The exact Taylor formula of the implied volatility

In a model driven by a multidimensional local diffusion, we study the behavior of the implied volatility \({\sigma}\) and its derivatives with respect to log-strike \(k\) and maturity \(T\) near expiry and at the money. We recover explicit limits of the derivatives \({\partial_{T}^{q}} \partial_{k}^{m} \sigma\) for \((T,x-k)\) approaching the origin within the parabolic region \(|x-k|\leq\lambda\sqrt{T}\), with \(x\) denoting the spot log-price of the underlying asset and where \(\lambda\) is a positive and arbitrarily large constant. Such limits yield the exact Taylor formula for the implied volatility within the parabola \(|x-k|\leq\lambda\sqrt{T}\). In order to include important models of interest in mathematical finance, e.g. Heston, CEV, SABR, the analysis is carried out under the weak assumption that the infinitesimal generator of the diffusion is only locally elliptic.     

A PANEL DATA APPROACH TO THE BEHAVIOURAL EQUILIBRIUM EXCHANGE RATE OF THE ZAR

The question of currency over- or undervaluation is often asked and implies the existence of an equilibrium exchange rate (EER). The aim of this research was to determine the long-term EER of the South African rand using the behavioural equilibrium exchange rate (BEER) methodology. This paper used a panel of data from South Africa's main trading partners to estimate the relationship between the EER and its fundamental determinants using dynamic ordinary least squares (OLS) and fully modified OLS. The average coefficients obtained describe the long-term behaviour of the individual countries' real exchange rates. Substituting the observed fundamental time series into the estimated equation derives the EER for each country and over- and undervaluation can be determined. The results indicated that the fundamental value of the exchange rate was driven by economic growth, the openness of the economy, its foreign reserves, the real gold price and capital expenditure. The exchange rate also fluctuated considerably around its equilibrium level but there is not long sustained periods of over- and undervaluation.     

Will the DSM Strategy Spur Innovation?

In summary, the DSM strategy appears laudable and overall very comprehensive. However, its impact will depend on whether the Commission manages to create a more suitable environment for innovation and entrepreneurship by upgrading skills, promoting more adaptive rulemaking, empowering end user choice, and avoiding rules that are hostile to innovation, such as excessive restrictions to text and data mining and the extension of obsolete rules to OTTs.     

Entrepreneurial attributes of human capital and contingency factors in the culinary tourism

This article analyses fuzzy and crisp set qualitative comparative analyses (QCA) as an original method to model culinary tourism success and a number of entrepreneurial attributes of human capital and contingency factors. Human capital factors were general business training, specific training in food and drink hospitality, and previous experience as a business owner. Contingency factors were size of business (number of employees), restaurant location, and gender of the business owner. Restaurant success was measured by whether these restaurants had waiting lists.     

The pro-competitive effect of campaign limits in non-majoritarian elections

We study a model of elections in non-majoritarian systems that captures the link between competition in policies and competition in campaign spending. We argue that the overall competitiveness of the political arena depends on both the endogenous number of parties contesting the election and the endogenous level of campaign spending. These two dimensions are linked together through their combined effect on the total equilibrium level of political rents. We illustrate the key insights of the model with an analysis of the competitive effects of campaign spending limits. We show that under some conditions spending caps can be pro-competitive, leading to an increase in the number of parties contesting the elections.