scholarly journals Estimating the Short Rate from the Term Structures in the Vasicek Model

2014 ◽  
Vol 61 (1) ◽  
pp. 87-103
Author(s):  
Jana Halgašová ◽  
Beáta Stehlíková ◽  
Zuzana Bučková
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Calibration Method ◽  
Current Level ◽  
Model Parameters ◽  
Bond Prices ◽  
Vasicek Model ◽  
Term Structures ◽  
Short Rate Models

Abstract In short rate models, bond prices and term structures of interest rates are determined by the parameters of the model and the current level of the instantaneous interest rate (so called short rate). The instantaneous interest rate can be approximated by the market overnight, which, however, can be influenced by speculations on the market. The aim of this paper is to propose a calibration method, where we consider the short rate to be a variable unobservable on the market and estimate it together with the model parameters for the case of the Vasicek model

Interest Rates and Business Returns

2007 ◽  
Vol 201 ◽  
pp. 4-7
Author(s):  
Martin Weale
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Rate Increase ◽  
Yield Curve ◽  
Current Level ◽  
Short Term ◽  
The Past ◽  
Financial Options ◽  
Very High ◽  
Business Returns

The July interest rate increase has taken the Bank of England's Base Rate to the highest value for six years. In figure 1 we show the forward estimates for the nominal short-term interest rate taken from the Bank of England's yield curve tables for both government debt and liabilities of commercial banks. These are in effect market forecasts of the short-term rate produced in the past. The graph shows that the market has been taken somewhat by surprise by rising short-term interest rates. Two years ago the market was forecasting a rate of around 4 per cent per annum for July 2007. Nor were the probabilities the market gave to an interest rate of 5.75 per cent per annum very high. Twelve months ago the market in financial options implied that the chance of the rate exceeding 5.66 per cent per annum was only 15 per cent. Even in January of this year the chance of it reaching its current level or higher was put at less than 25 per cent. The National Institute cannot claim a substantially better record at forecasting interest rates. We normally use market expectations, as calculated from the yield curve, to provide exogenous forecasts as input into our model in the short term.

scholarly journals Mortgage Prepayment and Path-Dependent Effects of Monetary Policy

2021 ◽  
Vol 111 (9) ◽  
pp. 2829-2878
Author(s):  
David Berger ◽  
Konstantin Milbradt ◽  
Fabrice Tourre ◽  
Joseph Vavra
Keyword(s):  
Monetary Policy ◽  
Interest Rate ◽  
Interest Rates ◽  
Current Level ◽  
Fixed Rate ◽  
Mortgage Prepayment ◽  
Recent Interest ◽  
Household Model ◽  
Path Dependent ◽  
The Relationship

How much ability does the Fed have to stimulate the economy by cutting interest rates? We argue that the presence of substantial debt in fixed-rate, prepayable mortgages means that the ability to stimulate the economy by cutting interest rates depends not just on their current level but also on their previous path. Using a household model of mortgage prepayment matched to detailed loan-level evidence on the relationship between prepayment and rate incentives, we argue that recent interest rate paths will generate substantial headwinds for future monetary stimuli. (JEL E32, E43, E52, E58, G21, G51)

scholarly journals Effect of correlation on bond prices in short rate models of interest rates

2018 ◽  
Vol 22 (2) ◽  
pp. 89-101
Author(s):  
Zuzana Girová ◽  
Beáta Stehíková
Keyword(s):  
Interest Rates ◽  
Bond Prices ◽  
Short Rate Models

scholarly journals EXTENSION OF VASICEK MODEL TO THE MODELLING OF INTEREST RATE

2020 ◽  
Vol 4 (2) ◽  
pp. 151-155
Author(s):  
Adaobi Udoye ◽  
Lukman Akinola ◽  
Eka Ogbaji
Keyword(s):  
Stochastic Process ◽  
Interest Rate ◽  
Interest Rates ◽  
Regression Method ◽  
Least Square ◽  
Interesting Aspect ◽  
Vasicek Model ◽  
Least Square Regression ◽  
Ito's Lemma ◽  
Random Times

Interest rate modelling is an interesting aspect of stochastic processes. It has been observed that interest rates fluctuates at random times, hence the need for its modelling as a stochastic process. In this paper, we apply the existing Vasicek model, Itô’s lemma and least-square regression method in the modelling and providing dynamics for a given interest rate.

Korean Treasury Bond Futures Pricing Model

2004 ◽  
Vol 12 (1) ◽  
pp. 1-22
Author(s):  
Youngsoo Choi ◽  
Se Jin O ◽  
Jae Yeong Seo
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Market Price ◽  
Alternative Methods ◽  
Vasicek Model ◽  
Market Participants ◽  
Treasury Bond ◽  
Cost Of Carry ◽  
The Interest Rate ◽  
The Cost

This paper proposes two alternative methods which are used for pricing the theoretical value of the KTB futures on the non-traded underlying asset; first method is to use the CKLS model, under which the volatility of interest rate changes is highly sensitive to the level of the interest rate, and then employ binomial trees to compute the theoretical value of futures, second one is to use the multifactor Vasicek model considering correlations between yields-to-maturity and then employ the Monte Carlo simulation to compute it. In the empirical study on KTB303 and KTB306, an CKLS methodology is superior to the conventional KORFX method based on the cost-of-carry model in terms of the size of difference between market price and theoretical price. However, the phenomena, the price discrepancy using the KOFEX methodology is very small for all test perlod, implies that the KOFEX one is being used for the most market participants. The reasons that an multifactor Vasicek methodlogy is performed poorly in comparison to another methods are 1) the Vasicek model might be not a good model for explaining the level of interest rates, or 2) the important point considered by the most market participants may be on the volatility or interest rate, not on the correlations between yields-to-maturity.

A FUNCTIONAL COEFFICIENT APPROACH TO MODELING THE FISHER HYPOTHESIS: WORLDWIDE EVIDENCE

2010 ◽  
Vol 15 (1) ◽  
pp. 93-118 ◽  
Author(s):  
Helmut Herwartz ◽  
Hans-Eggert Reimers
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Inflation Targeting ◽  
Model Parameters ◽  
Equilibrium Relation ◽  
Cross Sectional ◽  
Ex Post ◽  
Fisher Hypothesis ◽  
Cross Sectional Dimension ◽  
Potential Equilibrium

We pursue a semiparametric approach to examining core implications of the Fisher hypothesis, namely cointegration linking nominal interest rates and inflation, and homogeneity of the potential equilibrium relation. The sample is an unbalanced panel and comprises monthly time series from more than 100 economies. The time period of at most 45 years is subdivided into three regimes according to dominating monetary policies. To exploit the cross-sectional dimension for inference on parameter homogeneity, we apply mean group estimation of functional coefficients that allow the conditioning of key model parameters on economic states. The evidence in favor of cointegration is weakened over states of negative real interest rates that are likely to coincide with scenarios of high inflation. The ex post real interest rate is mostly diagnosed as unstable. The Fisher hypothesis is particularly confirmed for states characterized by large positive interest rate adjustments during the inflation-targeting regime.

scholarly journals How to handle negative interest rates in a CIR framework

SeMA Journal ◽  
2021 ◽  
Author(s):  
Marco Di Francesco ◽  
Kevin Kamm
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Yield Curve ◽  
Analytical Formula ◽  
Market Prices ◽  
Cir Model ◽  
Term Structures ◽  
Negative Interest Rates ◽  
The Difference ◽  
Mean Variance

AbstractIn this paper, we propose a new model to address the problem of negative interest rates that preserves the analytical tractability of the original Cox–Ingersoll–Ross (CIR) model without introducing a shift to the market interest rates, because it is defined as the difference of two independent CIR processes. The strength of our model lies within the fact that it is very simple and can be calibrated to the market zero yield curve using an analytical formula. We run several numerical experiments at two different dates, once with a partially sub-zero interest rate and once with a fully negative interest rate. In both cases, we obtain good results in the sense that the model reproduces the market term structures very well. We then simulate the model using the Euler–Maruyama scheme and examine the mean, variance and distribution of the model. The latter agrees with the skewness and fat tail seen in the original CIR model. In addition, we compare the model’s zero coupon prices with market prices at different future points in time. Finally, we test the market consistency of the model by evaluating swaptions with different tenors and maturities.

OPTION RISK MEASUREMENT WITH TIME-DEPENDENT PARAMETERS

2000 ◽  
Vol 03 (03) ◽  
pp. 581-589 ◽  
Author(s):  
C. F. LO ◽  
P. H. YUEN ◽  
C. H. HUI
Keyword(s):  
Interest Rate ◽  
Option Pricing ◽  
Risk Measurement ◽  
Time Dependent ◽  
Model Parameters ◽  
Cev Model ◽  
Equity Options ◽  
Market Values ◽  
Term Structures ◽  
Option Values

In value-at-risk (VaR) methodology of option risk measurement, the determination of market values of the current option positions under various market scenarios is critical. Under the full revaluation and factor sensitivity approach which are accepted by regulators, accurate revaluation and precise factor sensitivity calculation of options in response to significant moves in market variables are important for measuring option risks in terms of VaR figures. This paper provides a method for pricing equity options in the constant elasticity variance (CEV) model environment using the Lie-algebraic technique when the model parameters are time-dependent. Analytical solutions for option values incorporating time-dependent model parameters are obtained in various CEV processes. The numerical results, which are obtained by employing a very efficient computing algorithm similar to the one proposed by Schroder [11], indicate that the option values are sensitive to the time-dependent volatility term structures. It is also possible to generate further results using various functional forms for interest rate and dividend term structures. From the analytical option pricing formulae, one can achieve more accuracy to compute factor sensitivities using more realistic term-structures in volatility, interest rate and dividend yield. In view of the CEV model being empirically considered to be a better candidate in equity option pricing than the traditional Black–Scholes model, more precise risk management in equity options can be achieved by incorporating term-structures of interest rates, volatility and dividend into the CEV option valuation model.

Martingale Models for the Short Rate

2019 ◽  
pp. 280-295
Author(s):  
Tomas Björk
Keyword(s):  
Normal Distribution ◽  
Yield Curve ◽  
Mean Reversion ◽  
Point Of View ◽  
Bond Prices ◽  
Affine Models ◽  
Term Structures ◽  
Analytical Results ◽  
Bond Options ◽  
Short Rate Models

This chapter is devoted to an overview and analysis of the most common short rate models, such as the Vasiček, Dothan, Hull–White, and CIR models. These models are analyzed and classified from the point of view of positive short rates, normal distribution, mean reversion, and computability. In particular we present the theory of affine term structures, and discuss the inversion of the yield curve. Analytical results for bond prices and bond options are presented for all the affine models.

Commercial Banks

2017 ◽  
Author(s):  
Stefan Homburg
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Term Structure ◽  
Great Recession ◽  
Commercial Banks ◽  
Central Banks ◽  
The Great Recession ◽  
Term Structures ◽  
Market Interest Rate ◽  
Money Creation

Chapter 7 introduces commercial banks as creators of money and integrates them into the general equilibrium framework. The motivation to deviate from the standard approach that neglects commercial banks and entrusts all money creation to a central bank is twofold. First, apart from currency, central banks do not provide money directly but rather supply reserves that enable banks to create deposits. After the Great Recession, this transmission process staggered: increases in reserves outpaced increases in deposits. Any analysis of the monetary expansions starting in 2008 would remain incomplete and unsatisfactory unless it took account of this fact. Second, central banks normally control an overnight interbank interest rate that differs from the market interest rate on bonds. Considering an interbank market and its relationship with the bond market makes it possible to derive a term structure of interest rates. This is important because inverse term structures are good predictors for recessions.

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