Purpose -The purpose of this paper is to present an overview of weather derivatives markets and to highlight the importance of the contributing factors for weather risk management such as weather sensitivity, weather forecast, and economic growth. In this paper, the prospective of using weather derivatives in Portugal and why Portugal should use such instruments as well as the potential of Portugal's enterprises are presented. Design/methodology/approach -This paper attempts to distinguish the reasons for the appearance of a weather derivatives market and the growth potential of the European weather market. Findings -Successful development of a Portuguese weather derivatives market will require three things. For the successful development of weather derivatives market, a legal and economic framework is needed, as well as the development of new weather products, training of qualified specialists for working with these instruments and attracting companies interested in hedging their profits. A combination of these factors will help growth and will accelerate the development of a weather derivatives market in Portugal. Originality/value -The paper identifies some conditions that could allow the progress of the weather derivatives market in Portugal.

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This study develops a quasi-closed-form solution for the valuation of an American put option and the critical price of the underlying asset. This is an important area of research both because of a large number of transactions for American put options on different underlying assets (stocks, currencies, commodities, etc.) and because this type of evaluation plays a role in determining the value of other financial assets such as mortgages, convertible bonds or life insurance policies. The procedure used is commonly known as the method of lines, which is considered to be a formulation in which time is discrete rather than continuous. To improve the quality of the results obtained, the Richardson extrapolation is applied, which allows the convergence of the outputs to be accelerated to values close to reality. The model developed in this paper derives an explicit formula of the finite-maturity American put option. The results obtained, besides allowing us to quickly determine the option value and the critical price, enable the graphical representation—in two and three dimensions—of the option value as a function of the other components of the model.

The main objective of this study consists in developing a quasi-analytical solution for the valuation of commercial mortgages. We consider the existence of a single source of riskthe risk of defaulting on a mortgage -and therefore, the existence of a single state variable -the value of the mortgaged property. The value of the mortgage corresponds to the present value of the future payments on the loan, minus the value of the embedded American default option. The major difficulty in designing such a model consists in calculating the value of this option, since for that purpose it is necessary to determine the lowest property price below which it must be immediately exercised, i.e. the critical value of the property.Under such a framework, the partial differential equation for the value of the default option is that presented in Black and Scholes (1973). The boundary conditions applicable to the value of the default option are naturally different, given the possibility of early default. To obtain a quasi-closed form solution, instead of continuous time framework, a discrete time setting is considered for the differential equation -the "Method of Lines". The partial differential equation is transformed into an ordinary non-homogenous differential equation, replacing the derivative of the function [price of the option in relation to time] with a finite difference, and keeping the derivatives of the mortgaged property unchanged. In order to improve the performance of the model, Richardson's extrapolation is applied, allowing for the increase in the speed of convergence of the model results towards reasonable values.As compared to the alternative numerical valuation techniques, the proposed quasi-closed form solution provides much quicker mortgage valuation results and enhances the ability to perform the corresponding sensitivity analysis. The current work constitutes one of the first attempts to address the development of analytical solutions to mortgage valuation, using contingent claims analysis.

The main objective of this paper is to study how firm-specific factors affect the financial performance of tourism-related young small and micro-sized firms located in Algarve, Portugal, that started their activity during the last years of the debt crisis of Europe. The sample included 106 Portuguese small and micro-sized firms in the hospitality sector, established between 2012-2014, which remain active in 2019 and financial data from 2015 to 2018 was analysed. Descriptive statistics, group statistics, correlations, and regression model analyses were applied. The dependent variable representing profitability was the return on assets ratio (ROA). The independent variables were short-term, long-term and total debts, slack resources, sales growth, tangibility and size of the firm. A negative relationship between performance and long-term and short-term debts was found, confirming the theory that the most profitable firms tend to borrow less as they do not need external capital. Also, a negative relationship between ROA and tangibility was found, which means that as the level of tangible assets lessens, more intangible assets there are. These results give some hints to help tourism-related small and micro-sized firms located in Algarve take innovation, flexibility, and digitalisation strategies, particularly important during a pandemic crisis.