The short‐time behavior of VIX‐implied volatilities in a multifactor stochastic volatility framework

We consider a modeling setup where the volatility index (VIX) dynamics are explicitly computable as a smooth transformation of a purely diffusive, multidimensional Markov process. The framework is general enough to embed many popular stochastic volatility models. We develop closed‐form expansions and sharp error bounds for VIX futures, options, and implied volatilities. In particular, we derive exact asymptotic results for VIX‐implied volatilities, and their sensitivities, in the joint limit of short time‐to‐maturity and small log‐moneyness. The expansions obtained are explicit based on elementary functions and they neatly uncover how the VIX skew depends on the specific choice of the volatility and the vol‐of‐vol processes. Our results are based on perturbation techniques applied to the infinitesimal generator of the underlying process. This methodology has previously been adopted to derive approximations of equity (SPX) options. However, the generalizations needed to cover the case of VIX options are by no means straightforward as the dynamics of the underlying VIX futures are not explicitly known. To illustrate the accuracy of our technique, we provide numerical implementations for a selection of model specifications.     

Small local firms inside the supply chain: Challenges and perspectives

The authors provide the results of an empirical research carried out in north-east Italy and completed in 1992, which was aimed at investigating the rapport between large manufacturers operating on the multidomestic and global markets and the small local supplying concerns. This research identifies that the globalization process has had a strong impact in the relations with suppliers. The purchasing firms have adopted a particular approach when selecting the suppliers. This has involved widening their previous geographic areas of contact, even making use of foreign sources. Consequently, the local micro units either will become excluded from future business relations with the purchasing organizations, or will be relegated into lower levels of the supply chain. Today small and very small units working as suppliers with direct link with large-scale clients, face many challenges: they should now renew their know-how and skills, develop a new managerial and organizational sense, and recognise the need to invest in new forms other than machinery and processes. The empirical study clearly showed both the limits and the structural weakness of such small units and provided some indications for growth in their technical-productive potential.     

Markups,import competition and exporting

This paper analyses the relationship between markups and international trade at the firm level using a large sample of French manufacturing firms for the period 1995–2007. In particular, the paper investigates the effect of increasing import competition from China on firms' price–cost margins and the way in which exporting interacts with this effect. The results show robust evidence that firms in more direct competition with Chinese imports decrease their markups. However, firms that become exporters experience a smaller reduction in their price–cost margins. Consistent with these findings, the results also show that firms facing tougher competition from China are more likely to start exporting to avoid such competitive pressures.     

The effects of social media on brand attitude and WOM during a brand crisis: Evidences from the Barilla case

Brand crises endanger companies. Social media are a key platform where stakeholders elaborate and react to crises. This research explores whether social media audience and traditional mass media audience react differently to a brand crisis in terms of their (1) attitude towards the brand and (2) word-of-mouth (WOM). As to the brand attitude, we argue that stakeholders mainly exposed to the brand crisis via social media have a more negative reaction towards the brand compared to those who are principally exposed via traditional media. As to the behaviour, we posit that social media exposure intensifies WOM. By analysing the Barilla crisis, the findings suggest that the social media act as ‘multipliers’ of the reaction of stakeholders to a brand crisis.     

Innovation and Development: The Evidence From Innovation Surveys

In this article we investigate the existing evidence on innovation produced by innovation surveys in developing and emerging countries in Europe, Asia, Africa, and Latin America. We review the relevant literature, discuss methodological issues, and analyze the results for the countries with the most comparable surveys, considering the well-established findings of innovation surveys for Europe as a benchmark. From the evidence we considered, regional patterns are identified and some stylized facts on innovation and development are proposed, pointing out the specificity of innovation processes in economies engaged in industrialization and catching up.     

Feeding management of dairy cattle affect grassland dynamics in an alpine pasture

The effect of different supplementary feeding rates for grazing cattle on high-altitude pastures dynamics was evaluated. A field experiment was carried out during three years in a subalpine pasture area of the Eastern Alps. The investigated pasture area was 40?ha, located between 1820 and 2230?m?a.s.l. Two paddocks were chosen in the experiment and two herds of 12 cattle each were kept in the two enclosures for 5 weeks. For the first herd (HS), the supplementary feeding rate was 4.8?kg?OM?head^?1 per day, while for the second herd (LS), the rate was 1.6?kg?OM?head^?1 per day. The amount of herbage consumed by each cattle was determined using the n-alkane technique. To monitor the pasture vegetation dynamics, eight metal exclusion cages were placed in each paddock to determine herbage growth, utilization rates, vegetation composition and animal grazing selectivity. Grazing behaviour of dairy cattle, in terms of herbage intake and species selection was affected by the different feeding rates. Cattle grazing Paddock HS consumed 1.9?kg?OM?day^?1 of herbage less than Paddock LS. In the LS paddock, cattle grazed higher phytomass rates. When the animals were fed by higher concentrate rates, a more selective grazing seemed to significantly increase the pasture necromass component. The lower grazing selectivity favoured the development of species as Nardus stricta and Deschampsia caespitosa, which are well known for their low palatability. Distinct vegetation dynamic patterns were observed, with a reduction of hair grass and an increase of legumes in the Paddock LS.     

Pricing Policy and Partial Collusion

We study the pricing policy equilibria emerging in a partial collusion duopolistic framework where firms in the first stage of the game choose non-cooperatively the pricing strategy (perfect price discrimination or uniform pricing), and from the second stage onward collude on prices. We show that for intermediate discount factors and high firms’ asymmetry, the unique equilibrium is characterized by only the smaller firm choosing price discrimination. In the case of intermediate discount factors and low firms’ asymmetry, there are two possible equilibria: both firms price discriminate or no firm price discriminates. When the discount factor is particularly high or particularly low both firms price discriminate in equilibrium.     

Diversification Strategies and Corporate Coherence Evidence from Italian Leading Firms

This paper investigates the determinants of coherence and coherence change usinga sample of Italian leading firms in the period 1993–1996. Consistently with thehypotheses advanced by Teece et al. (1994), the econometric analysis highlightsthat relatedness between pairs of sectors and coherence of diversification strategiesare higher when firms are active in sectors sharing similar technological and marketingcharacteristics, and when they are positioned at different stages of the productive chain.Moreover, the findings that firms which enter the group of top 5 industry leaders aremore coherent than the average and that coherence is increasing for firms active insectors more sensitive to EU integration are consistent with the prediction that coherentfirms tend to outperform less coherent ones and that coherence is increasing in morecompetitive environments. Finally, the results show that a deepening of vertical integration strategies is good for coherence change, while an increase of diversification brings a reduction in coherence.     

Geodesics on the equilibrium manifold

We show the existence of a Riemannian metric on the equilibrium manifold such that a minimal geodesic connecting two (sufficiently close) regular equilibria intersects the set of critical equilibria in a finite number of points. This metric represents a solution to the following problem: given two (sufficiently close) regular equilibria, find the shortest path connecting them which encounters the set of critical equilibria in a finite number of points. Furthermore, this metric can be constructed in such a way to agree, outside an arbitrary small neighborhood of the set of critical equilibria, to any given metric with economic meaning.     

Notes and Comments: An approximation of caplet implied volatilities in Gaussian models

Abstract It is market practice to quote interest rate derivatives traded “over the counter” in terms of their implied volatility. For this reason, the term structure of at-the-money cap volatilities as well as the volatility surface of at-the-money swaptions are directly observed. This paper analyzes the case of caps. Any analysis of these markets would most likely report two main facts. The first is that the level of the volatility is inversely related to the level of the interest rates. The second is that the term structure is either a decreasing or a humped function of maturity. For a reference, see Rebonato (2003) and Brigo and Mercurio (2001). Rebonato (2003) suggests that the structure of implied volatility is humped in periods of normal market conditions and decreasing when markets are “excited”. Interpreting and explaining such phenomena is indeed an interesting and important issue. Mathematics Subject Classification (2000): 91B70 Journal of Economic Literature Classification: E43, C13