Option pricing and hedging with minimum local expected shortfall

We propose a versatile Monte-Carlo method for pricing and hedging options when the market is incomplete, for an arbitrary risk criterion (chosen here to be the expected shortfall), for a large class of stochastic processes, and in the presence of transaction costs. We illustrate the method on plain vanilla options when the price returns follow a Student-t distribution. We show that in the presence of fat-tails, our strategy allows to significantly reduce extreme risks, and generically leads to low Gamma hedging. Similarly, the inclusion of transaction costs reduces the Gamma of the optimal strategy.Comment: 23 pages, 7 figures, 8 table

Delta Hedged Option Valuation with Underlying Non-Gaussian Returns

The standard Black-Scholes theory of option pricing is extended to cope with underlying return fluctuations described by general probability distributions. A Langevin process and its related Fokker-Planck equation are devised to model the market stochastic dynamics, allowing us to write and formally solve the generalized Black-Scholes equation implied by dynamical hedging. A systematic expansion around a non-perturbative starting point is then implemented, recovering the Matacz's conjectured option pricing expression. We perform an application of our formalism to the real stock market and find clear evidence that while past financial time series can be used to evaluate option prices before the expiry date with reasonable accuracy, the stochastic character of volatility is an essential ingredient that should necessarily be taken into account in analytical option price modeling.Comment: Four pages; two eps figure

Effects of metronidazole and probiotics oligosaccharide on bacterial translocation in protein malnutrition

The present study aims to evaluate the effects of metronidazole, probiotics oligosaccharide on indigenous microflora and bacterial translocation (BT) in protein malnourished rats. Thirty male Wistarrats were divided into three groups: protein malnourished rats PM (group1, n = 10) were fed with maize only, protein malnourished rats (group 2, n = 10) were received metronidazole and protein malnourished rats (group 3, n = 10) were received both metronidazole and probiotics-oligosaccharide for fifteen days. Metronidazole (1000 mg/kg/day) was given via an orogastric feeding tube to the second and third groups. Lyophilized probiotics-oligosaccharide (0.5 mg/g body weight/day) was given in two doses via the same route to the third group. All animals were sacrificed after fifteen days of protein malnutrition and cultures of the mesenteric lymph nodes (MLNs), liver, spleen and cecal contents were done. Theincidence of bacterial translocation (BT) was 30% (3/10) in protein malnourished group 1,60% (06/10) in group 2 where protein malnutrition was associated with metronidazole and 25% (2.5/10) in group 3whose animals were subjected to protein malnutrition associated with metronidazole and probiotics oligosaccharide. A significant increase in the BT incidence was found in group 2 (P < 0.05), while a significant decrease was found in group 3 when compared to group 1. The total bacterial count of cecal flora was significantly low in group 3 than in group 1 (P < 0.01). These results suggest that the incidence of BT in protein malnutrition is increased by using an antibiotic while probioticsoligosaccharide decreases this incidence in protein malnutrition induced by antibiotic. Thus, weconclude that probiotics-oligosaccharide can effectively protect the intestinal mucosa and prevent BT in protein malnourished infants

Multifractal Properties of Price Fluctuations of Stocks and Commodities

We analyze daily prices of 29 commodities and 2449 stocks, each over a period of $\approx 15$ years. We find that the price fluctuations for commodities have a significantly broader multifractal spectrum than for stocks. We also propose that multifractal properties of both stocks and commodities can be attributed mainly to the broad probability distribution of price fluctuations and secondarily to their temporal organization. Furthermore, we propose that, for commodities, stronger higher order correlations in price fluctuations result in broader multifractal spectra.Comment: Published in Euro Physics Letters (14 pages, 5 figures

Asymmetric Conditional Volatility in International Stock Markets

Recent studies show that a negative shock in stock prices will generate more volatility than a positive shock of similar magnitude. The aim of this paper is to appraise the hypothesis under which the conditional mean and the conditional variance of stock returns are asymmetric functions of past information. We compare the results for the Portuguese Stock Market Index PSI 20 with six other Stock Market Indices, namely the S&P 500, FTSE100, DAX 30, CAC 40, ASE 20, and IBEX 35. In order to assess asymmetric volatility we use autoregressive conditional heteroskedasticity specifications known as TARCH and EGARCH. We also test for asymmetry after controlling for the effect of macroeconomic factors on stock market returns using TAR and M-TAR specifications within a VAR framework. Our results show that the conditional variance is an asymmetric function of past innovations raising proportionately more during market declines, a phenomenon known as the leverage effect. However, when we control for the effect of changes in macroeconomic variables, we find no significant evidence of asymmetric behaviour of the stock market returns. There are some signs that the Portuguese Stock Market tends to show somewhat less market efficiency than other markets since the effect of the shocks appear to take a longer time to dissipate.Comment: 11 pages, 3 figure

Accounting for risk of non linear portfolios: a novel Fourier approach

The presence of non linear instruments is responsible for the emergence of non Gaussian features in the price changes distribution of realistic portfolios, even for Normally distributed risk factors. This is especially true for the benchmark Delta Gamma Normal model, which in general exhibits exponentially damped power law tails. We show how the knowledge of the model characteristic function leads to Fourier representations for two standard risk measures, the Value at Risk and the Expected Shortfall, and for their sensitivities with respect to the model parameters. We detail the numerical implementation of our formulae and we emphasizes the reliability and efficiency of our results in comparison with Monte Carlo simulation.Comment: 10 pages, 12 figures. Final version accepted for publication on Eur. Phys. J.

Genomic and Metabolic Studies of the Impact of Probiotics on a Model Gut Symbiont and Host

Probiotics are deliberately ingested preparations of live bacterial species that confer health benefits on the host. Many of these species are associated with the fermentation of dairy products. Despite their increasing use, the molecular details of the impact of various probiotic preparations on resident members of the gut microbiota and the host are generally lacking. To address this issue, we colonized germ-free mice with Bacteroides thetaiotaomicron, a prominent component of the adult human gut microbiota, and Bifidobacterium longum, a minor member but a commonly used probiotic. Simultaneous whole genome transcriptional profiling of both bacterial species in their gut habitat and of the intestinal epithelium, combined with mass-spectrometric analysis of habitat-associated carbohydrates, revealed that the presence of B. longum elicits an expansion in the diversity of polysaccharides targeted for degradation by B. thetaiotaomicron (e.g., mannose- and xylose-containing glycans), and induces host genes involved in innate immunity. Although the overall transcriptome expressed by B. thetaiotaomicron when it encounters B. longum in the cecum is dependent upon the genetic background of the mouse (as assessed by a mixed analysis of variance [ANOVA] model of co-colonization experiments performed in NMRI and C57BL/6J animals), B. thetaiotaomicron's expanded capacity to utilize polysaccharides occurs independently of host genotype, and is also observed with a fermented dairy product-associated strain, Lactobacillus casei. This gnotobiotic mouse model provides a controlled case study of how a resident symbiont and a probiotic species adapt their substrate utilization in response to one another, and illustrates both the generality and specificity of the relationship between a host, a component of its microbiota, and intentionally consumed microbial species

Properties of a simple bilinear stochastic model: estimation and predictability

We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it has no linear predictability (zero two-point correlation) but a certain nonlinear predictability (non-zero three-point correlation). It can thus be considered as a paradigm for testing the existence of a possible nonlinear predictbility in a given time series. We present a rather exhaustive study of the process, including its ability to produce fat-tailed distribution from Gaussian innovations, the unstable characteristics of the inversion of the key nonlinear parameters and of the two initial conditions necessary for the implementation of a prediction scheme and an analysis of the associated super-exponential sensitivity of the inversion of the innovations in the presence of a large impluse. Our study emphasizes the conditions under which a degree of predictability can be achieved and describes a number of different attempts, which overall illuminates the properties of the process. In conclusion, notwithstanding its remarkable simplicity, the bilinear stochastic process exhibits remarkably rich and complex behavior, which makes it a serious candidate for the modeling of financial times series and of other complex systems.Comment: 35 pages, 5 figures, 8 table

Efficacy of Lactic Acid Bacteria (LAB) supplement in management of constipation among nursing home residents

<p>Abstract</p> <p>Background</p> <p>Constipation is a significant problem in the elderly, specifically nursing home and/or extended-care facility residents are reported to suffer from constipation. Lactic acid bacteria (LAB) are beneficial probiotic organisms that contribute to improved nutrition, microbial balance, and immuno-enhancement of the intestinal tract, as well as diarrhea and constipation effect. The objective of this study was to investigate the efficacy of this LAB supplement in the management of nursing home residents.</p> <p>Methods</p> <p>Nineteen subjects (8M, 11F; mean age 77.1 ± 10.1) suffering with chronic constipation were assigned to receive LAB (3.0 × 10¹¹CFU/g) twice (to be taken 30 minutes after breakfast and dinner) a day for 2 weeks in November 2008. Subjects draw up a questionnaire on defecation habits (frequency of defecation, amount and state of stool), and we collected fecal samples from the subjects both before entering and after ending the trial, to investigate LAB levels and inhibition of harmful enzyme activities. Results were tested with SAS and Student's t-test.</p> <p>Results</p> <p>Analysis of questionnaire showed that there was an increase in the frequency of defecation and amount of stool excreted in defecation habit after LAB treatment, but there were no significant changes. And it also affects the intestinal environment, through significantly increase (<it>p </it>< 0.05) fecal LAB levels. In addition, tryptophanase and urease among harmful enzyme activities of intestinal microflora were significantly decreased (<it>p </it>< 0.05) after LAB treatment.</p> <p>Conclusion</p> <p>LAB, when added to the standard treatment regimen for nursing home residents with chronic constipation, increased defecation habit such as frequency of defecation, amount and state of stool. So, it may be used as functional probiotics to improve human health by helping to prevent constipation.</p