Interest Rate and Some of Its Applications

Interest rates are a fundamental aspect of the economy and have a significant impact on various financial decisions such as borrowing, investing, and saving. They are the cost of borrowing money or the return on investment and are determined by various factors such as the supply and demand for credit, inflation expectations, and monetary policy decisions made by central banks. Changes in interest rates can have a major effect on the economy and can influence consumer spending, business investment, and overall economic growth. This makes it crucial for individuals, businesses, and policymakers to have a clear understanding of the dynamics of interest rates. Interest rates play an important role in determining the cost of borrowing money for individuals and businesses. A rise in interest rates can increase the cost of borrowing and make it more difficult for people and companies to access credit. This can lead to a decrease in consumer spending and business investment, which can slow down economic growth. On the other hand, a decrease in interest rates can make it easier for individuals and businesses to access credit and increase consumer spending and business investment, boosting economic growth. Central banks, such as the Federal Reserve in the United States, play a key role in determining interest rates by setting monetary policy. They use interest rate changes to influence the economy and reach their goals of stable prices, maximum employment, and moderate long-term interest rates. In conclusion, understanding the dynamics of interest rates is essential for making informed financial decisions and assessing the overall health of the economy. The impact of interest rates on the economy and individual financial decisions is far-reaching and long-lasting, making it a crucial topic for continued study and discussion.

Pricing Stochastic Barrier Options under Hull-White Interest Rate Model

A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stochastic barrier by means of partial differential equation methods and then derive the exact analytical solutions of the barrier options.Furthermore,a numerical example was given to show how to apply this model to pricing one structured product in realistic market.Therefore,this model can provide new insight for future research on structured products involving barrier options.

Monetary and fiscal factors in nominal interest rate variations in Sri Lanka under a deregulated regime

Background:This paper examines the role of monetary and fiscal factors in interest rate variations in Sri Lanka under its deregulated regime of interest rates.In addition the paper also examines the role of monetary factors in the variation of interest rates,using a quarterly dataset for the post-global recession period,when the exchange rate is determined by market forces.Results:Empirical analysis uses a dataset of nominal interest rates,money growth,income growth,changes in nominal exchange rate,and budget deficit.From the methodological point of view the paper involves vector autoregression model and Wald tests of Granger causality,followed by impulse response analysis while stationarity and the order of integration of the selected variables are confirmed involving the augmented Dickey-Fuller and the Phillips-Perron unit-root tests.Results:The paper confirms that both monetary and fiscal factors have significant effects on the variations of interest rates.Money growth triggers an increase in interest rates,which supports the Fisher equation view,while income growth has a negative impact.Budget deficit causes a rise in interest rates,but the role of the exchange rate is found to be almost insignificant,probably due to including exchange rate series that cover both the pegged and market-based regimes of exchange rates.The second part of the analysis,using a quarterly dataset for the post-global recession period,further establishes the positive impact of M2 money growth and income growth on interest rates.In this case,exchange rate depreciation causes an increase in interest rates.Conclusions:The significant role of monetary and fiscal factors in interest rate variations implies it would be possible to manage interest rates through a judiciary management of monetary and fiscal policies.

Simulation Methods of Stochastic Volatility Interest Rate Term Structure

A term structure model bearing features of stochastic volatility and stochastic mean drift with jump (SVJ-SD model for short) is built in the paper to describe the stochastic behavior of interest rates.Based on sample data of an interest rate of national bond repurchase,maximum likelihood (ML),linear Kalman filter and efficient method of moments (EMM) are used to estimate the model.While ML works well for simple models,it may lead to considerable deviation in parameter estimation when dynamic risks of interest rates are considered in them.Linear Kalman filter is a tractable and reasonably accurate technique for estimation cases where ML was not feasible.Moreover,when compared with the first two approaches,using EMM can obtain better parameter estimates for complex models with non-affine structures.

Study on models for control of interest rate risks

Analyses different interest rate risks, presents a new model for assessment of interest rates and thereby establishes the framework for control of interest

Effect of interest rate on economic performance: evidence from Islamic and non-Islamic economies

Background:Saving and investment are two of the most important tools for economic growth.The interest rate has always been considered an important determinant of saving and investment.However,according to Islamic teachings,riba or earning interest on saving or investment is forbidden,and thus,many Muslims try to avoid earning income from the interest rate.Therefore,the aim of this study is to assess the effects of this religious guideline on the financial decisions of an Islamic country’s population and its impact on saving and investment.Methods:We applied the random effect and system generalized method of moments(GMM)model separately to data of 17 non-Islamic and 17 Islamic countries from 2005 to 2013.Results:The results suggest that people in Islamic countries are not concerned about the interest rate on saving,but in non-Islamic countries,the interest rate,per capita income,and inflation have significant positive impacts,and national expenditure has a significant negative impact on saving.However,in Islamic countries,remittances received and national expenditure have negative significant impacts,and per capita income has a positive significant impact on saving.In the case of investment,interest rate and inflation show a negative effect on investment while trade affects investment positively in both Islamic and non-Islamic countries.Furthermore,domestic credit provided by banks has a negative significant effect on investment in non-Islamic countries,while in Islamic countries,remittances show a positive significant impact on investment.Conclusions:The governments and policy makers of Islamic countries should not imitate the economic policies of non-Islamic countries because religious factors play an important role in the interest rate-saving relationship.Instead,they should increase per capita income by improving employment conditions and by reducing remittances received and national expenditure.Policies on saving should not allow earning interest.Furthermore,in order to increase investment,efforts should be made to lower the interest rate and inflation,and to enhance remittances received and trade.These policies will increase saving and investment in Islamic countries,ultimately resulting in improved economic growth.

Central Bank Interest Rate Policy as a Pro-Crisis Instrument of Macroeconomic Regulation

Why does interest rate policy not work in the economy as economic theory suggests?To understand why,you need to look at the economy from a higher level of abstraction.With this approach,only two states of the economy can be distinguished.The first is a“normal”state;the second is crisis and recession.The“normal”state is the period after the recession and before the next crisis.During this period,the basic laws of the market economy work.During a crisis,the relationship between the level of interest rates and borrowing by households and businesses is broken.This explains the ineffectiveness of the policy of lowering interest rates.Different states of the economy have their own laws,and you cannot extrapolate tools that are successful under“normal”market conditions linearly to the crisis state of the economy.Why does the interest rate policy during the period of the“normal”state of the economy not adjust its development in order to prevent the onset of the crisis?Firstly,the conditions for the emergence of crisis phenomena are created by the interest rate policy at the very beginning of the business cycle,when central banks set and maintain low interest rates for a relatively long period.Secondly,by the end of the business cycle,the credit burden in economy reaches its maximum,so there is no further possibility of expanding effective demand by decreasing interest rates.Thirdly,interest rate policy is an instrument for rough adjustment of the economy,indiscriminately affecting all participants in economic relations.In an attempt to stimulate the economy,the central bank creates the conditions for increasing its imbalance.Fourth,at the end of the business cycle,the interest rate policy does not actually support the real economy,but only the stock market.Fifth,the Fed’s policy has formed a pro-crisis conditioned reflex among market participants.Thus,central banks should leave the determination of the level of interest rates to the free market.

Exchange rate,discount rate,interest rate and depreciation rate

exchange rate:汇率,外汇汇率,指一个国家的货币和另一个国家的货币的比价。中国人民银行每天公布人民币市场汇价。如:market Exchange Rates in RMB yuan set by the People’s Bank ofChina(September 4,1998)Currency Unit RateUS dollar 100 828.00Japanese yen 100 6.0291German mark 100 478.

Research on Dynamic Relationship Between Interest Rate&Exchange Rate—Based on the Analysis of Marketization of Interest Rate and Exchange Rate

This paper empirically analyzed the dynamic relationship between interest rate and exchange rate with VAR model and VECM using monthly data from 2008 to 2019.One of the main contributions of this paper is that it concentrated on studying how the marketization of interest rate and exchange rate plays a role in the transmission mechanism between these two rates by dividing the sample into 6 different groups according to the process of the marketization.The results show that there are long-term and short-term equilibrium relationship between interest rate and exchange rate.Also,interest rate could quickly respond to the changes in exchange rate after the marketization,which reflect that the marketization of interest rate is effective in China.However,exchange rate could not effectively respond to changes in interest rate.Thus,the marketization of exchange rate still needs to be improved.In addition,the results show that after marketization,an increase in the interest rate would lead to a decrease in exchange rate now,which could be a reference to the formulation of monetary policies.

Research on the Influence of Interest Rate Liberalization on Commercial Banks' Profitability in China

In order to explore the influence of interest rate liberalization on profitability,an empirical analysis is carried out with the panel data of commercial banks in China from 2009 to 2019.Then,the heterogeneity of the impact is studied among different banks.The results show that,first,interest rate liberalization and commercial banks'profitability have an inverted U-shaped relationship,whereby interest rate liberalization would increase the profitability of banks in the early stage but would reduce the profitability after reaching a peak inflection point at the later stage.Secondly,the impact varies among different banks,being more significant in urban commercial banks and large state-owned banks.

UNIFORM ESTIMATE ON FINITE TIME RUIN PROBABILITIES WITH RANDOM INTEREST RATE

We consider a discrete time risk model in which the net payout (insurance risk) {Xk,k=1,2,···} are assumed to take real values and belong to the heavy-tailed class L ∩ D and the discount factors (financial risk) {Yk,k=1,2,···} concentrate on [θ,L],where 0 < θ <1,L<∞,{Xk,k=1,2,···},and {Yk, k=1,2,···} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n ≥ 1, which is different from Tang Q H and Tsitsiashvili G (Adv Appl Prob, 2004, 36: 1278–1299).

Perturbation Analysis of Structured Least Squares Problems and Its Application in Calibration of Interest Rate Term Structure

A structured perturbation analysis of the least squares problem is considered in this paper.The new error bound proves to be sharper than that for general perturbations. We apply the new error bound to study sensitivity of changing the knots for curve fitting of interest rate term structure by cubic spline.Numerical experiments are given to illustrate the sharpness of this bound.

An Analysis of Competition over Interest Rate among Banks in China

In 2000, the central bank of China adopted a policy to gradually liberalize its interest rate, and thus raised the curtain of competition over interest rate among the banks in China. The objective of this study is to put a focus on the existing banking market environment and thereafter the gaming behaviors of the banks on different stages given the interest rate is loosened gradually as scheduled.

Macroeconomic control of interest rate in China

The macroeconomic control of interest rate is studied using the elastic theory and correlation analysis and the concrete influence of interest rate on the consumption, savings and investment in China are investigated. It is pointed out that although the interest rate mechanisms in China has gone through several adjustments and reforms, the results are not yet fully up to expectations. The interest rate does not adjust the national economic structure, and direct the trend of funds, nor regulate the general social supply and demand and balance the price and currency in circulation, to achieve a rational distribution of social resources. The interest rate policy of Central Bank does not have much actual influence on the economic departments, and this influence was continuously weakened in recent years. Countermeasures are suggested for improving the macro control of interest rate.

Analysis of exercise boundary of American interest rate option

<正>By applying the variational inequality technique,we analyzed the behavior of the exercise boundary of the American-style interest rate option under the assumption that the interest rates obey a mean-reverting random walk as given by the Vasicek model. The monotonicity,boundedness and C~∞-smoothness of the exercise boundary are proved in this paper.

Implied Bond and Derivative Prices Based on Non-Linear Stochastic Interest Rate Models

In this paper we expand the Box Method of Sorwar et al. (2007) to value both default free bonds and interest rate contingent claims based on one factor non-linear interest rate models. Further we propose a one-factor non-linear interest rate model that incorporates features suggested by recent research. An example shows the extended Box Method works well in practice.

Real Interest Rates,Real Wages and Economic Restructuring—Analysis Based on Dynamic Stochastic General Equilibrium(DSGE)

On the basis of research conducted by Long and Plosser(1983),this paper carries out an in-depth analysis on the relationship between real interest rates,real wage,and macro-economy and economic structure by simulating a dynamic stochastic general equilibrium(DSGE) model and comes to the following conclusions:(1) Increasing the level of real interest rates will expand the share of consumption in GDP,improve the macroeconomic structure,and promote steady economic development;(2) Increasing the level of real wages will enhance economic growth but will not change the economic structure of consumption and investments;(3) Increasing wages will enhance economic growth and expand its share in national income;(4) Increasing wages will not lower output level but will be favorable to the improvement of economic structure.Therefore,this paper argues for interest rates liberalization to achieve long-term,steady economic development in China.