scholarly journals Estimating the Domestic Short Rate in a Convergence Model of Interest Rates

2020 ◽  
Vol 75 (1) ◽  
pp. 33-48
Author(s):  
Zuzana Bučková ◽  
Zuzana Girová ◽  
Beáta Stehlíková
Keyword(s):  
Interest Rates ◽  
High Precision ◽  
Monetary Union ◽  
Optimization Problem ◽  
Vasicek Model ◽  
Dynamic Correlation ◽  
Zero Correlation ◽  
Original Case ◽  
Real Market ◽  
Convergence Model

AbstractIn this paper we study the convergence model of interest rates by Corzo and Schwartz. It models the situation when a country is going to enter a monetary union, for example the eurozone. We are interested in estimating the underlying short rate, which is a theoretical variable, not observed on the market. We use the procedure already employed for the Vasicek model to the eurozone data and for the case of a zero correlation we show that a similar procedure can be used also for the estimation of the domestic parameters and the short rate values. The assumption of the zero correlation allows us to simplify the optimization problem, but using simulations we show that our algorithm is robust to the specification of the correlation. It estimates the short rate with a high precision also in the original case of a nonzero correlation, as well as in the case of a dynamic correlation, when the correlation is modelled as a function of time. Finally, we use the algorithm to real market data and estimate the short rate before adoption of the euro currency in Slovakia, Estonia, Latvia and Lithuania.

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 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 PERHITUNGAN PREMI ASURANSI JOINT LIFE DENGAN MODEL VASICEK DAN CIR

2019 ◽  
Vol 8 (3) ◽  
pp. 246
Author(s):  
I MADE WAHYU WIGUNA ◽  
KETUT JAYANEGARA ◽  
I NYOMAN WIDANA
Keyword(s):  
Stochastic Process ◽  
Interest Rates ◽  
Life Insurance ◽  
Insurance Premium ◽  
Insurance Contract ◽  
Insurance Company ◽  
Vasicek Model ◽  
Cir Model ◽  
Premium Payment ◽  
Premium Price

Premium is a sum of money that must be paid by insurance participants to insurance company, based on  insurance contract. Premium payment are affected by interest rates. The interest rates change according to stochastic process. The purpose of this work is to calculate the price of joint life insurance premiums with Vasicek and CIR models. The price of a joint life insurance premium with Vasicek and CIR models, at the age of the insured 35 and 30 years has increased until the last year of the contract. The price of a joint life insurance premium with Vasicek model is more expensive than the premium price using CIR model.

scholarly journals Liquidity, interest rates and house prices in the euro area: a DSGE analysis

2016 ◽  
Vol 9 (1) ◽  
pp. 4-25 ◽  
Author(s):  
Margarita Rubio ◽  
José A. Carrasco-Gallego
Keyword(s):  
Interest Rates ◽  
Monetary Union ◽  
Euro Area ◽  
House Prices ◽  
Housing Prices ◽  
House Price ◽  
Dsge Model ◽  
Content Type ◽  
The Core ◽  
Dynamic Stochastic

Purpose This study aims to build a two-country monetary union dynamic stochastic general equilibrium (DSGE) model with housing to assess how different shocks contributed to the increase in housing prices and credit in the European Economic and Monetary Union. One of the countries is calibrated to represent the core group in the euro area, while the other one corresponds to the periphery. Design/methodology/approach In this paper, the authors explore how a liquidity shock (or a decrease in the interest rate) affects house prices and the real economy through the asset price and the collateral channel. Then, they analyze how a house price shock in the periphery and a technology shock in the core countries are transmitted to both economies. Findings The authors find that a combination of an increase in liquidity in the euro area coming from the common monetary policy, together with asymmetric house price and technology shocks, contributed to an increase in house prices in the euro area and a stronger credit growth in the peripheral economies. Originality/value This paper represents the theoretical counterpart to empirical studies that show, through macroeconometric models, the interrelation between liquidity and other shocks with house prices. Using a DSGE model with housing, the authors disentangle the mechanisms behind these empirical findings.

The Link between German Short- and Long-Term Interest Rates. Some Evidence against a Term Structure Oriented Monetary Policy / Der Zusammenhang zwischen kurz- und langfristigen Zinssätzen in Deutschland. Empirische Evidenz gegen eine zinsstrukturorientierte Geldpolitik

1998 ◽  
Vol 217 (2) ◽  
Author(s):  
Uwe Hassler ◽  
Dieter Nautz
Keyword(s):  
Monetary Policy ◽  
Central Bank ◽  
Interest Rates ◽  
Term Structure ◽  
Monetary Union ◽  
Stable Relationship ◽  
Monetary Targeting ◽  
Main Indicator ◽  
Short And Long Term

SummaryCritics of the Bundesbank's monetary policy recently suggested the abandonment of monetary targeting in favour of the term structure of interest rates as the main indicator of central bank policy. However, a term structure oriented policy requires a reliable link between short- and long-term interest rates. Our analysis clearly suggests that there is no stable relationship between German short- and long-term interest rates, in particular not after the German monetary union. Consequently, the empirical results of this paper indicate that this policy has not much chance of success.

Low Interest Rates do they Revise Household Saving Motives in the Euro Area?

e-Finanse ◽  
2016 ◽  
Vol 12 (1) ◽  
pp. 43-56
Author(s):  
Katarzyna Kochaniak
Keyword(s):  
Interest Rates ◽  
Monetary Union ◽  
Euro Area ◽  
Union Member ◽  
Household Saving ◽  
Low Interest Rates ◽  
The Impact

AbstractThis paper presents the impact of decreasing MFI interest rates on household deposits and saving goals in 12 Monetary Union member countries in the years 2009-2015. It analyses tendencies in household deposits (overnight, with agreed maturity and redeemable at notice), and attempts to link them with certain household saving motives (target, retirement and precautionary). The paper identifies those deposit categories which appeared as sensitive to declining interest rates and indicates the Eurozone countries whose populations are expected to revise their savings plans. Precise implications are drawn for target saving motives of households in Austria, Cyprus and Malta. However, in the case of two other motives, the analysis does not conclude on the impact of decreasing MFI interest rates.

A Public Investment Stimulus in Surplus Countries and Its Spillovers in the EA

2017 ◽  
Vol 239 ◽  
pp. R53-R62 ◽  
Author(s):  
Jan in't Veld
Keyword(s):  
Monetary Policy ◽  
The Netherlands ◽  
Interest Rates ◽  
Monetary Union ◽  
Euro Area ◽  
Public Investment ◽  
European Council ◽  
Individual Member ◽  
Fiscal Effort ◽  
Positive Spillovers

The Euro Area recommendations endorsed by the European Council in 2016 called for a differentiation of the fiscal effort by individual Member States, taking into account spillovers across Euro Area countries. This article shows model-based simulations of an increase in public investment in Germany and the Netherlands and their spillovers to the rest of the Euro Area. While spillovers in a monetary union may be small when monetary policy reacts by raising interest rates, when rates are kept constant and the stimulus is accommodated, spillovers can be sizeable. An increase in (productive) spending in Germany and the Netherlands can boost GDP in these countries and also have significant positive spillovers on the rest of EA GDP, while the effects on current accounts are likely to be small. Effects can be even larger when investment is directed to the most productive projects. With low borrowing costs at present, the increase in government debt for surplus countries will be modest, while there could be an improvement in debt ratios in the rest of the Euro Area.

scholarly journals A Single-Copter UWB-Ranging-Based Localization System Extendable to a Swarm of Drones

Drones ◽  
2021 ◽  
Vol 5 (3) ◽  
pp. 85 ◽  
Author(s):  
Christoph Steup ◽  
Jonathan Beckhaus ◽  
Sanaz Mostaghim
Keyword(s):  
Nonlinear Optimization ◽  
High Precision ◽  
Precision Measurement ◽  
Gradient Descent ◽  
Optimization Problem ◽  
Single Type ◽  
Localization System ◽  
Gradient Descent Algorithm ◽  
Update Rate ◽  
Anchor Points

This paper presents a single-copter localization system as a first step towards a scalable multihop drone swarm localization system. The drone was equipped with ultrawideband (UWB) transceiver modules, which can be used for communication, as well as distance measurement. The location of the drone was detected based on fixed anchor points using a single type of UWB transceiver. Our aim is to create a swarm localization system that enables drones to switch their role between an active swarm member and an anchor node to enhance the localization of the whole swarm. To this end, this paper presents our current baseline localization system and its performance regarding single-drone localization with fixed anchors and its integration into our current modular quadcopters, which was designed to be easily extendable to a swarm localization system. The distance between each drone and the anchors was measured periodically, and a specially tailored gradient descent algorithm was used to solve the resulting nonlinear optimization problem. Additional copter and wireless-specific adaptations were performed to enhance the robustness. The system was tested with a Vicon system as a position reference and showed a high precision of 0.2 m with an update rate of <10 Hz. Additionally, the system was integrated into the FINken copters of the SwarmLab and evaluated in multiple outdoor scenarios. These scenarios showed the generic usability of the approach, even though no accurate precision measurement was possible.

scholarly journals Finanspagten og issue-linkage inden for eurosystemet

Politik ◽  
2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Derek Beach
Keyword(s):  
Interest Rates ◽  
Monetary Union ◽  
Economic And Monetary Union ◽  
Economic Shocks ◽  
Issue Linkage ◽  
High Interest ◽  
Fiscal Compact ◽  
Market Pressure

This article claims that the reform negotiations of the euro can only be understood as a form of issue-linkage, where two groups of states (euro-winners and euro-losers) want either stricter rules for state scal behavior (euro-winners) or increased assistance mechanisms in the form of temporary aid packages or permanent transfers for countries hit by asymmetric economic shocks (euro-losers). e two issues were linked in the negotiations in 2011 and 2012, where a quid pro quo was reached, where Germany got ‘its’ Fiscal Compact that strengthened the rules for behavior in exchange for concessions on the transfer issue both in relation to accepting ECB interventions in the market to aid euro-losers facing high interest rates, and the entry into force of the permanent aid mechanism (ESM) a year ahead of schedule. Euro-losers were however only able to link the two issues when they were able to exploit their economic weakness and the risk that market pressure could result in the collapse of the euro. As this pressure has eased in the fall of 2012, the pace of reforms has slowed down, with few indications that further progress will be made on strengthening the transfer side of Economic and Monetary Union any time soon. 

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