Algebraic Properties of Arbitrage: An Application to Additivity of Discount Functions

Background: This paper aims to characterize the absence of arbitrage in the context of the Arbitrage Theory proposed by Kreps (1981) and Clark (2000) which involves a certain number of well-known financial markets. More specifically, the framework of this model is a linear (topological) space X in which a (convex) cone C defines a vector ordering. There exist markets for only some of the contingent claims of X which assign a price pi to the marketed claim mi . The main purpose of this paper is to provide some novel algebraic characterizations of the no arbitrage condition and specifically to derive the decomposability of discount functions with this approach. Methods: Traditionally, this topic has been focused from a topological or probabilistic point of view. However, in this manuscript the treatment of this topic has been by using purely algebraic tools. Results: We have characterized the absence of arbitrage by only using algebraic concepts, properties and structures. Thus, we have divided these characterizations into those concerning the preference relation and those involving the cone. Conclusion: This paper has provided some novel algebraic properties of the absence of arbitrage by assuming the most general setting. The additivity of discount functions has been derived as a particular case of the general theory

Combination of survival probabilities of the components in a system. An application to long-term financial valuation

The Net Present Value (NPV) is a well-known method to value an investment project. Nevertheless, this methodology exhibits a serious problem when the used discounting function decreases very rapidly, especially in (very) long-term projects, because the future cash-flows are not significant in the expression of the NPV. For this reason, this paper introduces a methodology to correct the discounting function used for valuing. To do this, a new operation between discounting functions is defined by reducing the (cumulative) instantaneous discount rate corresponding of the valuing discounting function with another appropriate discounting function. The result is a new discounting function which can be more adequate to value this class of investment projects

A Causal Analysis of Life Expectancy at Birth. Evidence from Spain

Background: From a causal point of view, there exists a set of socioeconomic indicators concerning life expectancy. The objective of this paper is to determine the indicators which exhibit a relation of causality with life expectancy at birth. Methods: Our analysis applies the Granger causality test, more specifically its version by Dumitrescu–Hurlin, starting from the information concerning life expectancy at birth and a set of socioeconomic variables corresponding to 17 Spanish regions, throughout the period 2006–2016. To do this, we used the panel data involving the information provided by the Spanish Ministry of Health, Consumer Affairs and Social Welfare (MHCSW) and the National Institute of Statistics (NIS). Results: Per capita income, and the rate of hospital beds, medical staff and nurses Granger-cause the variable “life expectancy at birth”, according to the Granger causality test applied to panel data (Dumitrescu–Hurlin’s version). Conclusions: Life expectancy at birth has become one of the main indicators able to measure the performance of a country’s health system. This analysis facilitates the identification of those factors which exhibit a unidirectional Granger-causality relationship with life expectancy at birth. Therefore, this paper provides useful information for the management of public health resources from the point of view of the maximization of social benefits

Life Expectancy at Birth in Europe: An Econometric Approach Based on Random Forests Methodology

The objective of this work is to identify and classify the relative importance of several socioeconomic factors which explain life expectancy at birth in the European Union (EU) countries in the period 2008–2017, paying special attention to greenhouse gas emissions and public environmental expenditures. Methods: The Random Forests methodology was employed, which allows classification of the socioeconomic variables considered in the analysis according to their relative importance to explain health outcomes. Results: Per capita income, the educational level of the population, and the variable AREA (which reflects the subdivision of Europe into four relatively homogeneous areas), followed by the public expenditures on environmental and social protection, are the variables with the highest relevance in explaining life expectancy at birth in Europe over the perip.1 he peusto el correo e inciod 2008–2017. Conclusions: We have identified seven sectors as the main sources of greenhouse gas emissions: Electricity, gas, steam, and air conditioning supply; manufacturing; transportation and storage; agriculture, forestry, and fishing; construction; wholesale and retail trade, repair of motor vehicles and motorcycles; and mining and quarrying. Therefore, any public intervention related to environmental policy should be aimed at these economic sectors. Furthermore, it will be more effective to focus on public programs with higher relevance to the health status of the population, such as environmental and social protection expenditures

Internet of Things and Their Coming Perspectives: A Real Options Approach

Internet of things is developing at a dizzying rate, and companies are forced to implement it in order to maintain their operational efficiency. The high flexibility inherent to these technologies makes it necessary to apply an appropriate measure, which properly assesses risks and rewards. Real options methodology is available as a tool which fits the conditions, both economic and strategic, under which investment in internet of things technologies is developed. The contribution of this paper is twofold. On the one hand, it offers an adequate tool to assess the strategic value of investment in internet of things technologies. On the other hand, it tries to raise awareness among managers of internet of things technologies because of their potential to contribute to economic and social progress. The results of the research described in this paper highlight the importance of taking action as quickly as possible if companies want to obtain the best possible performance. In order to enhance the understanding of internet of things technologies investment, this paper provides a methodology to assess the implementation of internet of things technologies by using the real options approach; in particular, the option to expand has been proposed for use in the decision-making process

A multifactor approach to the social discount rate

This work focuses on the appraisal of public and environmental projects and, more specifically, on the calculation of the social discount rate (SDR) for this kind of very long-term investment projects. As a rule, we can state that the instantaneous discount rate must be equal to the hazard rate of the public good or to the mortality rate of the population that the project is intended to. The hazard can be due to technical failures of the system, but, in this paper, we are going to consider different independent variables that can cause the hazard. That is, we are going to consider a multivariate hazard rate. In our empirical application, the Spanish forest surface will be the system and the forest fire will be the fail that can be caused by several factors. The aim of this work is to integrate the different variables that produce the fail in the calculation of the SDR from a multivariate hazard rate approach

Valuation of Barrier Options with the Binomial Pricing Model

Derivatives are products of different nature which are becoming increasingly common in financial markets. In certain cases, determining the assessment criteria can sometimes be a difficult task. Specifically, this paper focuses on one type of exotic option: the barrier option. This option has to satisfy some conceptual conditions which are specified at the time of its purchase and define its characteristics. In order to analyze this type of option more deeply, in this paper we choose a specific one, the so-called barrier option cap, whose value is going to be derived by the binomial pricing model

Relevance of financial information in quick loans negotiation

Nowadays, most loan transactions are contracted by using the exponential discounting as the underlying standard economic model to value this type of financial operations. In a framework of absence of fees to be paid by the borrower, the interest rate of the exponential discount function is, moreover, the true interest rate of the operation. Nevertheless, there exist a set of circumstances which make this identity false. Among others, these characteristics are: the use of linear discount as the underlying discount function, splitting time when using a nominal interest rate, and the existence of fees in a loan at 0% interest rate. All these cases will be analyzed in this paper in the context of the so-called quick loans

Approach of the value of an annuity when non-central moments of the capitalization factor are known: an R application with interest rates following normal and beta distributions

This paper proposes an expression of the value of an annuity with payments of 1 unit each when the interest rate is random. In order to attain this objective, we proceed on the assumption that the non-central moments of the capitalization factor are known. Specifically, to calculate the value of these annuities, we propose two different expressions. First, we suppose that the random interest rate is normally distributed; then, we assume that it follows the beta distribution. A practical application of these two methodologies is also implemented using the R statistical software

Loan Transactions with Random Dates for the First and Last Periodic Instalments

Usually, loan transactions contracted in practice are nonrandom; that is to say, all amounts received (principal) and paid (period instalments) by the borrower are previously agreed with the lender, as well as their respective dates. In this paper, two new alternative loan models are introduced, depending on whether the borrower survives or not to fulfil all repayment obligations. In this way, either the initial or the final date of repayments can be subject to this contingency. Additionally, the different parameters of such random transactions are determined, as well as several measures of profitability/cost for the lender/borrower, respectively. These transactions can be attractive for both the lender and the borrower, which therefore make them worthy of consideration and subsequent implementation for the benefit of both parties