HIGH‐ORDER SHORT‐TIME EXPANSIONS FOR ATM OPTION PRICES OF EXPONENTIAL LÉVY MODELS

The short‐time asymptotic behavior of option prices for a variety of models with jumps has received much attention in recent years. In this work, a novel second‐order approximation for at‐the‐money (ATM) option prices is derived for a large class of exponential Lévy models with or without Brownian component. The results hereafter shed new light on the connection between both the volatility of the continuous component and the jump parameters and the behavior of ATM option prices near expiration. In the presence of a Brownian component, the second‐order term, in time‐t, is of the form , with d₂ only depending on Y, the degree of jump activity, on σ, the volatility of the continuous component, and on an additional parameter controlling the intensity of the “small” jumps (regardless of their signs). This extends the well‐known result that the leading first‐order term is . In contrast, under a pure‐jump model, the dependence on Y and on the separate intensities of negative and positive small jumps are already reflected in the leading term, which is of the form . The second‐order term is shown to be of the form and, therefore, its order of decay turns out to be independent of Y. The asymptotic behavior of the corresponding Black–Scholes implied volatilities is also addressed. Our method of proof is based on an integral representation of the option price involving the tail probability of the log‐return process under the share measure and a suitable change of probability measure under which the pure‐jump component of the log‐return process becomes a Y‐stable process. Our approach is sufficiently general to cover a wide class of Lévy processes, which satisfy the latter property and whose Lévy density can be closely approximated by a stable density near the origin. Our numerical results show that the first‐order term typically exhibits rather poor performance and that the second‐order term can significantly improve the approximation's accuracy, particularly in the absence of a Brownian component.     

Testing Gibrat’s Law for Small, Young and Innovating Firms

This article analyses whether small, young, and innovating firms have experienced a greater employment growth than other Spanish firms over the period 1990–2000. The study draws upon a sample of 1272 manufacturing firms in which only 967 of the firms survived for the entire ten year period. The analyses test Gibrat’s law, both by least squares and by utilizing the procedure proposed by Heckman in which a probit survival equation is first estimated to correct for sample selection bias. Two estimators correcting for selection bias are utilized: one that incorporates the inverse Mill’s ratio and the other that employs maximum likelihood methods. All the results reject Gibrat’s law and support the proposition that small firms have grown larger. Additionally, the results show that old firms grow less than young ones, and innovating activity – both process and product – is a strong positive factor in the firm’s survival and its employment growth.     

Small businesses as a research subject: Some reflections on knowledge of small businesses and its effects on economic theory

Most economists agree in their view of small and medium-sized enterprises, or small businesses (SMEs), as a marginal scientific subject. They may go so far as to ignore them, either because they think these economic units do not lend themselves to conventional economic studies — studies which, for instance, take into account the sacred cow theory of economies of scale — or because they see them as being not really different from big businesses.However, at least a few economists have recognized, first, the many characteristics differentiating SMEs from big firms, and second, their increasing importance in terms of numbers and job creation within economies. Among these few, Schumpeter was one of the first to show the importance of entrepreneurs and SMEs as the main variable of change in an economy. Simon and Lucas also explained the difference between small and big firms through the differing abilities required by managers to run them. Penrose looked at the question from another point of view by highlighting the interstices taken up by SMEs to fulfil needs that cannot be fulfilled by bigger units. Critics of the theory of economies of scale showed that such economies may be offset by a number of diseconomies, thus justifying the efficiency of many SMEs. More recently, Mills and Schumann suggested that SMEs compensate for their lack of economies of scale by their production flexibility, particularly in today's turbulent economy.The limits of traditional economic theory are clearly demonstrated by the fact that it does not take account of all these theories, concepts and ideas. It thus neglects a number of important economic phenomena, including the persistence and current expansion of SMEs. Consideration of such phenomena may lead to the development of a new economic theory based on the concepts of instability and contingency, together with the behaviour of entrepreneurs and small firms, thus tending to contradict, in particular, the concept of equilibrium in conventional economic theory.A first version of this paper has been presented as invited speaker at the symposium of TETRA Group at Lyon, France, 30–31 May 1990. I thank the colleagues Fritz Rieger, Frances Solé Parrellada, Jacques Filion and the two referees for their very interesting suggestions on a preliminary second version.     

Empirical Findings on Business–Society Relations in Europe

Based on a theoretical exploration in a previous article, this paper empirically analyzes which issues of SD are taken into account by corporations and stakeholders in what way, and to what extent the concept of sustainable development (SD) can be achieved through stakeholder relations management (SRM) on the corporate level. An important basis for this empirical analysis is a referential framework, which specifies 14 issues of SD. In a first empirical step, the literature-based framework has been operationalized for the business world by analyzing sustainability reports. In a second empirical step, the operationalized framework served as the basis for a survey of selected MNCs. The analyses of the sustainability reports and the survey show how MNCs deal with particular issues of SD and what role they perceive particular stakeholders play. A key conclusion of the article is that SRM indeed promotes SD, but that it is no alternative to predictable government regulation.     

The Influence of Informality in a Local Agri-food Supply Chain in Brazil

During qualitative research on trust, conducted in a mariculture chain in southern Brazil, the theme of informality emerged spontaneously in most interviews. Although it is difficult to measure, some data and estimates point out that informality is still quite present worldwide, but especially in emerging and developing countries, and this situation was confirmed in the studied supply chain. In analysing the narratives, we noticed that this is a chronic issue which bothers the producers that are properly formalised mainly because of unfair competition, and hinders the organisation of the chain. Some factors foster the persistence of informality, such as family labour and temporary jobs, the low educational level of entrepreneurs, lack of adequate supervision and cultural aspects of producers and their families. We could corroborate the perspectives of modernisation (informality is still persistent), neo-liberal (informal entrepreneurs reject the bureaucracy of an over-regulated market) and post-structuralist (informality is a way of life related to identity, social position and/or resistance against the formal structure) theories. Our research has shown us that the situation found is contributing to a reduction in the number of formal producers and impairing the development of that local supply chain, as well as its sustainability.     

Endogenous direct advertising and price competition

This paper analyzes how the use of endogenous direct advertising affects the functioning of a horizontally-differentiated market. We formulate a two-stage game of pricing and informative advertising in which two firms, first, compete with mass advertising and, later, build a database using their historical sales records and compete by directly targeting the ads on their potential customers. We show that, compared to the case where firms only use mass advertising, direct advertising yields higher advertising efforts and an intertemporal reallocation of both market power and profits from the first to the second period. We also find that targeting increases the overall firms’ profit and the level of social welfare, but the impact on the average intertemporal price and consumer surplus is ambiguous. Finally, when reaching the potential market with mass advertising is sufficiently expensive, the use of direct advertising leads firms to provide the socially optimal level of advertising whereas, if mass advertising is cheap, firms tend to launch too little advertising in the first period and too much in the second.     

Size,R&D productivity and Decision Styles

We extend the size–innovation debate by incorporating decision-making style as a relevant factor in the innovation process. We propose that the size of firms affects the scale and quality of product innovation through the adoption of different decision-making styles. Using the literature on cognition, we conceptualize decision-making style as the degree to which firms rely on analytical information for decision making during the R&D process. Using longitudinal data of Spanish firms, we show that, as firms increase in size, they rely more extensively on analytical decision tools for the innovation activity. Additionally, we show that the size of firms is negatively related to product innovation productivity in terms of scale and positively related to the quality, and that these relationships are mediated by firms’ reliance on analytical decision-making style. We discuss theoretical and managerial implications for innovation research and practice.     

Is there a slowdown in agricultural productivity growth in South America?

This article estimates agricultural productivity growth in 10 South American countries in 1969–2009 with the objective of investigating if the slowdown being measured in other countries is present in the region. Results show that productivity growth accounts for half of the three‐fold increase in agricultural output during this period and that performance is sensitive to R&D investments in the sector. The slowdown found for the 1990s to 2000s in the U.S. and some European economies does not seem to be present yet in South America. The region's total factor productivity (TFP) growth rate increased steadily from 1.07% during the 1970s to 2.29% during the 2000s. Given lags in adoption and the adaptive nature of innovations in these economies, we have yet to see the potential effects in South American agriculture of decreases in R&D in advanced economies.     

Output gap in Brazil: a real-time data analysis

Recent literature for developed economies has shown that output gap estimates go through important revisions over time, impairing their reliability in real time. We organize a real-time data set for Brazil’s GDP and assess the revisions of the output gap estimated by four different methods. Similar to the findings of studies for developed economies, the output gap revisions in Brazil are substantial in all methods, with frequent changes in the output gap sign. In general, both the GDP data revision and the effect of adding new observations to the sample are relevant sources of output gap revisions. However, differently from those studies, we cannot assert that the latter source is preponderant.