Simple Formulas to Option Pricing and Hedging in the Black- Scholes Model

For option whose striking price equals the forward price of the underlying asset, the Black-Scholes pricing formula can be approximated in closed-form. A interesting result is that the derived equation is not only very simple in structure but also that it can be immediately inverted to obtain an explicit formula for implied volatility. In this contribution we present and compare the accuracy of three of such approximation formulas. The numerical analysis shows that the first order approximations are close only for small maturities, Polya approximations are remarkably accurate for a very large range of parameters, while logistic values are the most accurate only for extreme maturities.Option pricing; hedging; Taylor, Polya and logistic approximations

An efficient binomial approach to the pricing of options on stocks with cash dividends

In this contribution, we consider options written on stocks which pay cash dividends. Dividend payments have an effect on the value of options: high dividends imply lower call premia and higher put premia. While exact solutions to problems of evaluating both European and American call options and European put options are available in the literature, for American-style put options early exercise may be optimal at any time prior to expiration even in the absence of dividends. In this case numerical techniques, such as lattice approaches, are required. Discrete dividends produce a shift in the tree; as a result, the tree is no longer reconnecting beyond any dividend date. Methods based on non-recombining trees give consistent results, but they are computationally expensive. We analyze binomial algorithms and performed some empirical experiments.Options on stocks, discrete dividends, binomial lattices

Simulation techniques for generalized Gaussian densities

This contribution deals with Monte Carlo simulation of generalized Gaussian random variables. Such a parametric family of distributions has been proposed in many applications in science to describe physical phenomena and in engineering, and it seems also useful in modeling economic and financial data. For values of the shape parameter a within a certain range, the distribution presents heavy tails. In particular, the cases a=1/3 and a=1/2 are considered. For such values of the shape parameter, different simulation methods are assessed.Generalized Gaussian density, heavy tails, transformations of rendom variables, Monte Carlo simulation, Lambert W function

Cumulative prospect theory and second order stochastic dominance criteria: an application to mutual funds performance

In this note using the rules of stochastic dominance of the second order and the recent cumulative prospect theory for classified, according to their performance, a set of common funds. The criteria used are closely linked to the preferences of decision maker and refer to either hypothesis of aversion and of seeking to risk both hypothesis on the sign of derived second of the function which characterizes the losses and gains.

Marine Heatwaves in the Chesapeake Bay

Prolonged events of anomalously warm sea water temperature, or marine heatwaves (MHWs), have major detrimental effects to marine ecosystems and the world\u27s economy. While frequency, duration and intensity of MHWs have been observed to increase in the global oceans, little is known about their potential occurrence and variability in estuarine systems due to limited data in these environments. In the present study we analyzed a novel data set with over three decades of continuous in situ temperature records to investigate MHWs in the largest and most productive estuary in the US: the Chesapeake Bay. MHWs occurred on average twice per year and lasted 11 days, resulting in 22 MHW days per year in the bay. Average intensities of MHWs were 3°C, with maximum peaks varying between 6 and 8°C, and yearly cumulative intensities of 72°C × days on average. Large co-occurrence of MHW events was observed between different regions of the bay (50–65%), and also between Chesapeake Bay and the Mid-Atlantic Bight (40–50%). These large co-occurrences, with relatively short lags (2–5 days), suggest that coherent large-scale air-sea heat flux is the dominant driver of MHWs in this region. MHWs were also linked to large-scale climate modes of variability: enhancement of MHW days in the Upper Bay were associated with the positive phase of Niño 1+2, while enhancement and suppression of MHW days in both the Mid and Lower Bay were associated with positive and negative phases of North Atlantic Oscillation, respectively. Finally, as a result of long-term warming of the Chesapeake Bay, significant trends were detected for MHW frequency, MHW days and yearly cumulative intensity. If these trends persist, by the end of the century the Chesapeake Bay will reach a semi-permanent MHW state, when extreme temperatures will be present over half of the year, and thus could have devastating impacts to the bay ecosystem, exacerbating eutrophication, increasing the severity of hypoxic events, killing benthic communities, causing shifts in species composition and decline in important commercial fishery species. Improving our basic understanding of MHWs in estuarine regions is necessary for their future predictability and to guide management decisions in these valuable environments

Anthropogenic influences in a lagoonal environment: a multiproxy approach at the valo grande mouth, Cananéia-Iguape system (SE Brazil)

The Cananéia-Iguape system, SE Brazil, consists of a complex of lagoonal channels, located in a United Nations Educational, Scientific and Cultural Organization (UNESCO) Biosphere Reserve. Nevertheless, important environmental changes have occurred in approximately the last 150 yrs due to the opening of an artificial channel, the Valo Grande, connecting the Ribeira de Iguape River to the lagoonal system. Our objective is to assess the historical record of the uppermost layers of the sedimentary column of the lagoonal system in order to determine the history of environmental changes caused by the opening of the artificial channel. In this sense, an integrated geochemical-faunal approach is used. The environmental changes led significant modifications in salinity, in changes of the depositional patterns of sediments and foraminiferal assemblages (including periods of defaunation), and, more drastically, in the input of heavy metals to the coastal environment. The concentrations Pb in the core analyzed here were up to two times higher than the values measured in contaminated sediments from the Santos estuary, the most industrialized coastal zone in Brazil.O sistema Cananéia-Iguape (Sudeste do Brasil), consiste em um complexo de canais lagunares localizados no interior de uma Reserva da Biosfera (assim definida pela UNESCO). Não obstante, variações ambientais importantes ocorreram nos últimos 150 anos, devido à abertura de um canal artificial, o Valo Grande, conectando o Rio Ribeira de Iguape ao sistema lagunar. O objetivo deste trabalho foi determinar a história das variações ambientais no sistema lagunar, causadas pela abertura do canal artificial, através da análise das camadas superiores da coluna sedimentar de um testemunho coletado no sistema. Neste sentido, uma abordagem integrada, envolvendo variações geoquímicas e faunísticas foi utilizada. As variações ambientais ocorridas apontam para mudanças drásticas na salinidade, nos padrões de sedimentação, nas associações de foraminíferos (incluindo períodos azóicos) e, mais drasticamente, no aporte de metais para o sistema costeiro. As concentrações de Pb no testemunho coletado indicam valores duas vezes maiores do que os medidos em sedimentos contaminados do estuário de Santos, situado na zona costeira mais industrializada do Brasil.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP