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.

PRICES OF ASIAN OPTIONS UNDER STOCHASTIC INTEREST RATES

Asian options are the popular second generation derivative products and embedded in many structured notes to enhance upside performance.The embedded options,as a result,usually have a long duration.The movement of interest rates becomes more important in pricing such long-dated options.In this paper,the pricing of Asian options under stochastic interest rates is studied.Assuming Hull and White model for the interest rates,a closed-form formula for geometric-average options is derived.As a by-product,pricing formula is also given for plan-vanilla options under stochastic interest rates.

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 〈 0 〈 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）.

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.

Dynamic Behavior of Interest Rates in China

This paper intuitively examines the dynamic behavior of two highly relevant interest rates in China. The first one is the government rate, which is decided and published by the central bank and can be simulated by pure jump process. Estimation of the jump intension is given out. And by different robustness test, it keeps stable. The jump size has met the condition to make interest rate within reasonable bounds and shown some meaning of economic cycle behavior. The second one is the market rate, which is estimated by spline approximation based on the transaction data of government bonds. Several models, including Vasicek model, Vasicek-GARCH （1,1） model, CIR model, and CIR-GARCH（1,1）, are empirically tested and the best performance is done by the Vasicek-GARCH（1,1） model. Furthermore, the estimate bias problem due to the near unit root process is tested and evidenced by both traditional methods and GPH test. Impact of government rate on market rate is finally checked and analyzed.

Measuring China’s Interest Rate Liberalization Compared with Developed Countries

Financial repression does not suit the needs of economic and financial development in the long run, and interest rate liberalization is a natural choice for the development of China＇s financial markets＇. Based on a comparative analysis of interest rate liberalization processes between some developed countries and China and value assignment to key milestones in interest rate markets, the authors have measured the level of China＇s interest rate liberalization to be 80.64%, i.e., a complete liberalization has been initially achieved in China with the notable exception of the deposit interest rate market. Deposit interest rate liberalization is poised to be the last step in China＇s interest rate liberalization process.

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.

Analysis of exercise boundary of American interest rate option

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.

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.

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.

Term Structure of Interest Rates Based on Artificial Neural Network

In light of the nonlinear approaching capability of artificial neural networks （ ANN）, the term structure of interest rates is predicted using The generalized regression neural network （GRNN） and back propagation （BP） neural networks models. The prediction performance is measured with US interest rate data. Then, RBF and BP models are compared with Vasicek＇s model and Cox-Ingersoll-Ross （CIR） model. The comparison reveals that neural network models outperform Vasicek＇s model and CIR model, which are more precise and closer to the real market situation.

On the Distribution of Duration of First Negative Surplus for a Discrete Time Risk Model with Random Interest Rate

In this paper, we examine further annuity-due risk model presented by Cai （Probability in the Engineering and Informational Sciences, 16（2002）, 309-324）. We consider the computation for the distribution of duration of first negative surplus and the algorithm is shown for calculating probability that ruin occurs and the duration of first negative surplus takes any nonnegative integers values. Numerical illustration for the main result is given.

Empirical analysis of the monetary policy transmission through interest rate channel in China

With the deregulation of interest rates in China, the interest rate channel of monetary policy transmission is becoming more and more important. Firstly, this paper makes empirical studies on the transmission mechanism in China represented by the conventional interest rate channel of monetary policy transmission by using the Granger causality test. The result shows that there is no causality neither between investment expenditure and the market interest rate nor between household consumption and the market interest rate, which suggests that the transmission of monetary policy in China is impeded. Then the reasons from three aspects including interest rate liberalization, asset-backed securitization and household consumption behavior are analyzed.

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.

Managing Interest Rate Risk： An Evaluation of Indian Banks

Interest rate risk represents one of the key forms of financial risk faced by banks. It has given rise to an extensive body of research, .mainly focused on the estimation of sensitivity of bank stock returns to changes in interest rates. However, the analysis of the sources of bank interest rate risk has received much less attention in the literature. It is essential that banks have to monitor, maintain, and manage their assets and liabilities portfolios in a systematic manner taking into account the various risks involved in these areas. Balance sheet risk of a bank can be categorized into two major types of significant risks, which are liquidity risk and interest rate risk （IRR）. IRR is the risk to earning of capital arising from movement of interest rates. The need to manage IRR in Indian banks arises from movement of interest rates. The areas not much considered in the earlier research work are to manage IRR which influences critically the overall profitability of banks. The study was taken with an objective of analyzing the determinants of IRR and examining the strategy to manage such exposures testing the banks long run sustainability. The study had chosen 45 banks and collected secondary data for the financial year 2007 to 2012 to do the analysis of IRR management. The findings of the study were to suggest the ways to minimize the IRR and control its effect on the banks profit. The other findings were to test impact of IRR on the sustainability of the bank.

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.

A Model of Interest Rate and Loan Covenant Competition

This paper develops a model where two lenders to subprime borrowers compete with the interest rates charged and the severity of loan covenants. The model has a stable equilibrium, which demonstrates how an increase in the number of borrowers or an increase in the cost of meeting covenants will reduce the severity of the covenants required by lenders, and each of these changes will increase the difference in the severity of the loan covenant levels. An increase in the expected losses to the lender from relaxing covenants will increase the severity of loan covenants, and this will also make the levels of severity more dispersed. Additional analysis demonstrates how exogenous shifts affect the interest rates charged by the lenders and their profits

Analysis of the interest rate marketization risk of local banks in Henan Province --Taking four joint stock commercial banks as an example

With the accelerating process of interest rate marketization, the local banks in Henan Province face a greater risk of interest rate marketization, managing risk effectively can promote the development of local banks in Henan Province and the economic development of Henan Province. This paper analyzes the present situation of management of interest rate marketization in Henan Province, then puts forward some suggestions, such as promoting the development of intermediate business; promoting the product innovation; strengthening the management of assets and liabilities, improving the quality of employees, strengthening the management of non-performing loans, and etc.