Testing option pricing with the Edgeworth expansion

There is a well-developed framework, the Black-Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying asset is a Gaussian distribution. However, it is observed in the market that this hypothesis is flawed, leading to the introduction of a fudge factor, the so-called volatility smile. Therefore, it would be interesting to explore extensions of the Black-Scholes theory to non-Gaussian distributions. In this paper, we provide an explicit formula for the price of an option when the distributions of the returns of the underlying asset is parametrized by an Edgeworth expansion, which allows for the introduction of higher independent moments of the probability distribution, namely skewness and kurtosis. We test our formula with options in the Brazilian and American markets, showing that the volatility smile can be reduced. We also check whether our approach leads to more efficient hedging strategies of these instruments. (C) 2004 Elsevier B.V. All rights reserved.

The influence of the region between residues 220 and 344 and beyond in Phrixotrix railroad worm luciferases green and red bioluminescence

To find the regions having a major influence on the bioluminescence spectra of railroad worm luciferases, we constructed new chimeric luciferases switching the fragments from residues 1-219 and from 220-545 between Phrixotrix viviani (PxvGR; λmax = 548 nm) green light-emitting luciferase and Phrixothrix hirtus (PxhRE; λmax = 623 nm) red light-emitting luciferases. The emission spectrum (λmax = 571 nm) and KM for luciferin in the chimera PxRE220GR (1-219, PxhRE; 220-545, PxvGR) suggested that the region above residue 220 of PxvGR had a major effect on the active site. However, switching the sequence between the residues 226-344 from PxvGR luciferase into PxhRE (PxREGRRE) luciferase resulted in red light emission (λmax = 603 nm), indicating that the region 220-344 by itself does not determine the emission spectrum. Furthermore, the sequence before residue 220 of the green-emitting luciferase is incompatible for light emission with the sequence above residue 220 of PxhRE. These results suggest that the fragments before and after residue 220, which correspond to distinct subdomains, may fold differently in the green- and red-emitting luciferases, affecting the active site conformation.

Efeito da ingestão crônica de álcool na progressão de periodontite induzida em ratos da linhagem Fischer-344

Objective: Understand the effect of chronic alcohol on the progression of periodontitis induced in Fischer-344 rats. Methods: For the study, 22 Fischer-344 rats, two months old were used, divided into groups: alcohol (n=8), ligature (n=7) and control (n=7). On the first day, the animals in the alcohol group were exposed to ingestion of a water solution containing 20% alcohol (size/size), up to day 90. After thirty days from the beginning of the experiment, the animals in the alcohol group and the ligature group were submitted to the placement of a silk thread around the right maxillary second molar. Nothing was performed on the left side, serving as control. All the groups were submitted to euthanasia 60 days after ligature placement. To assess the destruction of periodontitis, a radiographic exam was used to measure the destruction of bone height. Results: The results of the study showed that on the side in which periodontitis was induced, the group that ingested alcohol suffered an increase in destruction, with statistical differences when compared with the ligature and control groups and increased bone destruction in the ligature group when compared to control. Conclusion: Within the limitations of the study, it was concluded that chronic alcohol consumption by Fischer-344 rats led to greater progression of induced periodontitis.