María del Carmen Valls Martínez

Progressive Current Accounts: Profit-Sharing Interest

Certain financial investments have different profitabilities according to the invested capital. In particular, there are some bank transactions, such as progressive current accounts, which discriminate nominal rates of interest, depending on the invested sums, that is, transactions whose underlying financial laws are not homogeneous of the first degree with respect to the amounts. More specifically, this discrimination occurs when assigning an equal rate to the capitals C in the same interval ]Ci,Ci+1]. This makes the financial law discontinuous with finite jumps, once the term has been fixed. Of course, it would be convenient, for a group of investors, to join their savings because greater rates of interest can be obtained. The question is how to distribute, in a rational way or with equity, among the individual agents, the interest obtained jointly. Our findings are based on a progressive sharing, using differential calculus.

INCREASING SPOT RATES OF INTEREST: STRUCTURE OF THE PRICE OF A DEFAULT FREE DISCOUNT BOND

This paper aims to establish a set of necessary and sufficient conditions that the expression of a default free bond must verify in a situation in which spot rates of interest increase. In this case, if the agent divides the period of his investment, that is, if he disinvests and, immediately, re-invests his capital in different issues of bonds, can obtain an advantage in the final amount. In order to do this, necessary conditions include an approximation of the forward interest rate, that is to say the logarithmic density, its limits to +∞ and -∞ and the second generalized derivative of the bond price. Sufficient conditions involve an auxiliary function using these limits and, finally, necessary and sufficient conditions are related with the logarithm of the bond price.

Un modelo de asignación de costes compartidos en situaciones de economías de escala

RESUMEN Determinados gastos de una empresa (limpieza, electricidad o renting, por ejemplo) tienen u ofrecen descuentos crecientes en función del volumen contratado. Este hecho hace pensar en la posibilidad de que varias empresas, o secciones dentro de una misma empresa, contraten conjuntamente estos servicios con el fin de aprovechar las economías de escala que surgen. El problema se plantea cuando hay que repartir de forma racional el coste total entre las empresas o secciones generadoras de dicho gasto. Habitualmente los descuentos o bonificaciones ofertadas van creciendo por tramos, lo que dificulta el planteamiento de una metodología, porque generalmente cualquier sistema de reparto se basa en una función continua. Para ello, se utiliza el cálculo infinitesimal. El objetivo de este trabajo es ofrecer un método que permita distribuir costes de forma equitativa, resolviendo incluso situaciones en las que la función que da el coste sea discontinua con un número finito de saltos.

Análisis de viabilidad de la banca ética en España a través de Triodos Bank. Comparativa económico-financiera con la banca tradicional

Ethical Banking is the answer to decades of financial speculation and investments away from an ethical and cooperative commitment of traditional banking. It is the necessary instrument to manage the banking business from transparency with social and environmental codes, without forgetting the economic profitability to resist and remain in a demanding financial system. The purpose of this paper, on the one hand, is to study the origin and characteristics of ethical banking, which, although not unconnected with economic downturns, makes it an alternative to dependence on the traditional banking sector; and, on the other hand, to examine the conditions and initiatives that Triodos Bank performs to position itself as a leading bank with ethical values and, in turn, to compare its results with those obtained by the main financial entities of conventional banking.

Loan transactions associated to continuous distributions of capital

The objective of this paper is to design a loan repayment plan adapted to the financed company with the aim to avoid a possible situation of illiquidity. More specifically, in this paper the sequence of payments which amortizes a loan is determined according to the distribution of the future income expected by the borrower. To do this, we will start from the concept of a continuous distribution of capital or, equivalently, a continuous annuity. The continuous distribution of capital will be derived from a continuous distribution of probability, to then obtain a discrete annuity which fits the future income of the debtor. On the other hand, it is noteworthy the analysis of the particular case of financial transactions with interest periods of different amplitude, which can facilitate the adjustment of the sequence of instalments to the timing of the real income of the borrower in loan transactions.

Savings operations over random periods

Due to the ageing of the population, public pension plans are increasingly being implemented by private savings schemes. This therefore gives rise to a wide range of innovative schemes to meet the varying needs of savers and financial institutions. Therefore, the aim of this paper is to propose a savings operation which includes the randomness derived from the contingency which supposes the eventual but unpredictable death of the saver. We have developed this type of operation by applying a financial-actuarial methodology and thereby deducing a way of calculating all amounts resulting from the savings operation, and introducing a new quantity derived from this randomness, namely the risk quota. Similarly, we have indicated how to calculate different measures of (gross and net) profitability, in random terms and the part corresponding to this randomness.

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.

SOME MATHEMATICAL PROPERTIES OF THE PRICE OF AN ARBITRAGE PROFITABLE RISKLESS BOND

It is well known that a discounting function describes the price of a default free bond. In this paper, some mathematical properties of this function are studied when it is subadditive. Subadditive discounting means that the total discount is minor when the year is divided into months and implies that the more divided the interval is into subintervals, the smaller the total discount will be. First, two sufficient conditions for a discounting function being subadditive (resp. superadditive) are shown; more precisely, the increase (resp. decrease) of the instantaneous discount rate and certain integral inequality are proposed as such sufficient conditions. On the other hand, the convexity (resp. concavity) of the Napierian logarithm of the discounting function is shown as a particular case of another more general sufficient condition. Finally, under certain conditions, subadditive discounting functions are necessarily regular.