Ana María Sánchez Pérez

Expected Present and Final Value of an Annuity when some Non-Central Moments of the Capitalization Factor are Unknown: Theory and an Application using R

The aim of this chapter is the development of three approaches for obtaining the value of an n-payment annuity, with payments of 1 unit each, when the interest rate is random. To calculate the value of these annuities, we are going to assume that only some non-central moments of the capitalization factor are known. The first technique consists in using a tetraparametric function which depends on the arctangent function. The second expression is derived from the so-called quadratic discounting whereas the third approach is based on the approximation of the mathematical expectation of the ratio of two random variables by Mood et al. (1974). A comparison of these methodologies through an application, using the R statistical software, shows that all of them lead to different results.

Assessing the Option to Abandon an Investment Project by the Binomial Options Pricing Model

Usually, traditional methods for investment project appraisal such as the net present value (hereinafter NPV) do not incorporate in their values the operational flexibility offered by including a real option included in the project. In this paper, real options, and more specifically the option to abandon, are analysed as a complement to cash flow sequence which quantifies the project. In this way, by considering the existing analogy with financial options, a mathematical expression is derived by using the binomial options pricing model. This methodology provides the value of the option to abandon the project within one, two, and in general periods. Therefore, this paper aims to be a useful tool in determining the value of the option to abandon according to its residual value, thus making easier the control of the uncertainty element within the project.

A Time-Perception Approach for the Treatment of Risk in Projects Appraisal

This paper presents a novel methodology to introduce the risk in the valuation of random investment projects. Traditionally, a constant risk‐adjusted premium has been added up to the interest rate to include the uncertainty associated with the project. Nevertheless, this method is not objective because the choice of this parameter is not directly identified with a risk measure inherent to the project. Our approach is based on a model that describes the perception that the lender (supplier) has about the expected time to obtain the payment of debts (which will be identified with the cash flows). Thus we will be able to eliminate the subjectivity of traditional valuation methods when considering the risk in investment projects.

The Magnitude and “Peanuts” Effects: Searching Implications

The framework of this paper is the field of decision-making processes in which people face the choice between probabilistic and dated rewards. Traditionally, the preferences for probabilistic outcomes have been analyzed by the Expected Utility (EU) model whilst the preferences for dated rewards have been studied by the Discounted Utility (DU) model. Nevertheless, recent empirical findings have revealed the existence of several anomalies or paradoxes in both contexts. Specifically, EU and DU models exhibit an anomaly affecting the amount of the reward, viz the “peanuts” and the magnitude effects, respectively, which seem to go in opposite directions. The aim of this paper is to analyze both effects jointly in a wide setting involving choices subject to risk and over a period of time, and thereby identify and consider the implications of one anomaly on the other.

Boundary Conditions of Options: A Demonstration Based on the Stochastic Discount

Abstract The aim of this paper is to provide a proof of the generally accepted boundary conditions of (call and put) financial options from a novel point of view. To do this, we will use an auxiliary discounting function which will be defined in this work. However, the financial options are derivative instruments whose function is risk hedging in contexts of uncertainty, whereby the employed discount function will be necessarily stochastic. More specifically, we will apply the classic properties of the magnitude “discount” to the so-defined discount function to obtain, in a natural way, the noteworthy boundary conditions of financial options. It is well-known that financial options (belonging to the field of stochastic finance) have been studied without any relation with the magnitude “discount” (more characteristic of the classic Financial Mathematics). Consequently, the principal contribution of this work is the construction of a stochastic discount function as a bridge connecting its associated discount and the financial options, being demonstrated that their properties can be mutually derived.

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.