scholarly journals New Approximations to Bond Prices in the Cox–Ingersoll–Ross Convergence Model with Dynamic Correlation

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1469
Author(s):  
Beáta Stehlíková
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Interest Rates ◽  
Parabolic Partial Differential Equation ◽  
Approximation Formula ◽  
Bond Prices ◽  
Order Of Accuracy ◽  
Dynamic Correlation ◽  
Approximate Analytical Solutions ◽  
Convergence Model

We study a particular case of a convergence model of interest rates. The bond prices are given as solutions of a parabolic partial differential equation and we consider different possibilities of approximating them, using approximate analytical solutions. We consider an approximation already suggested in the literature and compare it with a newly suggested one for which we derive the order of accuracy. Since the two formulae use different approaches and the resulting leading terms of the error depend on different parameter sets of the model, we propose their combination, which has a higher order of accuracy. Finally, we propose one more approach, which leads to higher accuracy of the resulting approximation formula.

scholarly journals Numerical Approximation of a Linear Parabolic PDE

2013 ◽  
Vol 61 (1) ◽  
pp. 59-63
Author(s):  
Samir Kumar Bhowmik
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Approximation ◽  
Finite Difference Approximation ◽  
Stability And Convergence ◽  
Difference Approximation ◽  
Parabolic Partial Differential Equation ◽  
Periodic Domain ◽  
Order Of Accuracy ◽  
Parabolic Pde

We study stability and convergence analysis of a finite difference approximation of a linear parabolic partial differential equation (PDE) in a periodic domain. In particular, we analyze consistency, stability and order of accuracy of a central space forward time scheme to solve the PDE. Dhaka Univ. J. Sci. 61(1): 59-63, 2013 (January) DOI: http://dx.doi.org/10.3329/dujs.v61i1.15097

On the bond pricing partial differential equation in a convergence model of interest rates with stochastic correlation

2020 ◽  
Vol 70 (4) ◽  
pp. 995-1002
Author(s):  
Beáta Stehlíková
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Interest Rates ◽  
Monetary Union ◽  
Financial Mathematics ◽  
Partial Differential ◽  
Stochastic Correlation ◽  
Wiener Processes ◽  
Random Shocks ◽  
Convergence Model

AbstractConvergence models of interest rates are used to model a situation, where a country is going to enter a monetary union and its short rate is affected by the short rate in the monetary union. In addition, Wiener processes which model random shocks in the behaviour of the short rates can be correlated. In this paper we consider a stochastic correlation in a selected convergence model. A stochastic correlation has been already studied in different contexts in financial mathematics, therefore we distinguish differences which come from modelling interest rates by a convergence model. We provide meaningful properties which a correlation model should satisfy and afterwards we study the problem of solving the partial differential equation for the bond prices. We find its solution in a separable form, where the term coming from the stochastic correlation is given in its series expansion for a high value of the correlation.

scholarly journals Cauchy-Dirichlet problem for the nonlinear degenerate parabolic equations

2005 ◽  
Vol 2005 (6) ◽  
pp. 607-617 ◽  
Author(s):  
Ismail Kombe
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dirichlet Problem ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Parabolic Partial Differential Equation ◽  
Nonlinear Parabolic ◽  
Nonlinear Degenerate Parabolic Equations ◽  
Degenerate Parabolic ◽  
Nonlinear Degenerate

We will investigate the nonexistence of positive solutions for the following nonlinear parabolic partial differential equation:∂u/∂t=ℒu+V(w)up−1inΩ×(0,T),1<p<2,u(w,0)=u0(w)≥0inΩ,u(w,t)=0on∂Ω×(0,T)whereℒis the subellipticp-Laplacian andV∈Lloc1(Ω).

scholarly journals On radial stationary solutions to a model of non-equilibrium growth

2013 ◽  
Vol 24 (3) ◽  
pp. 437-453 ◽  
Author(s):  
CARLOS ESCUDERO ◽  
ROBERT HAKL ◽  
IRENEO PERAL ◽  
PEDRO J. TORRES
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Stationary Solutions ◽  
Parabolic Partial Differential Equation ◽  
Radial Solutions ◽  
Variational Techniques ◽  
Existence And Multiplicity ◽  
Equilibrium Growth ◽  
Non Equilibrium

We present the formal geometric derivation of a non-equilibrium growth model that takes the form of a parabolic partial differential equation. Subsequently, we study its stationary radial solutions by means of variational techniques. Our results depend on the size of a parameter that plays the role of the strength of forcing. For small forcing we prove the existence and multiplicity of solutions to the elliptic problem. We discuss our results in the context of non-equilibrium statistical mechanics.

scholarly journals Time- or Space-Dependent Coefficient Recovery in Parabolic Partial Differential Equation for Sensor Array in the Biological Computing

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Guanglu Zhou ◽  
Boying Wu ◽  
Wen Ji ◽  
Seungmin Rho
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Sensor Array ◽  
Variational Iteration Method ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Variational Iteration

This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to handle. By the variational iteration method, we obtain the exact solution and the unknown coefficients. The results of numerical experiments and stable experiments imply that the variational iteration method is very suitable to solve these inverse problems.

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