution in the energy norm is O(h), where h denotes the mesh parameter.

  • A Computational Scheme for a Problem in the Zero‐coupon Bond Pricing
    2010
    Co-Authors: Tatiana P. Chernogorova, Radoslav L. Valkov
    Abstract:

    In this paper we derive a finite volume difference scheme for a degenerate parabolic equation with dynamical boundary conditions of zero‐coupon Bond pricing. We show that the system matrix of the discretization scheme is an M‐matrix, so that the discretization is monotone. This provides the non‐negativity of the price whit respect to time if the initial distribution is nonnegative. Then one can prove convergence of the numerical solution with rate of convergence O(h), where h denotes the mesh parameter [2]. Several numerical experiments show higher accuracy with comparison of known difference schemes near the boundary (degeneration).