Bayesian Estimating for cox Ingersoll Ross process

2021 ◽  
Vol 26 (5) ◽  
pp. 33-43
Author(s):  
Reyam abo-alhell ◽  
Muhannad F. Al Saadony
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Bayesian Estimation ◽  
Term Structure ◽  
The Other ◽  
Short Term ◽  
Interest Rate Models ◽  
Relative Complexity ◽  
Cir Process

the model of term structure of interest rates are consider the most significant and computationally difficult portion of the modern finance due to a relative complexity of using techniques. This article concerns the Bayesian estimation of interest rate models. Assume the short term interest rate follows the Cox Ingersoll Ross (CIR) process , this process has several feature. In particular mean reverting and the other feature is remanis non- negative , so this is what distinguishes it from previous models. It is implement in the R programing.  

scholarly journals CANDIDE et la monnaie

2009 ◽  
Vol 52 (1) ◽  
pp. 75-103
Author(s):  
Jean-Pierre Aubry ◽  
Pierre Duguay
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Term Structure ◽  
Structural Equations ◽  
Reduced Form ◽  
Real Sector ◽  
Short Term ◽  
The Real ◽  
Structure Equations

Abstract In this paper we deal with the financial sector of CANDIDE 1.1. We are concerned with the determination of the short-term interest rate, the term structure equations, and the channels through which monetary policy influences the real sector. The short-term rate is determined by a straightforward application of Keynesian liquidity preference theory. A serious problem arises from the directly estimated reduced form equation, which implies that the demand for high powered money, but not the demand for actual deposits, is a stable function of income and interest rates. The structural equations imply the opposite. In the term structure equations, allowance is made for the smaller variance of the long-term rates, but insufficient explanation is given for their sharper upward trend. This leads to an overstatement of the significance of the U.S. long-term rate that must perform the explanatory role. Moreover a strong structural hierarchy, by which the long Canada rate wags the industrial rate, is imposed without prior testing. In CANDIDE two channels of monetary influence are recognized: the costs of capital and the availability of credit. They affect the business fixed investment and housing sectors. The potential of the personal consumption sector is not recognized, the wealth and real balance effects are bypassed, the credit availability proxy is incorrect, the interest rate used in the real sector is nominal rather than real, and the specification of the housing sector is dubious.

scholarly journals The Rising Cost of Climate Change: Evidence from the Bond Market

2021 ◽  
pp. 1-45
Author(s):  
Michael D. Bauer ◽  
Glenn D. Rudebusch
Keyword(s):  
Climate Change ◽  
Interest Rate ◽  
Interest Rates ◽  
Term Structure ◽  
Mitigation Strategies ◽  
Social Cost Of Carbon ◽  
Carbon Mitigation ◽  
Interest Rate Models ◽  
Real Rate ◽  
The Social

Abstract Social discount rates (SDRs) are crucial for evaluating the costs of climate change. We show that the fundamental anchor for market-based SDRs is the equilibrium or steady-state real interest rate. Empirical interest rate models that allow for shifts in this equilibrium real rate find that it has declined notably since the 1990s, and this decline implies that the entire term structure of SDRs has shifted lower as well. Accounting for this new normal of persistently lower interest rates substantially boosts estimates of the social cost of carbon and supports a climate policy with stronger carbon mitigation strategies.

Alternative characterization of volatility of short-term interest rate

2018 ◽  
Vol 05 (02) ◽  
pp. 1850018
Author(s):  
Ramaprasad Bhar ◽  
Damien Lee
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Term Structure ◽  
Empirical Comparison ◽  
Short Term ◽  
Latent Factor ◽  
The Us ◽  
Alternative Characterization ◽  
Technical Details

Most reported stochastic volatility (SV) model for interest rates only deals with an AR specification for the latent factor process. We show in this paper the technical details for specifying the SV model for interest rates that includes an ARMA structure, a jump component and additional exogenous variables for the latent factor process. We demonstrate the efficacy of this approach with an application to the US short-term interest rate data. We find that the elasticity parameter of the variance is closer to 0.5, i.e., similar to that of the Cox–Ingersoll–Ross (1985) model of interest rates. This is quite a contrast to the finding Chan et al. [Chan, KC, GA Karolyi, F Longstaff and A Sanders (1992). The volatility of short-term interest rates: An empirical comparison of alternative models of term structure of interest rates, Journal of Finance, 47, 1209–1227]. who found the elasticity to be close to 1.5.

The path integral method in interest rate models

2020 ◽  
Vol 8 (1) ◽  
pp. 125-136
Author(s):  
V. S. Yanishevskyi ◽  
◽  
L. S. Nodzhak ◽  
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Term Structure ◽  
Path Integral ◽  
Integral Method ◽  
Interest Rate Models ◽  
Path Integral Representation ◽  
Merton Model ◽  
Integral Measure ◽  
Path Integral Method

An application of path integral method to Merton and Vasicek stochastic models of interest rate is considered. Two approaches to a path integral construction are shown. The first approach consists in using Wieners measure with the following substitution of solutions of stochastic equations into the models. The second approach is realised by using transformation from Wieners measure to the integral measure related to the stochastic variables of Merton and Vasicek equations. The introduction of boundary conditions is considered in the second approach in order to remove incorrect time asymptotes from the classic Merton and Vasicek models of interest rates. By the example of Merton model with zero drift, a Dirichlet boundary condition is considered. A path integral representation of term structure of interest rate is obtained. The estimate of the obtained path integrals is performed, where it is shown that the time asymptote is limited.

scholarly journals Interest Rate Volatility Prior to Monetary Union under Alternative Pre-Switch Regimes

2003 ◽  
Vol 4 (4) ◽  
pp. 433-457 ◽  
Author(s):  
Bernd Wilfling
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Term Structure ◽  
Monetary Union ◽  
Short Term ◽  
Financial Applications ◽  
Interest Rate Volatility ◽  
Floating Exchange Rates ◽  
Leaning Against The Wind ◽  
Arbitrary Term

Abstract The volatility of interest rates is relevant for many financial applications. Under realistic assumptions the term structure of interest rate differentials provides an important predictor of the term structure of interest rates. This paper derives the term structure of differentials in a situation in which two open economies plan to enter a monetary union in the future. Two systems of floating exchange rates prior to the union are considered, namely a free-float and a managed-float regime. The volatility processes of arbitrary-term differentials under the respective pre-switch arrangements are compared. The paper elaborates the singularity of extremely short-term (i.e. instantaneous) interest rates under extensive leaning-against-the-wind interventions and discusses policy issues.

scholarly journals Risk Management for Bonds with Embedded Options

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 790
Author(s):  
Antonio Díaz ◽  
Marta Tolentino
Keyword(s):  
Risk Management ◽  
Interest Rate ◽  
Interest Rates ◽  
Interest Rate Risk ◽  
Interest Rate Models ◽  
Management Measures ◽  
Interest Rate Risk Management ◽  
Embedded Options ◽  
The Interest Rate ◽  
Interest Rate Change

This paper examines the behavior of the interest rate risk management measures for bonds with embedded options and studies factors it depends on. The contingent option exercise implies that both the pricing and the risk management of bonds requires modelling future interest rates. We use the Ho and Lee (HL) and Black, Derman, and Toy (BDT) consistent interest rate models. In addition, specific interest rate measures that consider the contingent cash-flow structure of these coupon-bearing bonds must be computed. In our empirical analysis, we obtained evidence that effective duration and effective convexity depend primarily on the level of the forward interest rate and volatility. In addition, the higher the interest rate change and the lower the volatility, the greater the differences in pricing of these bonds when using the HL or BDT models.

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