Minimum Interest Rate Research Articles

Optimal Retirement Age and Lower Bound on Interest Rate

For a long time now, the monetary policies in the US and other industrialized countries have been a regime of cheap money with the interest rate often being negative. A low interest rate in the framework of the Keynesian monetary policy stimulates demand but is hard on the retirees who are mostly on a fixed income. This paper generates a simple model to understand the interaction between current wealth, savings rate, interest rate and retirement age. The model also suggests a lower bound on the interest rate. The minimum interest rate at which Americans of median age with median wealth and median income, and retiring at the age of 67, turns out to be 10%.

A caputo fractional order financial mathematical model analyzing the impact of an adaptive minimum interest rate and maximum investment demand

A key model for predictive analysis, particularly in finance, is the Rössler system. This study introduces an enhanced version of this model, incorporating minimum interest rates and maximum investment demands. To capture its temporal dynamics, we used the Caputo fractional order derivative, which allowed us to evaluate the memory effect that underpins these factors’ financial stability and volatility over time. The research establishes the existence and uniqueness of the model solution, confirming its reliability. Numerical solutions obtained via the homotopy perturbation method and simulations reveals a positive correlation between maximum investment demand and interest rates, highlighting the significant impact of long-term dependencies and non-local influences of demands on interest rates. The insights provide valuable guidance for navigating financial uncertainties and optimizing investment strategies for market stability, deepening our understanding of relationships in nonlinear financial systems.

How Do Life Insurers Respond to a Prolonged Low Interest Rate Environment? A Literature Review

Life insurers, whose contractual liabilities include providing minimum guaranteed interest rates to policyholders, are significantly affected by persistently low interest rates. Hence, this study reviews the literature on the prolonged low interest rate environment and its impact on the life insurance industry, incorporating multiple perspectives and practices in different countries. The effect of low interest rates on life insurance products depends on the sensitivity of the interest rate of each product type and the level of minimum interest rate guarantee. In addition, their impacts on the valuation of life insurance companies depend on shifts in the valuation interest rate, which is used to discount the present value of future benefits, as well as the financial and solvency issues faced by insurers. Overall, the literature suggests that insurers need both short- and long-term solutions to respond to a prolonged low interest rate environment.

An analytical study of participating policies with minimum rate guarantee and surrender option

We perform a detailed theoretical study of the value of a class of participating policies with four key features: (i) the policyholder is guaranteed a minimum interest rate on the policy reserve; (ii) the contract can be terminated by the holder at any time until maturity (surrender option); (iii) at the maturity (or upon surrender), a bonus is credited to the holder if the portfolio backing the policy outperforms the current policy reserve; (iv) due to solvency requirements, the contract ends if the value of the underlying portfolio of assets falls below the policy reserve.Our analysis is probabilistic and relies on optimal stopping and free boundary theory. We find a structure of the optimal surrender strategy which was undetected by previous (mostly numerical) studies on the topic. Optimal surrender of the contract is triggered by two ‘stop-loss’ boundaries and by a ‘too-good-to-persist’ boundary (in the language of Ekström and Vaicenavicius in Stoch. Process. Appl. 130: 806–823, 2020). Financial implications of this strategy are discussed in detail and supported by extensive numerical experiments.

The determinants of the lending interest rate in a cost-based approach: Theoretical model and empirical analysis

We develop a mathematical model to determine the lending interest rate applied by a financial institution in a cost-based approach. Our model mathematically isolates the four main components of the total cost of credit, including net operating costs, weighted average cost of funding, cost of risk and weighted cost of equity. Our equations enable us to determine the floor interest rate, which is the minimum interest rate that a financial institution should set for its credit operations to be profitable. The results of the empirical analyses carried out over a 15-year period, from 2004 to 2018, corroborate the suggestions of our model that interest rates follow the evolution of the floor interest rate. One of the contributions of our model is that the results can be useful in policies that seek to improve the credit conditions of financial institutions by reducing their credit costs rather than imposing low interest rates to them.

Application of preferential leasing at enterprises of the agro-industrial complex

The article deals with leasing operations for small enterprises of the agro-industrial complex. The following basic conditions of leasing transactions are considered: requirements for the lessee, minimum interest rate, minimum / maximum lease term, type of the financed property in the current market situation, industries and regions that are allowed for cooperation in the current market situation. The risk factors of the lessor and the lessee are analyzed. It is noted that when considering the segment of small and medium-sized enterprises of the agro-industrial complex, the main factor that determines the risk of the transaction is the uncertainty of the future profit of the lessee. A scheme for determining the risk of a leasing transaction is proposed. The risks of the lessee’s and lessor’s segments are considered. The conclusion is made about the high riskiness of leasing transactions for enterprises of the agro-industrial complex.

On the Market-Consistent Valuation of Participating Life Insurance Heterogeneous Contracts under Longevity Risk

The purpose of this paper is to conduct a market-consistent valuation of life insurance participating liabilities sold to a population of partially heterogeneous customers under the joint impact of biometric and financial risk. In particular, the heterogeneity between groups of policyholders stems from their offered minimum interest rate guarantees and contract maturities. We analyse the effects of these features on the company’s insolvency while embracing the insurer’s goal to achieve the same expected return for different cohorts of policyholders. Within our extensive numerical analyses, we determine the fair participation rates and other key figures, and discuss the implications for the stakeholders, taking account of various degrees of conservativeness of the insurer when pricing the contracts.

Implementation of infrastructure investment projects

The article examines infrastructure investment projects, their impact on the economy. The main attention is paid to road construction objects, because the road network still does not meet modern requirements. Due to the fact that infrastructure projects are diagnosed and classified according to areas of activity, systematized according to the forms of implementation, it is necessary to determine approaches to a targeted assessment of the effectiveness of such projects, depending on their classification, which are formulated in the article. Attention is focused on the need for alternative projects, which is facilitated by the digitalization of the economy. Infrastructure projects can be financed from several sources of budgets of all levels, off-budget funds, private investors ’ funds, joint and project financing, concession agreements, foreign investments and bank loans with a minimum interest rate.

Analysis of Fractional Order Chaotic Financial Model with Minimum Interest Rate Impact

The main objective of this paper is to construct and test fractional order derivatives for the management and simulation of a fractional order disorderly finance system. In the developed system, we add the critical minimum interest rate d parameter in order to develop a new stable financial model. The new emerging paradigm increases the demand for innovation, which is the gateway to the knowledge economy. The derivatives are characterized in the Caputo fractional order derivative and Atangana-Baleanu derivative. We prove the existence and uniqueness of the solutions with fixed point theorem and an iterative scheme. The interest rate begins to rise according to initial conditions as investment demand and price exponent begin to fall, which shows the financial system’s actual macroeconomic behavior. Specifically component of its application to the large scale and smaller scale forms, just as the utilization of specific strategies and instruments such fractal stochastic procedures and expectation.

The Determinants of the Interest Rate of Financial Institutions: Theoretical Model and Empirical Analysis

We develop a mathematical model for determining the interest rate applied by a financial institution. Our model mathematically isolates the four main components of the total cost of credit, including net operating costs, weighted average cost of financial resources, cost of risk and weighted cost of equity. Our equations enable to determine the floor interest rate, which is the minimum interest rate that a financial institution should set in order for its credit operations to be profitable. The results of the empirical analyses carried out over a 15-year period, from 2004 to 2018, corroborate the suggestions of our model that, interest rates follow the evolution of the floor interest rate. One of the contributions of our model is that the results can be useful in policies that seek to improve the credit conditions of financial institutions by reducing their credit costs rather than imposing low interest rates to them.

A microcredit contract model with a Black Scholes model under default risk

Microfinance has emerged as a new promise for alleviating poverty and improving the limited access to financial services by offering small loans, with no pledged collateral requirement, to the poor. Due to the unique features of microfinance, the credit-relationship between the lender and the borrower is considered to be the foundation of the business. Based on the concept of supply chain microfinance, this paper develops scenario-based stochastic microcredit contract models for a group case. In order to obtain a minimum interest rate, a Black-Scholes debt model estimates volatility directly from market observable returns on a borrower's equity. Next, incorporating the minimum interest rate, the stochastic microcredit models are developed to calculate a proper interest rate, while maintaining the financial sustainability of a corporation. The stochastic microcredit models also include financial statement analysis through financial ratios to reflect the microfinance business environment. Through the comparison of the effect of cash flow bullwhip, this study illustrates that the proposed model has the potential to decrease the bullwhip effect. By determining a proper interest rate in microcredit, the proposed models could be used by microfinance institutions as an effective credit risk tool.

Attitude of Women Cassava Farmers Towards Participation in Growth Enhancement Support Scheme in Oyo state, Nigeria

The study examined attitude of women cassava farmers towards the Growth Enhancement Support Scheme (GESS) in Oyo state. Three LGAs were purposively selected while random sampling was used to select 4 communities in each LGA with five respondents each using snowball method to give sample size of 180 respondents. Interview schedule was used for data collection and analysed using descriptive and inferential statistics. Results reveal that most of the respondents (67.8%) were within 31-50years of age, married (90.0%), literate (57.8%) with open market (x=1.98) and middlemen (x=1.78) being the preferred sources of inputs. More than half (52.7%) had over ten years of farming experience, 52.3% cultivated above 6 acres, 68.3% had high level of participation in GESS while 63.3 had favourable attitude towards GESS. Inadequate finance (x=1.94) and high illiteracy (x=1.93 were the constraints to participation. Significant relationship exists between education (χ2=2.315, p=0.040), level of participation (r=0.258, p= 0.000), sources of input (r=0.223, p= 0.003), constraint to participation (r=0.424, p=0.000) and attitude towards GESS. Though, many respondents were unable to access agricultural inputs from redemption centers yet they had favourable attitude towards GESS. Proper inputs distribution mechanism to eliminate diversion and financial institution with minimum interest rate and collateral should be employed. Keywords : Growth enhancement support scheme, women cassava farmers, participation

A utility- and CPT-based comparison of life insurance contracts with guarantees

Abstract Some recent literature studies whether contracts including financial guarantees can be preferred by a utility-maximizing investor. The main result for contracts exposed solely to financial risk (e.g. Doskeland and Nordahl, 2008; Dichtl and Drobetz, 2011) is that expected utility theory (EUT) fails to interpret demand for guarantees, while cumulative prospect theory (CPT) is able to support the demand. While the development of the financial market has a significant impact on the portfolio choice, some other non-financial risk might play an important role too. In the present paper, we take life insurance products as an example, where the long term nature of these contracts places a special emphasis on the uncertain lifetime of the investor. We incorporate the mortality risk and investigate its effect on the attractiveness of contracts offering minimum interest rate guarantees to EUT- and CPT-investors. For this purpose, we introduce two approaches for the consideration of multiple risk sources within CPT. We illustrate the theoretical framework with numerous simulations and our numerical results show that a long-term risk-averse EUT-investor prefers products with guarantees.

A Proposal on How the Regulator Should Set Minimum Interest Rate Guarantees in Participating Life Insurance Contracts

AbstractWe consider a contingent claim model framework for participating life insurance contracts and assume a competitive market with minimum solvency requirements as provided by Solvency II. In a first step, the implications of the regulator's imposing a particular interest rate guarantee on the insurer's asset allocation are analyzed in a reference situation. We study the sensitivity of the interaction between the interest rate guarantee and the asset allocation when the risk‐free interest rate changes. Particular attention is paid to the current market situation where the guaranteed interest rate is often close to the risk‐free interest rate. In a second step, we assess at what level the interest rate guarantee should be set by the regulator in order to maximize policyholders' utility. We show that the results yielded by the proposed concept to derive an optimal value for the interest rate guarantee are very stable for various model parameters.

Variable annuities and the option to seek risk: Why should you diversify?

We analyze the impacts of an additional rider incorporated in recent retirement products. The payoff is linked to the performance of a multi asset investment strategy and includes a minimum interest rate guarantee. In addition, the buyer receives the option to decide on the investments dynamically. Prominent examples are so called variable annuities. Due to the embedded guarantee, these products are interesting for risk averse investors who benefit from diversification. However, the price setting of the provider takes into account the most risky strategy. This implies that the investor mitigates optimally between the diversification and the worst case strategy. We analyze the distortion and utility effects caused by the additional rider in the presence of background risk and borrowing constraints. A simulation analysis sheds light on the question if the additional rider is worth its costs.

Wprowadzenie Do Zarządzania Finansami Przedsiębiorstw (Introduction to Entrepreneurial Financial Management)

Wprowadzenie Do Zarządzania Finansami Przedsiębiorstw (Introduction to Entrepreneurial Financial Management)

Information and default in consumer credit markets: Evidence from a natural experiment

Despite the prominent role that information plays in the economic theory of credit markets, no direct evidence exists on the causal relationship between the availability of information about loan applicants and loan performance. This paper provides such evidence by exploiting an unanticipated change in the amount of information visible in an online market for loans to measure the impact of lender information on loan outcomes. Conditional on data available in both periods, allowing lenders to access more borrower credit information substantially reduced default rates among high-risk borrowers by 17 percentage points on average but had almost no effect on low-risk borrowers. Immediate lender returns increased by about 12 percentage points and took 5 weeks to decay. Among high-risk loans, returns converged within credit grade bins. Using panel information on lenders, I find that the information improved loan performance in two ways: first, it significantly improved the screening performed by lenders already active on the website. Second, it attracted new lenders who were better at screening loan applicants and earned higher returns. I test whether the reform resulted in selection among loan applicants using data that is unobserved by lenders in both periods. I find that there was no change in unobserved credit quality among loan applicants, but that the information improved lenders’ ability to select the (unobservably) higher quality borrowers from the pool of applicants. I also find suggestive evidence that lenders’ beliefs about loan applicants, as measured by the minimum interest rate at which they were willing to lend, converged.

Risk comparison of different bonus distribution approaches in participating life insurance

The fair pricing of explicit and implicit options in life insurance products has received broad attention in the academic literature over the past years. Participating life insurance (PLI) contracts have been the focus especially. These policies are typically characterized by a term life insurance, a minimum interest rate guarantee, and bonus participation rules with regard to the insurer’s asset returns or reserve situation. Researchers replicate these bonus policies quite differently. We categorize and formally present the most common PLI bonus distribution mechanisms. These bonus models closely mirror the Danish, German, British, and Italian regulatory framework. Subsequently, we perform a comparative analysis of the different bonus models with regard to risk valuation. We calibrate contract parameters so that the compared contracts have a net present value of zero and the same safety level as the initial position, using risk-neutral valuation. Subsequently, we analyze the effect of changes in the asset volatility and in the initial reserve amount (per contract) on the value of the default put option (DPO), while keeping all other parameters constant. Our results show that DPO values obtained with the PLI bonus distribution model of Bacinello (2001), which replicates the Italian regulatory framework, are most sensitive to changes in volatility and initial reserves.

Analytical Pricing of An Insurance Embedded Option: Alternative Formulas and Gaussian Approximation

Analytical pricing of a double-trigger option with the Black-Scholes-Vasicek ( BSV ) state price deflator is considered. In the context of market-consistent valuation of insurance liabilities, the option appears as embedded option of index-linked endowment policies that provide combined protection against inflation and a minimum interest rate guarantee by death. A first analytical pricing formula in terms of the standard bivariate normal distribution is derived. Then, using alternatively the canonical BSV deflator, a second integral representation is derived. Based on an elementary Gaussian integral in three variables a third integral decomposition is obtained and approximated by closed-form Gaussian expressions using a simple approximation by Lin of the normal tail probability integral. Similarly to the invariance of the Black-Scholes and Margrabe formulas with respect to the market prices of the risk factors, two of the alternative double-trigger option pricing formulas and the proposed Gaussian approximation also share this property. A numerical example rounds up the analysis by showing accuracy of the Gaussian approximation within some few negligible basis points.

Variable Annuities and the Option to Seek Risk - Why Should You Diversify?

We analyze the impacts of an additional rider which is incorporated in recent retirement planning products. The payoff of these products is linked to the performance of a multi asset investment strategy and includes a minimum interest rate guarantee on the contributions.In addition, the buyer receives the option to decide on the investments dynamically. Prominent examples are so called variable annuities, in particular guaranteed minimum accumulation benefits (GMABs). Due to the embedded guarantee, these products are interesting for risk averse investors who, in general, benefit from diversification. However, to stay on the safe side the price setting of the provider must take into account the most risky strategy.This implies that the investor mitigates optimally between the diversification and the worst case strategy. We analyze the distortion and utility effects caused by the additional rider in the presence of background risk and borrowing constraints. A simulation analysis sheds light on the question if the additional rider is worth its costs. We take account of the utility gained by the possibility to adapt to individual preferences and changing personal pension situations. In particular, we illustrate to what extent these gains can compensate the utility loss caused by the upper price setting due to the worst case strategy.